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Tang J, Cheng R. Lossless Spin-Orbit Torque in Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}. PHYSICAL REVIEW LETTERS 2024; 132:136701. [PMID: 38613287 DOI: 10.1103/physrevlett.132.136701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Revised: 08/22/2023] [Accepted: 02/23/2024] [Indexed: 04/14/2024]
Abstract
We formulate and quantify the spin-orbit torque (SOT) in intrinsic antiferromagnetic topological insulator MnBi_{2}Te_{4} of a few septuple-layer thick in charge-neutral condition, which exhibits pronounced layer-resolved characteristics and even-odd contrast. Contrary to traditional current-induced torques, our SOT is not accompanied by Ohm's currents, thus being devoid of Joule heating. We study the SOT-induced magnetic resonances, where in the tri-septuple-layer case we identify a peculiar exchange mode that is blind to microwaves but can be exclusively driven by the predicted SOT. As an inverse effect, the dynamical magnetic moments generate a pure adiabatic current, which occurs concomitantly with the SOT and gives rise to an overall reactance for the MnBi_{2}Te_{4}, enabling a lossless conversion of electric power into magnetic dynamics.
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Affiliation(s)
- Junyu Tang
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Ran Cheng
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
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2
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Two-dimensional Thouless pumping of light in photonic moiré lattices. Nat Commun 2022; 13:6738. [PMID: 36347871 PMCID: PMC9643509 DOI: 10.1038/s41467-022-34394-3] [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: 06/01/2022] [Accepted: 10/21/2022] [Indexed: 11/09/2022] Open
Abstract
Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice. Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries. Extending the control over topological system will open the doors to both fundamental studies and applications. Here the authors demonstrate thouless topological transport of light in a bulk tunable moiré lattice.
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Fu Q, Wang P, Kartashov YV, Konotop VV, Ye F. Two-Dimensional Nonlinear Thouless Pumping of Matter Waves. PHYSICAL REVIEW LETTERS 2022; 129:183901. [PMID: 36374696 DOI: 10.1103/physrevlett.129.183901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
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Affiliation(s)
- Qidong Fu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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4
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You O, Liang S, Xie B, Gao W, Ye W, Zhu J, Zhang S. Observation of Non-Abelian Thouless Pump. PHYSICAL REVIEW LETTERS 2022; 128:244302. [PMID: 35776444 DOI: 10.1103/physrevlett.128.244302] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 01/17/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
Thouless pump provides robust ways to realize quantized transport of waves and particles, and it casts the static 2D quantum Hall effect onto 1D dynamic systems where one of the momentum dimensions is replaced by the evolution time or path parameter. In the past few decades, various types of Abelian Thouless pump have been achieved theoretically and experimentally. However, the study of non-Abelian Thouless pump is scarce, which tells us that the order of two evolution loops with the same base point cannot be changed, and there has been no experimental observation of non-Abelian Thouless pump. Here we report the observation of a non-Abelian Thouless pump in coupled acoustic waveguide array. The non-Abelian property originates from the noncommutative combination of two different ℤ_{3} pump cycles that traverse across multiple band degeneracies in the parameter space in a three-band system. Moreover, we can pump a specific initial state to any state on any lattice site by applying these two ℤ_{3} pump cycles multiple times in a well-designed sequence. Our study paves the way for exploring and utilizing non-Abelian dynamical effects in classical wave systems and may offer different recipes for quantum walking, quantum optics, and quantum computation.
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Affiliation(s)
- Oubo You
- Department of Physics, University of Hong Kong, Hong Kong, China
| | - Shanjun Liang
- Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, Hong Kong Polytechnic University, Hong Kong, China
| | - Biye Xie
- Department of Physics, University of Hong Kong, Hong Kong, China
| | - Wenlong Gao
- Department of Physics, Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
| | - Weimin Ye
- College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, 410073, China
| | - Jie Zhu
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong, China
| | - Shuang Zhang
- Department of Physics, University of Hong Kong, Hong Kong, China
- Department of Electronic and Electrical Engineering, University of Hong Kong, Hong Kong, China
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Li J, Shen C, Huang TJ, Cummer SA. Acoustic tweezer with complex boundary-free trapping and transport channel controlled by shadow waveguides. SCIENCE ADVANCES 2021; 7:7/34/eabi5502. [PMID: 34407929 PMCID: PMC8373113 DOI: 10.1126/sciadv.abi5502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 06/28/2021] [Indexed: 06/13/2023]
Abstract
Acoustic tweezers use ultrasound for contact-free, bio-compatible, and precise manipulation of particles from millimeter to submicrometer scale. In microfluidics, acoustic tweezers typically use an array of sources to create standing wave patterns that can trap and move objects in ways constrained by the limited complexity of the acoustic wave field. Here, we demonstrate spatially complex particle trapping and manipulation inside a boundary-free chamber using a single pair of sources and an engineered structure outside the chamber that we call a shadow waveguide. The shadow waveguide creates a tightly confined, spatially complex acoustic field inside the chamber without requiring any interior structure that would interfere with net flow or transport. Altering the input signals to the two sources creates trapped particle motion along an arbitrary path defined by the shadow waveguide. Particle trapping, particle manipulation and transport, and Thouless pumping are experimentally demonstrated.
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Affiliation(s)
- Junfei Li
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Chen Shen
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
- Department of Mechanical Engineering, Rowan University, Glassboro, NJ 08028, USA
| | - Tony Jun Huang
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
| | - Steven A Cummer
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.
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6
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Funo K, Lambert N, Nori F, Flindt C. Shortcuts to Adiabatic Pumping in Classical Stochastic Systems. PHYSICAL REVIEW LETTERS 2020; 124:150603. [PMID: 32357046 DOI: 10.1103/physrevlett.124.150603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be nonzero even in the absence of a bias. However, as the driving speed is increased, nonadiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.
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Affiliation(s)
- Ken Funo
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Neill Lambert
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Franco Nori
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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7
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Lee CH, Li L, Gong J. Hybrid Higher-Order Skin-Topological Modes in Nonreciprocal Systems. PHYSICAL REVIEW LETTERS 2019; 123:016805. [PMID: 31386404 DOI: 10.1103/physrevlett.123.016805] [Citation(s) in RCA: 54] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Revised: 04/23/2019] [Indexed: 06/10/2023]
Abstract
Higher-order phases are characterized by corner or hinge modes that arise due to the interesting interplay of localization mechanisms along two or more dimensions. In this work, we introduce and construct a novel class of "hybrid" higher-order skin-topological boundary modes in nonreciprocal systems with two or more open boundaries. Their existence crucially relies on nonreciprocal pumping in addition to topological localization. Unlike usual non-Hermitian "skin" modes, they can exist in lattices with vanishing net reciprocity due to the selective nature of nonreciprocal pumping: While the bulk modes remain extended due to the cancellation of nonreciprocity within each unit cell, boundary modes experience a curious spontaneous breaking of reciprocity in the presence of topological localization, thereby experiencing the non-Hermitian skin effect. The number of possible hybridization channels increases rapidly with dimensionality, leading to a proliferation of distinct phases. In addition, skin modes or hybrid skin-topological modes can restore unitarity and are hence stable, allowing for experimental observations and manipulations in non-Hermitian photonic and electrical metamaterials.
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Affiliation(s)
- Ching Hua Lee
- Institute of High Performance Computing, A*STAR, Singapore 138632
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
| | - Linhu Li
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
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8
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Long Y, Ren J. Floquet topological acoustic resonators and acoustic Thouless pumping. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:742. [PMID: 31370615 DOI: 10.1121/1.5114914] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2018] [Accepted: 02/28/2019] [Indexed: 06/10/2023]
Abstract
Constructing the topological states can serve as a promising approach for robust acoustic wave transports and manipulations. Here, the authors develop a scheme to realize acoustic topological states and adiabatic Thouless pumping in acoustic Floquet resonator systems. The directional acoustic wave can be robustly manipulated and pumped adiabatically from one side to the opposite side due to the non-trivial topological nature. The physical mechanism behind these phenomena can be understood by effective one-dimensional Aubry-André-Harper Hamiltonian, with an additional synthetic dimension originating from Floquet spatially periodic modulation. This Aubry-André-Harper acoustic resonator system can be regarded as a projection from a two-dimensional topological Hofstadter model for the integer quantum Hall effect. The authors' scheme provides a promising method for synthesizing acoustic topological states for efficient acoustic wave manipulations. Introducing the topological mechanism to the control wave will become an alternative method besides the conventional effective acoustic parameter methods.
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Affiliation(s)
- Yang Long
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, People's Republic of China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, People's Republic of China
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9
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Quantized spin pump on helical edge states of a topological insulator. Sci Rep 2019; 9:3378. [PMID: 30833644 PMCID: PMC6399345 DOI: 10.1038/s41598-019-39002-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 12/31/2018] [Indexed: 11/08/2022] Open
Abstract
We report a theoretical study of the quantized spin pump in a traditional quantum pump device that is based on the helical edge states of a quantum spin Hall insulator. By introducing two time-dependent magnetizations out of phase as the pumping parameters, we found that when the Fermi energy resides in the energy gap opened by magnetization, an integer number of charges or spins can be pumped out in a pumping cycle and ascribed to the possible topological interface state born in between the two pumping potentials. The quantized pump current can be fully spin-polarized, spin-unpolarized, or pure spin current while its direction can be abruptly reversed by some system parameters such as the pumping phase and local gate voltage. Our findings may shed light on generation of a quantized spin pump.
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10
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Liu S, Shao LB, Hou QZ, Xue ZY. Quantum anomalous Hall phase in a one-dimensional optical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:124001. [PMID: 29380747 DOI: 10.1088/1361-648x/aaab89] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
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Affiliation(s)
- Sheng Liu
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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11
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Ma W, Zhou L, Zhang Q, Li M, Cheng C, Geng J, Rong X, Shi F, Gong J, Du J. Experimental Observation of a Generalized Thouless Pump with a Single Spin. PHYSICAL REVIEW LETTERS 2018; 120:120501. [PMID: 29694055 DOI: 10.1103/physrevlett.120.120501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 01/17/2018] [Indexed: 06/08/2023]
Abstract
Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.
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Affiliation(s)
- Wenchao Ma
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Longwen Zhou
- Department of Physics, National University of Singapore, Singapore 117543, Singapore
| | - Qi Zhang
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Min Li
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chunyang Cheng
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jianpei Geng
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Fazhan Shi
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117543, Singapore
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
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12
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Privitera L, Russomanno A, Citro R, Santoro GE. Nonadiabatic Breaking of Topological Pumping. PHYSICAL REVIEW LETTERS 2018; 120:106601. [PMID: 29570317 DOI: 10.1103/physrevlett.120.106601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Indexed: 06/08/2023]
Abstract
We study Thouless pumping out of the adiabatic limit. Our findings show that despite its topological nature, this phenomenon is not generically robust to nonadiabatic effects. Indeed, we find that the Floquet diagonal ensemble value of the pumped charge shows a deviation from the topologically quantized limit which is quadratic in the driving frequency for a sudden switch on of the driving. This is reflected also in the charge pumped in a single period, which shows a nonanalytic behavior on top of an overall quadratic decrease. Exponentially small corrections are recovered only with a careful tailoring of the driving protocol. We also discuss thermal effects and the experimental feasibility of observing such a deviation.
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Affiliation(s)
| | - Angelo Russomanno
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56127 Pisa, Italy
- International Centre for Theoretical Physics (ICTP), P.O.Box 586, I-34014 Trieste, Italy
| | - Roberta Citro
- Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno and Spin-CNR Unità, Via Giovanni Paolo II, 132, I-84084 Fisciano (Sa), Italy
| | - Giuseppe E Santoro
- SISSA, Via Bonomea 265, I-34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), P.O.Box 586, I-34014 Trieste, Italy
- CNR-IOM Democritos National Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
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14
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Ma YQ. Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042133. [PMID: 25375464 DOI: 10.1103/physreve.90.042133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Indexed: 06/04/2023]
Abstract
We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.
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Affiliation(s)
- Yu-Quan Ma
- School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
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15
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Wang L, Soluyanov AA, Troyer M. Proposal for direct measurement of topological invariants in optical lattices. PHYSICAL REVIEW LETTERS 2013; 110:166802. [PMID: 23679630 DOI: 10.1103/physrevlett.110.166802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Indexed: 06/02/2023]
Abstract
We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atoms in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provides a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier function techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the Z(2) topological invariant of time-reversal symmetric insulators.
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Affiliation(s)
- Lei Wang
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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16
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Jiang L, Levchenko SV, Rappe AM. Rigorous definition of oxidation states of ions in solids. PHYSICAL REVIEW LETTERS 2012; 108:166403. [PMID: 22680739 DOI: 10.1103/physrevlett.108.166403] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2009] [Revised: 06/14/2011] [Indexed: 06/01/2023]
Abstract
We present justification and a rigorous procedure for electron partitioning among atoms in extended systems. The method is based on wave-function topology and the modern theory of polarization, rather than charge density partitioning or wave-function projection, and, as such, reformulates the concept of oxidation state without assuming real-space charge transfer between atoms. This formulation provides rigorous electrostatics of finite-extent solids, including films and nanowires.
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Affiliation(s)
- Lai Jiang
- The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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17
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Low T, Jiang Y, Katsnelson M, Guinea F. Electron pumping in graphene mechanical resonators. NANO LETTERS 2012; 12:850-854. [PMID: 22273444 DOI: 10.1021/nl2038985] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The combination of high-frequency vibrations and metallic transport in graphene makes it a unique material for nanoelectromechanical devices. In this Letter, we show that graphene-based nanoelectromechanical devices are extremely well suited for charge pumping due to the sensitivity of its transport coefficients to perturbations in electrostatic potential and mechanical deformations, with the potential for novel small scale devices with useful applications.
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Affiliation(s)
- Tony Low
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA.
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18
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Whitesides GM, Weisbecker CS. Measurements of the Conductivity of Individual 10 Nm Carbon Nanotubes. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-349-263] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTCatalytically grown carbon fibers approximately 10 nm in diameter and several microns long were characterized by transmission electron microscopy and determined to be multiple-walled nanotubes, and a technique was developed to measure the conductivity of an individual nanotube. Nanotubes were dispersed in solvents and precipitated onto lithographically defined gold contacts to make a ‘nano-wire’ circuit. Non-contact AFM was used to image the nano-wires, and a resistance of 11.4 (± 1.0) MΩ was measured through a single nanotube at 23°C. A resistivity of 9.5×10−5 Ω m was estimated for carbon conducting along the axis of a fiber. Local heating of nanotubes appeared to occur at high current densities. The nanotubes could sustain currents on the order of 10 μA per fiber, but application of currents on the order of 100 μA per fiber resulted in rapid decomposition in air and breaking of the circuit.
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Talyanskii VI, Novikov DS, Simons BD, Levitov LS. Quantized adiabatic charge transport in a carbon nanotube. PHYSICAL REVIEW LETTERS 2001; 87:276802. [PMID: 11800906 DOI: 10.1103/physrevlett.87.276802] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2001] [Indexed: 05/23/2023]
Abstract
The coupling of a semimetallic carbon nanotube to a surface acoustic wave (SAW) is proposed as a vehicle to realize quantized adiabatic charge transport. We demonstrate that electron backscattering from a periodic SAW potential can be used to induce a miniband spectrum at energies near the Fermi level. Within the framework of Luttinger liquid theory, electron interaction is shown to enhance minigaps and thereby improve current quantization.
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Affiliation(s)
- V I Talyanskii
- Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, United Kingdom
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Wagner M. Probing pauli blocking factors in quantum pumps with broken time-reversal symmetry. PHYSICAL REVIEW LETTERS 2000; 85:174-177. [PMID: 10991187 DOI: 10.1103/physrevlett.85.174] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2000] [Indexed: 05/23/2023]
Abstract
A recently demonstrated quantum electron pump is discussed within the framework of photon-assisted tunneling. Because of lack of time-reversal symmetry, different results are obtained for the pump current depending on whether or not final-state Pauli blocking factors are used when describing the tunneling process. While in both cases the current depends quadratically on the driving amplitude for moderate pumping, a marked difference is predicted for the temperature dependence. With blocking factors the pump current decreases roughly linearly with temperature until k(B)T approximately Planck's over 2piomega is reached, whereas without them it is unaffected by temperature, indicating that the entire Fermi sea participates in the transport.
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Affiliation(s)
- M Wagner
- Hitachi Cambridge Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
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Affiliation(s)
- J. E. Avron
- Department of Physics, Technion, 32000 Haifa, Israel
| | - J. Berger
- Department of Physics, Technion, 32000 Haifa, Israel
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Shilton JM, Talyanskii VI, Pepper M, Ritchie DA, Frost JE, Ford CJ, Smith CG, Jones GA. High-frequency single-electron transport in a quasi-one-dimensional GaAs channel induced by surface acoustic waves. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 1996; 8:L531-L539. [PMID: 22146295 DOI: 10.1088/0953-8984/8/38/001] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report on an experimental investigation of the direct current induced by transmitting a surface acoustic wave (SAW) with frequency 2.7 GHz through a quasi-one-dimensional (1D) channel defined in a GaAs - AlGaAs heterostructure by a split gate, when the SAW wavelength was approximately equal to the channel length. At low SAW power levels the current reveals oscillatory behaviour as a function of the gate voltage with maxima between the plateaux of quantized 1D conductance. At high SAW power levels, an acoustoelectric current was observed at gate voltages beyond pinch-off. In this region the current displays a step-like behaviour as a function of the gate voltage (or of the SAW power) with the magnitude corresponding to the transfer of one electron per SAW cycle. We interpret this as due to trapping of electrons in the moving SAW-induced potential minima with the number of electrons in each minimum being controlled by the electron - electron interactions. As the number of electrons is reduced, the classical Coulomb charging energy becomes the Mott - Hubbard gap between two electrons and finally the system becomes a sliding Mott insulator with one electron in each well.
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Affiliation(s)
- J M Shilton
- Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
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23
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Shih WK, Niu Q. Nonadiabatic particle transport in a one-dimensional electron system. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:11902-11910. [PMID: 9975330 DOI: 10.1103/physrevb.50.11902] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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24
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Liu C, Niu Q. Nonequilibrium effect in an electron turnstile. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:18320-18323. [PMID: 10008485 DOI: 10.1103/physrevb.48.18320] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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25
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White JD, Wagner M. Intrinsic electron-pumping mechanism in the oscillating-barrier turnstile. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:2799-2802. [PMID: 10008685 DOI: 10.1103/physrevb.48.2799] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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26
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Liu C, Niu Q. Nonadiabatic effect in a quantum charge pump. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:13031-13034. [PMID: 10005519 DOI: 10.1103/physrevb.47.13031] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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27
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Williams DA. Coherent nonequilibrium phonons: An induced Peierls distortion. PHYSICAL REVIEW LETTERS 1992; 69:2551-2554. [PMID: 10046523 DOI: 10.1103/physrevlett.69.2551] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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28
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Avron JE, Klein M, Pnueli A, Sadun L. Hall conductance and adiabatic charge transport of leaky tori. PHYSICAL REVIEW LETTERS 1992; 69:128-131. [PMID: 10046206 DOI: 10.1103/physrevlett.69.128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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29
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Datta S, Anantram MP. Steady-state transport in mesoscopic systems illuminated by alternating fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:13761-13764. [PMID: 10001479 DOI: 10.1103/physrevb.45.13761] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Liu C, Niu Q. Centralized distribution of adiabatic current in a split Bloch band. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:9046-9053. [PMID: 10000766 DOI: 10.1103/physrevb.45.9046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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31
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Hekking F, Nazarov YV. Photovoltaic effect in quantum adiabatic transport as a way to pump electrons. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:11506-11509. [PMID: 9999278 DOI: 10.1103/physrevb.44.11506] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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32
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Hekking F, Nazarov YV. Pauli pump for electrons. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:9110-9113. [PMID: 9998886 DOI: 10.1103/physrevb.44.9110] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kouwenhoven LP, Johnson AT, van der Vaart NC, van der Enden A, Harmans CJPM, Foxon CT. Quantized current in a quantum dot turnstile. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/bf01307634] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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34
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van Wees BJ. Electron transport in a mesoscopic annulus, driven by a time-dependent magnetic flux. PHYSICAL REVIEW LETTERS 1991; 66:2033-2036. [PMID: 10043373 DOI: 10.1103/physrevlett.66.2033] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Guinea F, Garca N. Scanning tunneling microscopy, resonant tunneling, and counting electrons: A quantum standard of current. PHYSICAL REVIEW LETTERS 1990; 65:281-284. [PMID: 10042879 DOI: 10.1103/physrevlett.65.281] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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