1
|
Wang H, Xu W, Zhu Z, Yang B. Photonic Weyl Waveguide and Saddle-Chips-like Modes. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:620. [PMID: 38607154 PMCID: PMC11013772 DOI: 10.3390/nano14070620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Revised: 03/21/2024] [Accepted: 03/28/2024] [Indexed: 04/13/2024]
Abstract
Topological Weyl semimetals are characterized by open Fermi arcs on their terminal surfaces, these materials not only changed accepted concepts of the Fermi loop but also enabled many exotic phenomena, such as one-way propagation. The key prerequisite is that the two terminal surfaces have to be well separated, i.e., the Fermi arcs are not allowed to couple with each other. Thus, their interaction was overlooked before. Here, we consider coupled Fermi arcs and propose a Weyl planar waveguide, wherein we found a saddle-chips-like hybridized guiding mode. The hybridized modes consist of three components: surface waves from the top and bottom surfaces and bulk modes inside the Weyl semimetal. The contribution of these three components to the hybridized mode appears to be z-position-dependent rather than uniform. Beyond the conventional waveguide framework, those non-trivial surface states, with their arc-type band structures, exhibit strong selectivity in propagation direction, providing an excellent platform for waveguides. Compared with the conventional waveguide, the propagation direction of hybridized modes exhibits high z-position-dependency. For example, when the probe plane shifts from the top interface to the bottom interface, the component propagating horizontally becomes dimmer, while the component propagating vertically becomes brighter. Experimentally, we drilled periodic holes in metal plates to sandwich an ideal Weyl meta-crystal and characterize the topological guiding mode. Our study shows the intriguing behaviors of topological photonic waveguides, which could lead to beam manipulation, position sensing, and even 3D information processing on photonic chip. The Weyl waveguide also provides a platform for studying the coupling and the interaction between surface and bulk states.
Collapse
Affiliation(s)
- Hanyu Wang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Wei Xu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Zhihong Zhu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Biao Yang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| |
Collapse
|
2
|
Giwa R, Hosur P. Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals. PHYSICAL REVIEW LETTERS 2023; 130:156402. [PMID: 37115867 DOI: 10.1103/physrevlett.130.156402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2022] [Revised: 12/21/2022] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Abstract
Using semiclassics to surmount the hurdle of bulk-surface inseparability, we derive the superconductor vortex spectrum in nonmagnetic Weyl semimetals and show that it stems from the Berry phase of orbits made of Fermi arcs on opposite surfaces and bulk chiral modes. Tilting the vortex transmutes it between bosonic, fermionic, and supersymmetric, produces periodic peaks in the density of states that signify novel nonlocal Majorana modes, and yields a thickness-independent spectrum at magic "magic angles." We propose (Nb,Ta)P as candidate materials and tunneling spectroscopy as the ideal experiment.
Collapse
Affiliation(s)
- Rauf Giwa
- University of Houston, Houston, Texas 77204, USA
| | - Pavan Hosur
- University of Houston, Houston, Texas 77204, USA
- Texas Center for Superconductivity at the University of Houston, Houston, Texas 77204, USA
| |
Collapse
|
3
|
Yan Z, Wu Z, Huang W. Vortex End Majorana Zero Modes in Superconducting Dirac and Weyl Semimetals. PHYSICAL REVIEW LETTERS 2020; 124:257001. [PMID: 32639774 DOI: 10.1103/physrevlett.124.257001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Revised: 06/01/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Time-reversal invariant Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with s-wave pairing and the doping is lower than a critical level, straight π-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between time-reversal invariant Dirac and Weyl semimetals and Majorana zero modes in vortices.
Collapse
Affiliation(s)
- Zhongbo Yan
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Zhigang Wu
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Wen Huang
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| |
Collapse
|
4
|
Avraham N, Kumar Nayak A, Steinbok A, Norris A, Fu H, Sun Y, Qi Y, Pan L, Isaeva A, Zeugner A, Felser C, Yan B, Beidenkopf H. Visualizing coexisting surface states in the weak and crystalline topological insulator Bi 2TeI. NATURE MATERIALS 2020; 19:610-616. [PMID: 32203460 DOI: 10.1038/s41563-020-0651-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2017] [Accepted: 02/27/2020] [Indexed: 06/10/2023]
Abstract
Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi2TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its 'side' surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi2TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.
Collapse
Affiliation(s)
- Nurit Avraham
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
| | - Abhay Kumar Nayak
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Aviram Steinbok
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Andrew Norris
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Huixia Fu
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Yan Sun
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
| | - Yanpeng Qi
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, China
| | - Lin Pan
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
| | - Anna Isaeva
- Technische Universit ̈at Dresden, Dresden, Germany
- Leibniz IFW Dresden, Dresden, Germany
| | | | - Claudia Felser
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
| | - Binghai Yan
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Haim Beidenkopf
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| |
Collapse
|
5
|
Lau A, Ortix C. Topological Semimetals in the SnTe Material Class: Nodal Lines and Weyl Points. PHYSICAL REVIEW LETTERS 2019; 122:186801. [PMID: 31144876 DOI: 10.1103/physrevlett.122.186801] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Revised: 07/30/2018] [Indexed: 06/09/2023]
Abstract
We theoretically show that IV-VI semiconducting compounds with low-temperature rhombohedral crystal structure represent a new potential platform for topological semimetals. By means of minimal k·p models, we find that the two-step structural symmetry reduction of the high-temperature rocksalt crystal structure, comprising a rhombohedral distortion along the [111] direction followed by a relative shift of the cation and anion sublattices, gives rise to topologically protected Weyl semimetal and nodal line semimetal phases. We derive general expressions for the nodal features and apply our results to SnTe, showing explicitly how Weyl points and nodal lines emerge in this system. Experimentally, the topological semimetals could potentially be realized in the low-temperature ferroelectric phase of SnTe, GeTe, and related alloys.
Collapse
Affiliation(s)
- Alexander Lau
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
| | - Carmine Ortix
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
- Dipartimento di Fisica "E. R. Caianiello," Universitá di Salerno, IT-84084 Fisciano, Italy
| |
Collapse
|
6
|
Hu H, Hou J, Zhang F, Zhang C. Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings. PHYSICAL REVIEW LETTERS 2018; 120:240401. [PMID: 29956976 DOI: 10.1103/physrevlett.120.240401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2017] [Indexed: 06/08/2023]
Abstract
The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C=±2, ±1, 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.
Collapse
Affiliation(s)
- Haiping Hu
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Fan Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| |
Collapse
|
7
|
Zheng H, Chang G, Huang SM, Guo C, Zhang X, Zhang S, Yin J, Xu SY, Belopolski I, Alidoust N, Sanchez DS, Bian G, Chang TR, Neupert T, Jeng HT, Jia S, Lin H, Hasan MZ. Mirror Protected Dirac Fermions on a Weyl Semimetal NbP Surface. PHYSICAL REVIEW LETTERS 2017; 119:196403. [PMID: 29219493 DOI: 10.1103/physrevlett.119.196403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2016] [Indexed: 06/07/2023]
Abstract
The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbP's (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high-resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbP's already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology.
Collapse
Affiliation(s)
- Hao Zheng
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Guoqing Chang
- Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
| | - Shin-Ming Huang
- Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
| | - Cheng Guo
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Xiao Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Songtian Zhang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jiaxin Yin
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Su-Yang Xu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Ilya Belopolski
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Nasser Alidoust
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Daniel S Sanchez
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Guang Bian
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Tay-Rong Chang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Titus Neupert
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Horng-Tay Jeng
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Shuang Jia
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hsin Lin
- Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
| | - M Zahid Hasan
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
8
|
Liu WE, Hankiewicz EM, Culcer D. Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions. MATERIALS (BASEL, SWITZERLAND) 2017; 10:E807. [PMID: 28773167 PMCID: PMC5551850 DOI: 10.3390/ma10070807] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Revised: 07/03/2017] [Accepted: 07/10/2017] [Indexed: 11/17/2022]
Abstract
Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.
Collapse
Affiliation(s)
- Weizhe Edward Liu
- School of Physics and Australian Research Council Centre of Excellence in Low-Energy ElectronicsTechnologies, UNSW Node, The University of New South Wales, Sydney 2052, Australia.
| | - Ewelina M Hankiewicz
- Institute for Theoretical Physics and Astrophysics, Würzburg University, Am Hubland, 97074 Würzburg,Germany.
| | - Dimitrie Culcer
- School of Physics and Australian Research Council Centre of Excellence in Low-Energy ElectronicsTechnologies, UNSW Node, The University of New South Wales, Sydney 2052, Australia.
| |
Collapse
|