1
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Rieland L, Wagner J, Bernhardt R, Wang T, Abdul-Aziz O, Stein P, Pogna EAA, Dal Conte S, Cerullo G, Hedayat H, van Loosdrecht PHM. Ultrafast Optical Control of Exciton Diffusion in WSe 2/Graphene Heterostructures Revealed by Heterodyne Transient Grating Spectroscopy. NANO LETTERS 2024; 24:9824-9831. [PMID: 39056490 DOI: 10.1021/acs.nanolett.4c01516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/28/2024]
Abstract
Using heterodyne transient grating spectroscopy, we observe a significant enhancement of exciton diffusion in a monolayer WSe2 stacked on graphene. The diffusion dynamics can be optically tuned within a few picoseconds by altering the photoexcited carrier density in graphene. The effective diffusion constant in initial picoseconds in the WSe2/graphene heterostructure is (40.3 ± 4.5) cm2 s-1, representing a substantial improvement over (2.1 ± 0.8) cm2 s-1, typical for an isolated WSe2 monolayer. This enhancement can be understood in terms of a transient screening of impurities, charge traps, and defect states in WSe2 by photoexcited charge carriers in graphene. Furthermore, diffusion within WSe2 is affected by interlayer interactions, such as charge transfer, varying with the incident excitation fluence. These findings underscore the dynamical nature of screening and diffusion processes in heterostructures of 2D semiconductors and graphene and provide insights for future applications of these systems in ultrafast optoelectronic devices.
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Affiliation(s)
- Lukas Rieland
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Julian Wagner
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Robin Bernhardt
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Tianyi Wang
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Omar Abdul-Aziz
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Philipp Stein
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Eva A A Pogna
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, 20133 Milano, Italy
| | - Stefano Dal Conte
- Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy
| | - Giulio Cerullo
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, 20133 Milano, Italy
- Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy
| | - Hamoon Hedayat
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
| | - Paul H M van Loosdrecht
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, Köln D-50937, Germany
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2
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Rossi A, Zipfel J, Maity I, Lorenzon M, Dandu M, Barré E, Francaviglia L, Regan EC, Zhang Z, Nie JH, Barnard ES, Watanabe K, Taniguchi T, Rotenberg E, Wang F, Lischner J, Raja A, Weber-Bargioni A. Anomalous Interlayer Exciton Diffusion in WS 2/WSe 2 Moiré Heterostructure. ACS NANO 2024; 18:18202-18210. [PMID: 38950893 PMCID: PMC11256890 DOI: 10.1021/acsnano.4c00015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2024] [Revised: 05/28/2024] [Accepted: 06/05/2024] [Indexed: 07/03/2024]
Abstract
Stacking van der Waals crystals allows for the on-demand creation of a periodic potential landscape to tailor the transport of quasiparticle excitations. We investigate the diffusion of photoexcited electron-hole pairs, or excitons, at the interface of WS2/WSe2 van der Waals heterostructure over a wide range of temperatures. We observe the appearance of distinct interlayer excitons for parallel and antiparallel stacking and track their diffusion through spatially and temporally resolved photoluminescence spectroscopy from 30 to 250 K. While the measured exciton diffusivity decreases with temperature, it surprisingly plateaus below 90 K. Our observations cannot be explained by classical models like hopping in the moiré potential. A combination of ab initio theory and molecular dynamics simulations suggests that low-energy phonons arising from the mismatched lattices of moiré heterostructures, also known as phasons, play a key role in describing and understanding this anomalous behavior of exciton diffusion. Our observations indicate that the moiré potential landscape is dynamic down to very low temperatures and that the phason modes can enable efficient transport of energy in the form of excitons.
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Affiliation(s)
- Antonio Rossi
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Advanced
Light Source, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Center
for Nanotechnology Innovation @ NEST, Instituto
Italiano di Tecnologia, 56127 Pisa, Italy
| | - Jonas Zipfel
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Indrajit Maity
- Imperial
College London, South Kensington Campus, London SW7 2AZ, U.K.
| | - Monica Lorenzon
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Medha Dandu
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Elyse Barré
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Luca Francaviglia
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Emma C. Regan
- Department
of Physics, University of California at
Berkeley, Berkeley, California 94720, United States
| | - Zuocheng Zhang
- Department
of Physics, University of California at
Berkeley, Berkeley, California 94720, United States
| | - Jacob H. Nie
- Department
of Physics, University of California at
Berkeley, Berkeley, California 94720, United States
- Department
of Physics, University of California at
Santa Barbara, Santa
Barbara, California 93106, United States
| | - Edward S. Barnard
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Kenji Watanabe
- Research
Center for Functional Materials, National
Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0047, Japan
| | - Takashi Taniguchi
- International
Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0047, Japan
| | - Eli Rotenberg
- Advanced
Light Source, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Feng Wang
- Department
of Physics, University of California at
Berkeley, Berkeley, California 94720, United States
| | - Johannes Lischner
- Imperial
College London, South Kensington Campus, London SW7 2AZ, U.K.
| | - Archana Raja
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Alexander Weber-Bargioni
- The
Molecular Foundry, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
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3
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Knorr W, Brem S, Meneghini G, Malic E. Polaron-induced changes in moiré exciton propagation in twisted van der Waals heterostructures. NANOSCALE 2024. [PMID: 38623653 DOI: 10.1039/d4nr00136b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/17/2024]
Abstract
Twisted transition metal dichalcogenides (TMDs) present an intriguing platform for exploring excitons and their transport properties. By introducing a twist angle, a moiré superlattice forms, providing a spatially dependent exciton energy landscape. Based on a microscopic many-particle theory, we investigate in this work polaron-induced changes in exciton transport properties in the exemplary MoSe2/WSe2 heterostructure. We demonstrate that polaron formation and the associated enhancement of the moiré exciton mass lead to a significant band flattening. As a result, the moiré inter-cell tunneling and the propagation velocity undergo noticeable temperature and twist-angle dependent changes. We predict a reduction of the hopping strength ranging from 80% at a twist angle of 1° to 30% at 3° at room temperature. The provided microscopic insights into the spatio-temporal exciton dynamics in presence of a moiré potential further expand the possibilities to tune charge and energy transport in 2D materials.
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Affiliation(s)
- Willy Knorr
- Department of Physics, Philipps University, 35037 Marburg, Germany.
| | - Samuel Brem
- Department of Physics, Philipps University, 35037 Marburg, Germany.
| | | | - Ermin Malic
- Department of Physics, Philipps University, 35037 Marburg, Germany.
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4
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Gong Y, Yue S, Liang Y, Du W, Bian T, Jiang C, Bao X, Zhang S, Long M, Zhou G, Yin J, Deng S, Zhang Q, Wu B, Liu X. Boosting exciton mobility approaching Mott-Ioffe-Regel limit in Ruddlesden-Popper perovskites by anchoring the organic cation. Nat Commun 2024; 15:1893. [PMID: 38424438 PMCID: PMC10904778 DOI: 10.1038/s41467-024-45740-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 02/01/2024] [Indexed: 03/02/2024] Open
Abstract
Exciton transport in two-dimensional Ruddlesden-Popper perovskite plays a pivotal role for their optoelectronic performance. However, a clear photophysical picture of exciton transport is still lacking due to strong confinement effects and intricate exciton-phonon interactions in an organic-inorganic hybrid lattice. Herein, we present a systematical study on exciton transport in (BA)2(MA)n-1PbnI3n+1 Ruddlesden-Popper perovskites using time-resolved photoluminescence microscopy. We reveal that the free exciton mobilities in exfoliated thin flakes can be improved from around 8 cm2 V-1 s-1 to 280 cm2V-1s-1 by anchoring the soft butyl ammonium cation with a polymethyl methacrylate network at the surface. The mobility of the latter is close to the theoretical limit of Mott-Ioffe-Regel criterion. Combining optical measurements and theoretical studies, it is unveiled that the polymethyl methacrylate network significantly improve the lattice rigidity resulting in the decrease of deformation potential scattering and lattice fluctuation at the surface few layers. Our work elucidates the origin of high exciton mobility in Ruddlesden-Popper perovskites and opens up avenues to regulate exciton transport in two-dimensional materials.
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Affiliation(s)
- Yiyang Gong
- South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou, 510006, P.R. China
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China
| | - Shuai Yue
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China
| | - Yin Liang
- School of Materials Science and Engineering, Peking University, Beijing, 100871, P.R. China
| | - Wenna Du
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China
| | - Tieyuan Bian
- Department of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, 999077, P.R. China
| | - Chuanxiu Jiang
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China
| | - Xiaotian Bao
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
| | - Shuai Zhang
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China
| | - Mingzhu Long
- South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou, 510006, P.R. China
| | - Guofu Zhou
- South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou, 510006, P.R. China
| | - Jun Yin
- Department of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, 999077, P.R. China
| | - Shibin Deng
- Ultrafast Electron Microscopy Laboratory, School of Physics, Nankai University, Tianjin, 300071, P.R. China
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University, Tianjin, 300071, P.R. China
| | - Qing Zhang
- School of Materials Science and Engineering, Peking University, Beijing, 100871, P.R. China.
| | - Bo Wu
- South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou, 510006, P.R. China.
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China.
| | - Xinfeng Liu
- CAS Key Laboratory of Standardization and Measurement for Nanotechnology, National Center for Nanoscience and Technology, Beijing, 100190, P.R. China.
- University of Chinese Academy of Sciences, Beijing, 100049, P.R. China.
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5
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Gauriot N, Ashoka A, Lim J, See ST, Sung J, Rao A. Direct Imaging of Carrier Funneling in a Dielectric Engineered 2D Semiconductor. ACS NANO 2024; 18:264-271. [PMID: 38196169 PMCID: PMC10786151 DOI: 10.1021/acsnano.3c05957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Revised: 11/23/2023] [Accepted: 12/01/2023] [Indexed: 01/11/2024]
Abstract
In atomically thin transition-metal dichalcogenides (TMDCs), the environmental sensitivity of the strong Coulomb interaction offers promising approaches to create spatially varying potential landscapes in the same continuous material by tuning its dielectric environment. Thus, allowing for control of transport. However, a scalable and CMOS-compatible method for achieving this is required to harness these effects in practical applications. In addition, because of their ultrashort lifetime, observing the spatiotemporal dynamics of carriers in monolayer TMDCs, on the relevant time scale, is challenging. Here, we pattern and deposit a thin film of hafnium oxide (HfO2) via atomic layer deposition (ALD) on top of a monolayer of WSe2. This allows for the engineering of the dielectric environment of the monolayer and design of heterostructures with nanoscale spatial resolution via a highly scalable postsynthesis methodology. We then directly image the transport of photoexcitations in the monolayer with 50 fs time resolution and few-nanometer spatial precision, using a pump probe microscopy technique. We observe the unidirectional funneling of charge carriers, from the unpatterned to the patterned areas, over more than 50 nm in the first 20 ps with velocities of over 2 × 103 m/s at room temperature. These results demonstrate the possibilities offered by dielectric engineering via ALD patterning, allowing for arbitrary spatial patterns that define the potential landscape and allow for control of the transport of excitations in atomically thin materials. This work also shows the power of the transient absorption methodology to image the motion of photoexcited states in complex potential landscapes on ultrafast time scales.
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Affiliation(s)
- Nicolas Gauriot
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - Arjun Ashoka
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - Juhwan Lim
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - Soo Teck See
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - Jooyoung Sung
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
- Department
of Physics and Chemistry, DGIST, Daegu 42988, Republic of Korea
| | - Akshay Rao
- Cavendish
Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
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6
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Wietek E, Florian M, Göser J, Taniguchi T, Watanabe K, Högele A, Glazov MM, Steinhoff A, Chernikov A. Nonlinear and Negative Effective Diffusivity of Interlayer Excitons in Moiré-Free Heterobilayers. PHYSICAL REVIEW LETTERS 2024; 132:016202. [PMID: 38242648 DOI: 10.1103/physrevlett.132.016202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 11/10/2023] [Indexed: 01/21/2024]
Abstract
Interlayer exciton diffusion is studied in atomically reconstructed MoSe_{2}/WSe_{2} heterobilayers with suppressed disorder. Local atomic registry is confirmed by characteristic optical absorption, circularly polarized photoluminescence, and g-factor measurements. Using transient microscopy we observe propagation properties of interlayer excitons that are independent from trapping at moiré- or disorder-induced local potentials. Confirmed by characteristic temperature dependence for free particles, linear diffusion coefficients of interlayer excitons at liquid helium temperature and low excitation densities are almost 1000 times higher than in previous observations. We further show that exciton-exciton repulsion and annihilation contribute nearly equally to nonlinear propagation by disentangling the two processes in the experiment and simulations. Finally, we demonstrate effective shrinking of the light emission area over time across several hundreds of picoseconds at the transition from exciton- to the plasma-dominated regimes. Supported by microscopic calculations for band gap renormalization to identify the Mott threshold, this indicates transient crossing between rapidly expanding, short-lived electron-hole plasma and slower, long-lived exciton populations.
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Affiliation(s)
- Edith Wietek
- Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - Matthias Florian
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jonas Göser
- Fakultät für Physik, Munich Quantum Center, and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, 80539 München, Germany
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Alexander Högele
- Fakultät für Physik, Munich Quantum Center, and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, 80539 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | | | - Alexander Steinhoff
- Institut für Theoretische Physik, Universität Bremen, 28334 Bremen, Germany
- Bremen Center for Computational Materials Science, Universität Bremen, 28334 Bremen, Germany
| | - Alexey Chernikov
- Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
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7
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Kim DS, Dominguez RC, Mayorga-Luna R, Ye D, Embley J, Tan T, Ni Y, Liu Z, Ford M, Gao FY, Arash S, Watanabe K, Taniguchi T, Kim S, Shih CK, Lai K, Yao W, Yang L, Li X, Miyahara Y. Electrostatic moiré potential from twisted hexagonal boron nitride layers. NATURE MATERIALS 2024; 23:65-70. [PMID: 37563291 DOI: 10.1038/s41563-023-01637-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 07/10/2023] [Indexed: 08/12/2023]
Abstract
Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.
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Affiliation(s)
- Dong Seob Kim
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Roy C Dominguez
- Department of Physics, Texas State University, San Marcos, TX, USA
| | | | - Dingyi Ye
- Department of Physics, Washington University in St Louis, St Louis, MO, USA
| | - Jacob Embley
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Tixuan Tan
- Department of Physics, and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong, China
| | - Yue Ni
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Zhida Liu
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Mitchell Ford
- Department of Physics, Texas State University, San Marcos, TX, USA
| | - Frank Y Gao
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Saba Arash
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Suenne Kim
- Department of Photonics and Nanoelectronics, Hanyang University, Ansan, South Korea
| | - Chih-Kang Shih
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Keji Lai
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA
| | - Wang Yao
- Department of Physics, and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong, China
| | - Li Yang
- Department of Physics, Washington University in St Louis, St Louis, MO, USA
| | - Xiaoqin Li
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, TX, USA.
- Center for Dynamics and Control of Materials and Texas Materials Institute, The University of Texas at Austin, Austin, TX, USA.
| | - Yoichi Miyahara
- Department of Physics, Texas State University, San Marcos, TX, USA.
- Materials Science, Engineering and Commercialization Program (MSEC), Texas State University, San Marcos, TX, USA.
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8
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Zhu G, Zhang L, Li W, Shi X, Zou Z, Guo Q, Li X, Xu W, Jie J, Wang T, Du W, Xiong Q. Room-temperature high-speed electrical modulation of excitonic distribution in a monolayer semiconductor. Nat Commun 2023; 14:6701. [PMID: 37872139 PMCID: PMC10593816 DOI: 10.1038/s41467-023-42568-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Accepted: 10/16/2023] [Indexed: 10/25/2023] Open
Abstract
Excitons in monolayer semiconductors, benefitting from their large binding energies, hold great potential towards excitonic circuits bridging nano-electronics and photonics. However, achieving room-temperature ultrafast on-chip electrical modulation of excitonic distribution and flow in monolayer semiconductors is nontrivial. Here, utilizing lateral bias, we report high-speed electrical modulation of the excitonic distribution in a monolayer semiconductor junction at room temperature. The alternating charge trapping/detrapping at the two monolayer/electrode interfaces induces a non-uniform carrier distribution, leading to controlled in-plane spatial variations of excitonic populations, and mimicking a bias-driven excitonic flow. This modulation increases with the bias amplitude and eventually saturates, relating to the energetic distribution of trap density of states. The switching time of the modulation is down to 5 ns, enabling high-speed excitonic devices. Our findings reveal the trap-assisted exciton engineering in monolayer semiconductors and offer great opportunities for future two-dimensional excitonic devices and circuits.
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Affiliation(s)
- Guangpeng Zhu
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Lan Zhang
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Wenfei Li
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Xiuqi Shi
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Zhen Zou
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Qianqian Guo
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Xiang Li
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Weigao Xu
- Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, PR China
| | - Jiansheng Jie
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China
| | - Tao Wang
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China.
| | - Wei Du
- Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Institute of Functional Nano and Soft Materials (FUNSOM), Soochow University, Suzhou, 215123, PR China.
| | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, PR China
- Frontier Science Center for Quantum Information, Beijing, 100084, PR China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, PR China
- Collaborative Innovation Center of Quantum Matter, Beijing, PR China
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9
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Glazov MM. Excitons in atomically thin materials flow faster than they fly. NATURE NANOTECHNOLOGY 2023; 18:972-973. [PMID: 37524906 DOI: 10.1038/s41565-023-01448-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/02/2023]
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10
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Troue M, Figueiredo J, Sigl L, Paspalides C, Katzer M, Taniguchi T, Watanabe K, Selig M, Knorr A, Wurstbauer U, Holleitner AW. Extended Spatial Coherence of Interlayer Excitons in MoSe_{2}/WSe_{2} Heterobilayers. PHYSICAL REVIEW LETTERS 2023; 131:036902. [PMID: 37540866 DOI: 10.1103/physrevlett.131.036902] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 06/09/2023] [Indexed: 08/06/2023]
Abstract
We report on the spatial coherence of interlayer exciton ensembles as formed in MoSe_{2}/WSe_{2} heterostructures and characterized by point-inversion Michelson-Morley interferometry. Below 10 K, the measured spatial coherence length of the interlayer excitons reaches values equivalent to the lateral expansion of the exciton ensembles. In this regime, the light emission of the excitons turns out to be homogeneously broadened in energy with a high temporal coherence. At higher temperatures, both the spatial coherence length and the temporal coherence time decrease, most likely because of thermal processes. The presented findings point towards a spatially extended, coherent many-body state of interlayer excitons at low temperature.
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Affiliation(s)
- Mirco Troue
- Walter Schottky Institute and Physics Department, Technical University of Munich, Am Coulombwall 4a, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany
| | - Johannes Figueiredo
- Walter Schottky Institute and Physics Department, Technical University of Munich, Am Coulombwall 4a, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany
| | - Lukas Sigl
- Walter Schottky Institute and Physics Department, Technical University of Munich, Am Coulombwall 4a, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany
| | - Christos Paspalides
- Walter Schottky Institute and Physics Department, Technical University of Munich, Am Coulombwall 4a, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany
| | - Manuel Katzer
- Institute for Theoretical Physics, Nonlinear Optics and Quantum Electronics, Technical University of Berlin, 10623 Berlin, Germany
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Malte Selig
- Institute for Theoretical Physics, Nonlinear Optics and Quantum Electronics, Technical University of Berlin, 10623 Berlin, Germany
| | - Andreas Knorr
- Institute for Theoretical Physics, Nonlinear Optics and Quantum Electronics, Technical University of Berlin, 10623 Berlin, Germany
| | - Ursula Wurstbauer
- Institute of Physics, Münster University, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany
| | - Alexander W Holleitner
- Walter Schottky Institute and Physics Department, Technical University of Munich, Am Coulombwall 4a, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany
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11
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Chand SB, Woods JM, Quan J, Mejia E, Taniguchi T, Watanabe K, Alù A, Grosso G. Interaction-driven transport of dark excitons in 2D semiconductors with phonon-mediated optical readout. Nat Commun 2023; 14:3712. [PMID: 37349290 DOI: 10.1038/s41467-023-39339-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 06/08/2023] [Indexed: 06/24/2023] Open
Abstract
The growing field of quantum information technology requires propagation of information over long distances with efficient readout mechanisms. Excitonic quantum fluids have emerged as a powerful platform for this task due to their straightforward electro-optical conversion. In two-dimensional transition metal dichalcogenides, the coupling between spin and valley provides exciting opportunities for harnessing, manipulating, and storing bits of information. However, the large inhomogeneity of single layers cannot be overcome by the properties of bright excitons, hindering spin-valley transport. Nonetheless, the rich band structure supports dark excitonic states with strong binding energy and longer lifetime, ideally suited for long-range transport. Here we show that dark excitons can diffuse over several micrometers and prove that this repulsion-driven propagation is robust across non-uniform samples. The long-range propagation of dark states with an optical readout mediated by chiral phonons provides a new concept of excitonic devices for applications in both classical and quantum information technology.
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Affiliation(s)
- Saroj B Chand
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - John M Woods
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - Jiamin Quan
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - Enrique Mejia
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
- Department of Electrical Engineering, City College of the City University of New York, New York, NY, 10031, USA
- Physics Program, Graduate Center, City University of New York, New York, NY, 10016, USA
| | - Gabriele Grosso
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA.
- Physics Program, Graduate Center, City University of New York, New York, NY, 10016, USA.
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12
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Li WH, Lin JD, Lo PY, Peng GH, Hei CY, Chen SY, Cheng SJ. The Key Role of Non-Local Screening in the Environment-Insensitive Exciton Fine Structures of Transition-Metal Dichalcogenide Monolayers. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13111739. [PMID: 37299642 DOI: 10.3390/nano13111739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 05/21/2023] [Accepted: 05/23/2023] [Indexed: 06/12/2023]
Abstract
In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe2-monolayers, one of the best-known two-dimensional (2D) transition-metal dichalcogenides (TMDs), in various dielectric-layered environments by solving the first-principles-based Bethe-Salpeter equation. While the physical and electronic properties of atomically thin nanomaterials are normally sensitive to the variation of the surrounding environment, our studies reveal that the influence of the dielectric environment on the exciton fine structures of TMD-MLs is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role in suppressing the dielectric environment factor and drastically shrinking the fine structure splittings between bright exciton (BX) states and various dark-exciton (DX) states of TMD-MLs. The intriguing non-locality of screening in 2D materials can be manifested by the measurable non-linear correlation between the BX-DX splittings and exciton-binding energies by varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML suggest the robustness of prospective dark-exciton-based optoelectronics against the inevitable variation of the inhomogeneous dielectric environment.
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Affiliation(s)
- Wei-Hua Li
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Jhen-Dong Lin
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Ping-Yuan Lo
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Guan-Hao Peng
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Ching-Yu Hei
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Shao-Yu Chen
- Center of Condensed Matter Sciences, National Taiwan University, Taipei 106, Taiwan
- Center of Atomic Initiative for New Material, National Taiwan University, Taipei 106, Taiwan
| | - Shun-Jen Cheng
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
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13
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Wagner K, Iakovlev ZA, Ziegler JD, Cuccu M, Taniguchi T, Watanabe K, Glazov MM, Chernikov A. Diffusion of Excitons in a Two-Dimensional Fermi Sea of Free Charges. NANO LETTERS 2023. [PMID: 37220259 DOI: 10.1021/acs.nanolett.2c03796] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Propagation of light-emitting quasiparticles is of central importance across the fields of condensed matter physics and nanomaterials science. We experimentally demonstrate diffusion of excitons in the presence of a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. Light emission from tightly bound exciton states in electrically gated WSe2 monolayer is detected using spatially and temporally resolved microscopy. The measurements reveal a nonmonotonic dependence of the exciton diffusion coefficient on the charge carrier density in both electron and hole doped regimes. Supported by analytical theory describing exciton-carrier interactions in a dissipative system, we identify distinct regimes of elastic scattering and quasiparticle formation determining exciton diffusion. The crossover region exhibits a highly unusual behavior of an increasing diffusion coefficient with increasing carrier densities. Temperature-dependent diffusion measurements further reveal characteristic signatures of freely propagating excitonic complexes dressed by free charges with effective mobilities up to 3 × 103 cm2/(V s).
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Affiliation(s)
- Koloman Wagner
- Institute of Applied Physics and Wüzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
- Department of Physics, University of Regensburg, 93053 Regensburg, Germany
| | | | - Jonas D Ziegler
- Institute of Applied Physics and Wüzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
- Department of Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Marzia Cuccu
- Institute of Applied Physics and Wüzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | | | - Alexey Chernikov
- Institute of Applied Physics and Wüzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
- Department of Physics, University of Regensburg, 93053 Regensburg, Germany
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14
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Choi J, Embley J, Blach DD, Perea-Causín R, Erkensten D, Kim DS, Yuan L, Yoon WY, Taniguchi T, Watanabe K, Ueno K, Tutuc E, Brem S, Malic E, Li X, Huang L. Fermi Pressure and Coulomb Repulsion Driven Rapid Hot Plasma Expansion in a van der Waals Heterostructure. NANO LETTERS 2023; 23:4399-4405. [PMID: 37154560 DOI: 10.1021/acs.nanolett.3c00678] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Transition metal dichalcogenide heterostructures provide a versatile platform to explore electronic and excitonic phases. As the excitation density exceeds the critical Mott density, interlayer excitons are ionized into an electron-hole plasma phase. The transport of the highly non-equilibrium plasma is relevant for high-power optoelectronic devices but has not been carefully investigated previously. Here, we employ spatially resolved pump-probe microscopy to investigate the spatial-temporal dynamics of interlayer excitons and hot-plasma phase in a MoSe2/WSe2 twisted bilayer. At the excitation density of ∼1014 cm-2, well exceeding the Mott density, we find a surprisingly rapid initial expansion of hot plasma to a few microns away from the excitation source within ∼0.2 ps. Microscopic theory reveals that this rapid expansion is mainly driven by Fermi pressure and Coulomb repulsion, while the hot carrier effect has only a minor effect in the plasma phase.
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Affiliation(s)
- Junho Choi
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Jacob Embley
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Daria D Blach
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2050, United States
| | - Raül Perea-Causín
- Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Daniel Erkensten
- Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Dong Seob Kim
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Long Yuan
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2050, United States
| | - Woo Young Yoon
- Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Keiji Ueno
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan
| | - Emanuel Tutuc
- Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Samuel Brem
- Department of Physics, Philipps University of Marburg, 35037 Marburg, Germany
| | - Ermin Malic
- Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden
- Department of Physics, Philipps University of Marburg, 35037 Marburg, Germany
| | - Xiaoqin Li
- Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Libai Huang
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2050, United States
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15
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Ziegler JD, Cho Y, Terres S, Menahem M, Taniguchi T, Watanabe K, Yaffe O, Berkelbach TC, Chernikov A. Mobile Trions in Electrically Tunable 2D Hybrid Perovskites. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2210221. [PMID: 36811916 DOI: 10.1002/adma.202210221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/27/2023] [Indexed: 05/05/2023]
Abstract
2D hybrid perovskites are currently in the spotlight of material research for light-harvesting and -emitting applications. It remains extremely challenging, however, to externally control their optical response due to the difficulties of introducing electrical doping. Here, an approach of interfacing ultrathin sheets of perovskites with few-layer graphene and hexagonal boron nitride into gate-tunable, hybrid heterostructures, is demonstrated. It allows for bipolar, continuous tuning of light emission and absorption in 2D perovskites by electrically injecting carriers to densities as high as 1012 cm-2 . This reveals the emergence of both negatively and positively charged excitons, or trions, with binding energies up to 46 meV, among the highest measured for 2D systems. Trions are shown to dominate light emission and propagate with mobilities reaching 200 cm2 V-1 s-1 at elevated temperatures. The findings introduce the physics of interacting mixtures of optical and electrical excitations to the broad family of 2D inorganic-organic nanostructures. The presented strategy to electrically control the optical response of 2D perovskites highlights it as a promising material platform toward electrically modulated light-emitters, externally guided charged exciton currents, and exciton transistors based on layered, hybrid semiconductors.
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Affiliation(s)
- Jonas D Ziegler
- Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden, 01062, Dresden, Germany
| | - Yeongsu Cho
- Department of Chemistry, Columbia University, New York, New York, 10027, USA
| | - Sophia Terres
- Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden, 01062, Dresden, Germany
| | - Matan Menahem
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, 305-0047, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, 305-0047, Japan
| | - Omer Yaffe
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Timothy C Berkelbach
- Center for Computational Quantum Physics, Flatiron Institute, New York, 10010, USA
- Department of Chemistry, Columbia University, New York, 10027, USA
| | - Alexey Chernikov
- Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden, 01062, Dresden, Germany
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16
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Tan QH, Li YM, Lai JM, Sun YJ, Zhang Z, Song F, Robert C, Marie X, Gao W, Tan PH, Zhang J. Quantum interference between dark-excitons and zone-edged acoustic phonons in few-layer WS 2. Nat Commun 2023; 14:88. [PMID: 36604415 PMCID: PMC9816112 DOI: 10.1038/s41467-022-35714-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 12/15/2022] [Indexed: 01/07/2023] Open
Abstract
Fano resonance which describes a quantum interference between continuum and discrete states, provides a unique method for studying strongly interacting physics. Here, we report a Fano resonance between dark excitons and zone-edged acoustic phonons in few-layer WS2 by using the resonant Raman technique. The discrete phonons with large momentum at the M-point of the Brillouin zone and the continuum dark exciton states related to the optically forbidden transition at K and Q valleys are coupled by the exciton-phonon interactions. We observe rich Fano resonance behaviors across layers and modes defined by an asymmetry-parameter q: including constructive interference with two mirrored asymmetry Fano peaks (weak coupling, q > 1 and q < - 1), and destructive interference with Fano dip (strong coupling, ∣q∣ < < 1). Our results provide new insight into the exciton-phonon quantum interference in two-dimensional semiconductors, where such interferences play a key role in their transport, optical, and thermodynamic properties.
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Affiliation(s)
- Qing-Hai Tan
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China ,grid.59025.3b0000 0001 2224 0361Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore
| | - Yun-Mei Li
- grid.12955.3a0000 0001 2264 7233Department of Physics, Xiamen University, Xiamen, 361005 China
| | - Jia-Min Lai
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Yu-Jia Sun
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Zhe Zhang
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Feilong Song
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Cedric Robert
- grid.462768.90000 0004 0383 4043University of Toulouse, INSA-CNRS-UPS, LPCNO, 135 Av. Rangueil, 31077 Toulouse, France
| | - Xavier Marie
- grid.462768.90000 0004 0383 4043University of Toulouse, INSA-CNRS-UPS, LPCNO, 135 Av. Rangueil, 31077 Toulouse, France
| | - Weibo Gao
- grid.59025.3b0000 0001 2224 0361Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore ,grid.59025.3b0000 0001 2224 0361The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, 637371 Singapore, Singapore ,grid.4280.e0000 0001 2180 6431Centre for Quantum Technologies, National University of Singapore, Singapore, 117543 Singapore
| | - Ping-Heng Tan
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Jun Zhang
- grid.9227.e0000000119573309State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China ,grid.410726.60000 0004 1797 8419Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China ,grid.410726.60000 0004 1797 8419CAS Center of Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100049 China
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17
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Raiber S, Faria Junior PE, Falter D, Feldl S, Marzena P, Watanabe K, Taniguchi T, Fabian J, Schüller C. Ultrafast pseudospin quantum beats in multilayer WSe 2 and MoSe 2. Nat Commun 2022; 13:4997. [PMID: 36008400 PMCID: PMC9411176 DOI: 10.1038/s41467-022-32534-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 08/04/2022] [Indexed: 11/09/2022] Open
Abstract
Layered van-der-Waals materials with hexagonal symmetry offer an extra degree of freedom to their electrons, the so-called valley index or valley pseudospin, which behaves conceptually like the electron spin. Here, we present investigations of excitonic transitions in mono- and multilayer WSe2 and MoSe2 materials by time-resolved Faraday ellipticity (TRFE) with in-plane magnetic fields, B∥, of up to 9 T. In monolayer samples, the measured TRFE time traces are almost independent of B∥, which confirms a close to zero in-plane exciton g factor g∥, consistent with first-principles calculations. In contrast, we observe pronounced temporal oscillations in multilayer samples for B∥ > 0. Our first-principles calculations confirm the presence of a non-zero g∥ for the multilayer samples. We propose that the oscillatory TRFE signal in the multilayer samples is caused by pseudospin quantum beats of excitons, which is a manifestation of spin- and pseudospin layer locking in the multilayer samples.
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Affiliation(s)
- Simon Raiber
- Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Paulo E Faria Junior
- Institut für Theoretische Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Dennis Falter
- Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Simon Feldl
- Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Petter Marzena
- Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0044, Japan
| | - Jaroslav Fabian
- Institut für Theoretische Physik, Universität Regensburg, D-93040, Regensburg, Germany
| | - Christian Schüller
- Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040, Regensburg, Germany.
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18
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Kurilovich AA, Mantsevich VN, Mardoukhi Y, Stevenson KJ, Chechkin AV, Palyulin VV. Non-Markovian diffusion of excitons in layered perovskites and transition metal dichalcogenides. Phys Chem Chem Phys 2022; 24:13941-13950. [PMID: 35621272 DOI: 10.1039/d2cp00557c] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The diffusion of excitons in perovskites and transition metal dichalcogenides shows clear anomalous, subdiffusive behaviour in experiments. In this paper we develop a non-Markovian mobile-immobile model which provides an explanation of this behaviour through paired theoretical and simulation approaches. The simulation model is based on a random walk on a 2D lattice with randomly distributed deep traps such that the trapping time distribution involves slowly decaying power-law asymptotics. The theoretical model uses coupled diffusion and rate equations for free and trapped excitons, respectively, with an integral term responsible for trapping. The model provides a good fitting of the experimental data, thus, showing a way for quantifying the exciton diffusion dynamics.
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Affiliation(s)
- Aleksandr A Kurilovich
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
| | - Vladimir N Mantsevich
- Chair of Semiconductors and Cryoelectronics & Quantum Technology Center, Physics Department, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Yousof Mardoukhi
- Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany
| | - Keith J Stevenson
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany.,Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.,Akhiezer Institute for Theoretical Physics National Science Center "Kharkov Institute of Physics and Technology", 61108, Kharkov, Ukraine
| | - Vladimir V Palyulin
- RAIC Center, Skolkovo Institute of Science and Technology, 121205, Moscow, Russia.
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19
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Uddin SZ, Higashitarumizu N, Kim H, Yi J, Zhang X, Chrzan D, Javey A. Enhanced Neutral Exciton Diffusion in Monolayer WS 2 by Exciton-Exciton Annihilation. ACS NANO 2022; 16:8005-8011. [PMID: 35467828 DOI: 10.1021/acsnano.2c00956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Dominant recombination pathways in monolayer transition metal dichalcogenides (TMDCs) depend primarily on background carrier concentration, generation rate, and applied strain. Charged excitons formed in the presence of background carriers mainly recombine nonradiatively. Neutral excitons recombine completely radiatively at low generation rates, but experience nonradiative exciton-exciton annihilation (EEA) at high generation rates. Strain can suppress EEA, resulting in near-unity photoluminescence quantum yield (PL QY) at all exciton densities. Although exciton diffusion is the primary channel of energy transport in excitonic materials and a critical optoelectronic design consideration, the combined effects of these factors on exciton diffusion are not clearly understood. In this work, we decouple the diffusion of neutral and charged excitons with chemical counterdoping and explore the effect of strain and generation rate on exciton diffusion. According to the standard semiconductor paradigm, a shorter carrier recombination lifetime should lead to a smaller diffusion length. Surprisingly, we find that increasing generation rate shortens the exciton lifetime but increases the diffusion length in unstrained monolayers of TMDCs. When we suppress EEA by strain, both lifetime and diffusion length become independent of generation rate. During EEA one exciton nonradiatively recombines and kinetically energizes another exciton, which then diffuses fast. Our results probe concentration-dependent diffusion of pure neutral excitons by counterdoping and elucidate how strain controls exciton transport and many-body interactions in TMDC monolayers.
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Affiliation(s)
- Shiekh Zia Uddin
- Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Naoki Higashitarumizu
- Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Hyungjin Kim
- Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jun Yi
- NSF Nanoscale Science and Engineering Center, University of California, Berkeley, California 94720, United States
| | - Xiang Zhang
- NSF Nanoscale Science and Engineering Center, University of California, Berkeley, California 94720, United States
- Faculties of Sciences and Engineering, The University of Hong Kong, Hong Kong, China
| | - Daryl Chrzan
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, United States
| | - Ali Javey
- Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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Chand SB, Woods JM, Mejia E, Taniguchi T, Watanabe K, Grosso G. Visualization of Dark Excitons in Semiconductor Monolayers for High-Sensitivity Strain Sensing. NANO LETTERS 2022; 22:3087-3094. [PMID: 35290068 DOI: 10.1021/acs.nanolett.2c00436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Transition-metal dichalcogenides (TMDs) are layered materials that have a semiconducting phase with many advantageous optoelectronic properties, including tightly bound excitons and spin-valley locking. In tungsten-based TMDs, spin- and momentum-forbidden transitions give rise to dark excitons that typically are optically inaccessible but represent the lowest excitonic states of the system. Dark excitons can deeply affect the transport, dynamics, and coherence of bright excitons, hampering device performance. Therefore, it is crucial to create conditions in which these excitonic states can be visualized and controlled. Here, we show that compressive strain in WS2 enables phonon scattering of photoexcited electrons between momentum valleys, enhancing the formation of dark intervalley excitons. We show that the emission and spectral properties of momentum-forbidden excitons are accessible and strongly depend on the local strain environment that modifies the band alignment. This mechanism is further exploited for strain sensing in two-dimensional semiconductors, revealing a gauge factor exceeding 104.
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Affiliation(s)
- Saroj B Chand
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York 10031, New York, United States
| | - John M Woods
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York 10031, New York, United States
| | - Enrique Mejia
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York 10031, New York, United States
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Gabriele Grosso
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York 10031, New York, United States
- Physics Program, Graduate Center, City University of New York, New York 10016, New York, United States
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21
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Rosati R, Wagner K, Brem S, Perea-Causín R, Ziegler JD, Zipfel J, Taniguchi T, Watanabe K, Chernikov A, Malic E. Non-equilibrium diffusion of dark excitons in atomically thin semiconductors. NANOSCALE 2021; 13:19966-19972. [PMID: 34821228 DOI: 10.1039/d1nr06230a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Atomically thin semiconductors provide an excellent platform to study intriguing many-particle physics of tightly-bound excitons. In particular, the properties of tungsten-based transition metal dichalcogenides are determined by a complex manifold of bright and dark exciton states. While dark excitons are known to dominate the relaxation dynamics and low-temperature photoluminescence, their impact on the spatial propagation of excitons has remained elusive. In our joint theory-experiment study, we address this intriguing regime of dark state transport by resolving the spatio-temporal exciton dynamics in hBN-encapsulated WSe2 monolayers after resonant excitation. We find clear evidence of an unconventional, time-dependent diffusion during the first tens of picoseconds, exhibiting strong deviation from the steady-state propagation. Dark exciton states are initially populated by phonon emission from the bright states, resulting in creation of hot (unequilibrated) excitons whose rapid expansion leads to a transient increase of the diffusion coefficient by more than one order of magnitude. These findings are relevant for both fundamental understanding of the spatio-temporal exciton dynamics in atomically thin materials as well as their technological application by enabling rapid diffusion.
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Affiliation(s)
- Roberto Rosati
- Department of Physics, Philipps-Universität Marburg, Renthof 7, D-35032 Marburg, Germany.
| | - Koloman Wagner
- Department of Physics, University of Regensburg, Regensburg D-93053, Germany
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - Samuel Brem
- Department of Physics, Philipps-Universität Marburg, Renthof 7, D-35032 Marburg, Germany.
| | - Raül Perea-Causín
- Chalmers University of Technology, Department of Physics, 412 96 Gothenburg, Sweden
| | - Jonas D Ziegler
- Department of Physics, University of Regensburg, Regensburg D-93053, Germany
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - Jonas Zipfel
- Department of Physics, University of Regensburg, Regensburg D-93053, Germany
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Alexey Chernikov
- Department of Physics, University of Regensburg, Regensburg D-93053, Germany
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - Ermin Malic
- Department of Physics, Philipps-Universität Marburg, Renthof 7, D-35032 Marburg, Germany.
- Chalmers University of Technology, Department of Physics, 412 96 Gothenburg, Sweden
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22
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Rosati R, Lengers F, Carmesin C, Florian M, Kuhn T, Jahnke F, Lorke M, Reiter DE. Electron Dynamics in a Two-Dimensional Nanobubble: A Two-Level System Based on Spatial Density. NANO LETTERS 2021; 21:9896-9902. [PMID: 34812637 DOI: 10.1021/acs.nanolett.1c02864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Nanobubbles formed in monolayers of transition metal dichalcogenides (TMDCs) on top of a substrate feature localized potentials in which electrons can be captured. We show that the captured electronic density can exhibit a nontrivial spatiotemporal dynamics, whose movements can be mapped to states in a two-level system illustrated as points of an electronic Poincaré sphere. These states can be fully controlled, i.e, initialized and switched, by multiple electronic wave packets. Our results could be the foundation for novel implementations of quantum circuits.
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Affiliation(s)
- Roberto Rosati
- Department of Physics, Philipps-Universität Marburg, Renthof 7, D-35032 Marburg, Germany
| | - Frank Lengers
- Institut of Solid State Theory, University of Münster, 48149 Münster, Germany
| | - Christian Carmesin
- Institute for Theoretical Physics, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany
| | - Matthias Florian
- Institute for Theoretical Physics, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany
| | - Tilmann Kuhn
- Institut of Solid State Theory, University of Münster, 48149 Münster, Germany
| | - Frank Jahnke
- Institute for Theoretical Physics, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany
| | - Michael Lorke
- Institute for Theoretical Physics, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany
| | - Doris E Reiter
- Institut of Solid State Theory, University of Münster, 48149 Münster, Germany
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23
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Dirnberger F, Ziegler JD, Faria Junior PE, Bushati R, Taniguchi T, Watanabe K, Fabian J, Bougeard D, Chernikov A, Menon VM. Quasi-1D exciton channels in strain-engineered 2D materials. SCIENCE ADVANCES 2021; 7:eabj3066. [PMID: 34714670 PMCID: PMC8555901 DOI: 10.1126/sciadv.abj3066] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 09/10/2021] [Indexed: 06/13/2023]
Abstract
Strain engineering is a powerful tool in designing artificial platforms for high-temperature excitonic quantum devices. Combining strong light-matter interaction with robust and mobile exciton quasiparticles, two-dimensional transition metal dichalcogenides (2D TMDCs) hold great promise in this endeavor. However, realizing complex excitonic architectures based on strain-induced electronic potentials alone has proven to be exceptionally difficult so far. Here, we demonstrate deterministic strain engineering of both single-particle electronic bandstructure and excitonic many-particle interactions. We create quasi-1D transport channels to confine excitons and simultaneously enhance their mobility through locally suppressed exciton-phonon scattering. Using ultrafast, all-optical injection and time-resolved readout, we realize highly directional exciton flow with up to 100% anisotropy both at cryogenic and room temperatures. The demonstrated fundamental modification of the exciton transport properties in a deterministically strained 2D material with effectively tunable dimensionality has broad implications for both basic solid-state science and emerging technologies.
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Affiliation(s)
- Florian Dirnberger
- Department of Physics, City College of New York, New York, NY 10031, USA
| | - Jonas D. Ziegler
- Department of Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Paulo E. Faria Junior
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Rezlind Bushati
- Department of Physics, City College of New York, New York, NY 10031, USA
- Department of Physics, The Graduate Center, City University of New York, New York, NY 10016, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Jaroslav Fabian
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Dominique Bougeard
- Department of Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Alexey Chernikov
- Department of Physics, University of Regensburg, 93040 Regensburg, Germany
- Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Würzburg-Dresden Cluster of Excellence ct.qmat, Dresden University of Technology, Dresden 01187, Germany
| | - Vinod M. Menon
- Department of Physics, City College of New York, New York, NY 10031, USA
- Department of Physics, The Graduate Center, City University of New York, New York, NY 10016, USA
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