We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($\mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avila's global theory of quasiperiodic Schrödinger operators, we obtain exact mobility edges and prove that the mobility edge is identical to the boundary of $\mathcal{PT}$-symmetry breaking, which also proves the existence of correspondence between extended (localized) states and $\mathcal{PT}$-symmetry ($\mathcal{PT}$-symmetry-broken) states. Furthermore, we generalize the models to more general cases with non-reciprocal hopping, which breaks $\mathcal{PT}$ symmetry and generally induces skin effect, and obtain a general and analytical expression of mobility edges. While the localized states are not sensitive to the boundary conditions, the extended states become skin states when the periodic boundary condition is changed to open boundary condition. This indicates that the skin states and localized states can coexist with their boundary determined by the mobility edges.
We study a non-Hermitian Aubry-André-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single…
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($\mathcal{PT}$) symmetry. The localization transition induced by the non-Hermitian quasiperiodic potential is found to occur at the $\mathcal{PT}$-symmetry-breaking point. Our results also demonstrate the existence of energy dependent mobility edges, which separate the extended states from localized states and are only associated with the real part of eigen-energies. The level statistics and Loschmidt echo dynamics are al…
The investigations of the spectral and dynamical delocalization-localization (DL) transition have revealed intriguing features in a wide range of non-Hermitian systems. The present study aims at exploring the spectral and dynamical properties in a non-Hermitian quasiperiodic system with asymmetric hopping in the presence of Rashba Spin-Orbit (RSO) interaction. In particular, in such systems, we have identified that the DL transition is associated with a concurrent change in the energy spectrum, where the eigenstates always break the time-reversal symmetry for all strenghts of the quasiperiodic…
The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs. While most of the previous studies are concerned with one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this work, we disclose an exactly solvable 2D quasicrystal model with parity-ti…
We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponential decaying hopping and complex potentials as well as its dual model, which is just a non-Hermitian generalization of the Ganeshan-Pixley-Das Sarma model with nonreciprocal nearest-neighboring hopping. The presence of non-Hermitian term destroys the self-duality symmetry and thus prevents us exploring the localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, the Lyapunov exponent of the Ganeshan-Pixley-Das S…
The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additio…
According to the topological band theory of a Hermitian system, the different electronic phases are classified in terms of topological invariants, wherein the transition between the two phases characterized by a different topological invariant is the primary signature of a topological phase transition. Recently, it has been argued that the delocalization-localization transition in a quasicrystal, described by the non-Hermitian $\mathcal{PT}$-symmetric extension of the Aubry-André-Harper (AAH) Hamiltonian can also be identified as a topological phase transition. Interestingly, the $\mathcal{PT}…
Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localizat…
Non-Hermitian effects could create rich dynamical and topological phase structures. In this work, we show that the collaboration between lattice dimerization and non-Hermiticity could generally bring about mobility edges and multiple localization transitions in one-dimensional quasicrystals. Non-Hermitian extensions of the Aubry-André-Harper (AAH) model with staggered onsite potential and dimerized hopping amplitudes are introduced to demonstrate our results. Reentrant localization transitions due to the interplay between quasiperiodic gain/loss and lattice dimerization are found. Quantized wi…
Non-Hermitian quasicrystals possess PT and metal-insulator transitions induced by gain and loss or nonreciprocal effects. In this work, we uncover the nature of localization transitions in a generalized Aubry-Andre-Harper model with dimerized hopping amplitudes and complex onsite potential. By investigating the spectrum, adjacent gap ratios and inverse participation ratios, we find an extended phase, a localized phase and a mobility edge phase, which are originated from the interplay between hopping dimerizations and non-Hermitian onsite potential. The lower and upper bounds of the mobility ed…
Topological metal-insulator transitions in one-dimensional non-Hermitian quasicrystals: beyond PT-symmetry
College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与光电工程学院）；Qingdao Key Laboratory of Advanced Optoelectronics（青岛先进光电子重点实验室）；Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE（教育部海洋高端装备工程研究中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit（马久实验室，CNRS-南法大学-苏黎世联邦理工学院-新加坡国立大学-南洋理工大学国际联合研究单位）；Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University（同济大学物理科学与技术学院，声子学与热能科学中心，中欧纳米声子学联合实验室，上海市特殊人工微结构材料与技术重点实验室）
The cooperation between time-periodic driving fields and non-Hermitian effects could endow systems with distinctive spectral and transport properties. In this work, we uncover an intriguing class of non-Hermitian Floquet matter in one-dimensional quasicrystals, which is characterized by the emergence of multiple driving-induced ${\cal PT}$-symmetry breaking/restoration, mobility edges, and reentrant localization transitions. These findings are demonstrated by investigating the spectra, level statistics, inverse participation ratios and wavepacket dynamics of a periodically quenched nonreciproc…
Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its impact is particularly illustrating in non-Hermitian quasicrystals where the interplay between non-Hermiticity and quasiperiodicity results in the concurrence of the delocalization-localization transition, the parity-time (PT)-symmetry breaking, and the onset of the non-Hermitian skin effects. Here we experimentally simulate non-Hermitian quasicrystals using …
Anomalous Localization and Mobility Edges in Non-Hermitian Quasicrystals with Disordered Imaginary Gauge Fields
Sanli Honors College, School of Physics and Electronics Engineering, Shanxi University（山西大学物理与电子工程学院三立荣誉学院）；Institute of Theoretical Physics and State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学理论物理研究所量子光学技术与器件国家重点实验室）；State Key Laboratory of Quantum Optics Technologies and Devices, Institute of Laser Spectroscopy, Shanxi University（山西大学激光光谱研究所量子光学技术与器件国家重点实验室）
By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for the study of general non-Hermitian quasicrystals with both complex phase factor and non-reciprocal hopping. Specially, the localization-delocalization transition point, $\mathcal{PT}$-symmetry-breaking point and the winding number transition points are determined by LEs of its dual Hermitian model. The analysis was based on Avila's global theory, and we found that winding number is directly related to the acceleration, the slope of the LE, while quantization of acceleration is the crucial ingredient of Avila…
University of Science and Technology of China（中国科学技术大学）；CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics（中国科学院强耦合量子物质物理重点实验室）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理学院）；International Center for Quantum Design of Functional Materials (ICQD)（功能材料量子设计国际中心）；Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the "non-Hermitian skin effect." The NH skin effect is one of the primary challenges to defining a topological theory of NH Hamiltonians, as the sensitivity to boundary conditions invalidates the traditional bulk-boundary correspondence. The NH skin effect has recently been connected to the winding number, a topological invariant unique to NH systems. In this paper, we e…
There is a common belief in the condensed matter community that bulk quantities become insensitive to the boundary condition in the infinite-volume limit. Here we reconsider this statement in terms of recent arguments of non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for the non-Hermitian Hamiltonians-, in the traditional Green's function formalism. We find the criterion for quantities to be sensitive/insensitive against the boundary condition in Hermitian correlated/disordered systems, which is characterized by the residue theorem. We also discuss the uncerta…
Institute for Condensed Matter Theory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校凝聚态理论研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院物理系CeFEMA-LaPMET）
