1
|
Chen Y, Huang Y, Li Q, Tong B, Kuang G, Xi C, Watanabe K, Taniguchi T, Liu G, Zhu Z, Lu L, Zhang FC, Wu YH, Wang L. Tunable even- and odd-denominator fractional quantum Hall states in trilayer graphene. Nat Commun 2024; 15:6236. [PMID: 39043699 PMCID: PMC11266615 DOI: 10.1038/s41467-024-50589-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 07/10/2024] [Indexed: 07/25/2024] Open
Abstract
Fractional quantum Hall (FQH) states are exotic quantum many-body phases whose elementary charged excitations are anyons obeying fractional braiding statistics. While most FQH states are believed to have Abelian anyons, the Moore-Read type states with even denominators - appearing at half filling of a Landau level (LL) - are predicted to possess non-Abelian excitations with appealing potential in topological quantum computation. These states, however, depend sensitively on the orbital contents of the single-particle LL wavefunctions and the LL mixing. Here we report magnetotransport measurements on Bernal-stacked trilayer graphene, whose multiband structure facilitates interlaced LL mixing, which can be controlled by external magnetic and displacement fields. We observe robust FQH states including even-denominator ones at filling factors ν = - 9/2, - 3/2, 3/2 and 9/2. In addition, we fine-tune the LL mixing and crossings to drive quantum phase transitions of these half-filling states and neighbouring odd-denominator ones, exhibiting related emerging and waning behaviour.
Collapse
Affiliation(s)
- Yiwei Chen
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Yan Huang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Qingxin Li
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Bingbing Tong
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Hefei National Laboratory, Hefei, 230088, China
| | - Guangli Kuang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Science, Hefei, 230031, China
| | - Chuanying Xi
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Science, Hefei, 230031, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Guangtong Liu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Hefei National Laboratory, Hefei, 230088, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, China.
| | - Zheng Zhu
- Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Hefei National Laboratory, Hefei, 230088, China
- Songshan Lake Materials Laboratory, Dongguan, 523808, China
| | - Fu-Chun Zhang
- Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100049, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Ying-Hai Wu
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China.
| | - Lei Wang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
| |
Collapse
|
2
|
Yang K. Graviton-like excitation observed with predicted chirality in fractional quantum Hall liquids. Innovation (N Y) 2024; 5:100641. [PMID: 38881799 PMCID: PMC11180327 DOI: 10.1016/j.xinn.2024.100641] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2024] [Accepted: 05/16/2024] [Indexed: 06/18/2024] Open
Affiliation(s)
- Kun Yang
- Physics Department, Florida State University, Tallahassee, FL 32306, USA
| |
Collapse
|
3
|
Lu H, Chen BB, Wu HQ, Sun K, Meng ZY. Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands. PHYSICAL REVIEW LETTERS 2024; 132:236502. [PMID: 38905653 DOI: 10.1103/physrevlett.132.236502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Revised: 04/26/2024] [Accepted: 05/14/2024] [Indexed: 06/23/2024]
Abstract
Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous time-reversal symmetry breaking have garnered attention. While the thermodynamics of integer quantum anomalous Hall (IQAH) states have been systematically studied, our theoretical knowledge on thermodynamic properties of FQAH states has been severely limited. Here, we delve into the general thermodynamic response and collective excitations of both IQAH and FQAH states within the paradigmatic flat Chern-band model with remote band considered. Our key findings include (i) in both ν=1 IQAH and ν=1/3 FQAH states, even without spin fluctuations, the charge-neutral collective excitations would lower the onset temperature of these topological states, to a value significantly smaller than the charge gap, due to band mixing and multiparticle scattering; (ii) by employing large-scale thermodynamic simulations in FQAH states in the presence of strong interband mixing between C=±1 bands, we find that the lowest collective excitations manifest as the zero-momentum excitons in the IQAH state, whereas in the FQAH state, they take the form of magnetorotons with finite momentum; (iii) the unique charge oscillations in FQAH states are exhibited with distinct experimental signatures, which we propose to detect in future experiments.
Collapse
|
4
|
Liang J, Liu Z, Yang Z, Huang Y, Wurstbauer U, Dean CR, West KW, Pfeiffer LN, Du L, Pinczuk A. Evidence for chiral graviton modes in fractional quantum Hall liquids. Nature 2024; 628:78-83. [PMID: 38538799 DOI: 10.1038/s41586-024-07201-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Accepted: 02/16/2024] [Indexed: 04/01/2024]
Abstract
Exotic physics could emerge from interplay between geometry and correlation. In fractional quantum Hall (FQH) states1, novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of fluctuations of an internal quantum metric under a quantum geometry description2-5. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons. They are characterized by polarized states with chirality6-8 of +2 or -2, and energy gaps coinciding with the fundamental neutral collective excitations (namely, magnetorotons9,10) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here we observe chiral spin-2 long-wavelength magnetorotons using inelastic scattering of circularly polarized lights, providing strong evidence for CGMs in FQH liquids. At filling factor v = 1/3, a gapped mode identified as the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum S = -2, which persists at extremely long wavelength. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The modes have characteristic energies and sharp peaks with marked temperature and filling-factor dependence, corroborating the assignment of long-wavelength magnetorotons. The observations capture the essentials of CGMs and support the FQH geometrical description, paving the way to unveil rich physics of quantum metric effects in topological correlated systems.
Collapse
Affiliation(s)
- Jiehui Liang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Ziyu Liu
- Department of Physics, Columbia University, New York, NY, USA
| | - Zihao Yang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Yuelei Huang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | | | - Cory R Dean
- Department of Physics, Columbia University, New York, NY, USA
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Lingjie Du
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China.
- Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou, China.
| | - Aron Pinczuk
- Department of Physics, Columbia University, New York, NY, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
| |
Collapse
|
5
|
Onyszczak M, Uzan-Narovlansky AJ, Tang Y, Wang P, Jia Y, Yu G, Song T, Singha R, Khoury JF, Schoop LM, Wu S. A platform for far-infrared spectroscopy of quantum materials at millikelvin temperatures. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:103903. [PMID: 37823766 DOI: 10.1063/5.0160321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 09/25/2023] [Indexed: 10/13/2023]
Abstract
Optical spectroscopy of quantum materials at ultralow temperatures is rarely explored, yet it may provide critical characterizations of quantum phases not possible using other approaches. We describe the development of a novel experimental platform that enables optical spectroscopic studies, together with standard electronic transport, of materials at millikelvin temperatures inside a dilution refrigerator. The instrument is capable of measuring both bulk crystals and micrometer-sized two-dimensional van der Waals materials and devices. We demonstrate its performance by implementing photocurrent-based Fourier transform infrared spectroscopy on a monolayer WTe2 device and a multilayer 1T-TaS2 crystal, with a spectral range available from the near-infrared to the terahertz regime and in magnetic fields up to 5 T. In the far-infrared regime, we achieve spectroscopic measurements at a base temperature as low as ∼43 mK and a sample electron temperature of ∼450 mK. Possible experiments and potential future upgrades of this versatile instrumental platform are envisioned.
Collapse
Affiliation(s)
- Michael Onyszczak
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | | | - Yue Tang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Pengjie Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Yanyu Jia
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Guo Yu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Tiancheng Song
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Ratnadwip Singha
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Jason F Khoury
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Leslie M Schoop
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Sanfeng Wu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
6
|
Yuzhu W, Bo Y. Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect. Nat Commun 2023; 14:2317. [PMID: 37085543 PMCID: PMC10121662 DOI: 10.1038/s41467-023-38036-0] [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: 08/10/2022] [Accepted: 04/06/2023] [Indexed: 04/23/2023] Open
Abstract
Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.
Collapse
Affiliation(s)
- Wang Yuzhu
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore
| | - Yang Bo
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore.
- Institute of High Performance Computing, A*STAR, Singapore, 138632, Singapore.
| |
Collapse
|
7
|
Salgado-Rebolledo P, Palumbo G. Nonrelativistic supergeometry in the Moore-Read fractional quantum Hall state. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.065020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
8
|
Kirmani A, Bull K, Hou CY, Saravanan V, Saeed SM, Papić Z, Rahmani A, Ghaemi P. Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers. PHYSICAL REVIEW LETTERS 2022; 129:056801. [PMID: 35960588 DOI: 10.1103/physrevlett.129.056801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2021] [Revised: 05/27/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.
Collapse
Affiliation(s)
- Ammar Kirmani
- Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225, USA
- Physics Department, City College of the City University of New York, New York, New York 10031, USA
| | - Kieran Bull
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Chang-Yu Hou
- Schlumberger-Doll Research, Cambridge, Massachusetts 02139, USA
| | - Vedika Saravanan
- Department of Electrical Engineering, City College of the City University of New York, New York, New York 10031, USA
| | - Samah Mohamed Saeed
- Department of Electrical Engineering, City College of the City University of New York, New York, New York 10031, USA
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Armin Rahmani
- Department of Physics and Astronomy and Advanced Materials Science and Engineering Center, Western Washington University, Bellingham, Washington 98225, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Pouyan Ghaemi
- Physics Department, City College of the City University of New York, New York, New York 10031, USA
- Graduate Center of the City University of New York, New York, New York 10016, USA
| |
Collapse
|
9
|
Nguyen DX, Haldane FDM, Rezayi EH, Son DT, Yang K. Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems. PHYSICAL REVIEW LETTERS 2022; 128:246402. [PMID: 35776452 DOI: 10.1103/physrevlett.128.246402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 05/12/2022] [Indexed: 05/06/2023]
Abstract
We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.
Collapse
Affiliation(s)
- Dung Xuan Nguyen
- Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| | - F D M Haldane
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - E H Rezayi
- Physics Department, California State University Los Angeles, Los Angeles, California 90032, USA
| | - Dam Thanh Son
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Kun Yang
- NHMFL and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| |
Collapse
|
10
|
Liu Z, Wurstbauer U, Du L, West KW, Pfeiffer LN, Manfra MJ, Pinczuk A. Domain Textures in the Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2022; 128:017401. [PMID: 35061454 DOI: 10.1103/physrevlett.128.017401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 10/18/2021] [Accepted: 12/12/2021] [Indexed: 06/14/2023]
Abstract
Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.
Collapse
Affiliation(s)
- Ziyu Liu
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - Ursula Wurstbauer
- Institute of Physics, University of Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany
| | - Lingjie Du
- School of Physics, and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - Aron Pinczuk
- Department of Physics, Columbia University, New York, New York 10027, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
| |
Collapse
|
11
|
Ma KKW, Wang R, Yang K. Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges. PHYSICAL REVIEW LETTERS 2021; 126:206801. [PMID: 34110185 DOI: 10.1103/physrevlett.126.206801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 04/28/2021] [Indexed: 06/12/2023]
Abstract
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be broken at low-energy. This makes it important to understand how SUSY is realized and broken, and study their consequences. We show that an N=(1,0) SUSY, arguably the simplest type, can be realized at the edge of the Moore-Read quantum Hall state. Depending on the absence or presence of edge reconstruction, both SUSY-preserving and SUSY broken phases can be realized in the same system, allowing for their unified description. The significance of the gapless fermionic Goldstino mode in the SUSY broken phase is discussed.
Collapse
Affiliation(s)
- Ken K W Ma
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Ruojun Wang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Kun Yang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| |
Collapse
|
12
|
Liu Z, Balram AC, Papić Z, Gromov A. Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers. PHYSICAL REVIEW LETTERS 2021; 126:076604. [PMID: 33666472 DOI: 10.1103/physrevlett.126.076604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 01/22/2021] [Indexed: 05/06/2023]
Abstract
We introduce different types of quenches to probe the nonequilibrium dynamics and multiple collective modes of bilayer fractional quantum Hall states. We show that applying an electric field in one layer induces oscillations of a spin-1 degree of freedom, whose frequency matches the long-wavelength limit of the dipole mode. On the other hand, oscillations of the long-wavelength limit of the quadrupole mode, i.e., the spin-2 graviton, as well as the combination of two spin-1 states, can be activated by a sudden change of band mass anisotropy. We construct an effective field theory to describe the quench dynamics of these collective modes. In particular, we derive the dynamics for both the spin-2 and the spin-1 states and demonstrate their excellent agreement with numerics.
Collapse
Affiliation(s)
- Zhao Liu
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China
| | - Ajit C Balram
- Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai 600113, India
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Andrey Gromov
- Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| |
Collapse
|