Nonreciprocal nonhermitian systems provide an unconventional localization mechanism of topological zero modes via the nonhermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I show that such nonreciprocal mechanical metamaterials reveal their underlying biorthogonality in the directly observable response of the system to external excitation. Applied to the ground-breaking experiment, this nonreciprocal response theory predicts that the zero-mode skin effect goes along an extended phase where the system is highly sensitive to physical perturbations, leading to a diverging response in the limit of a large system.
We study the one-dimensional nonreciprocal lattices with real nearest neighboring hopping and find that the energy spectra under open boundary conditions can be entirely real or imaginary. We further investigate the spectral properties and the non-Hermitian skin effect in the one-dimensional mosaic lattices with real nonreciprocal hopping introduced at equally spaced sites. The eigenenergies of such lattices undergo a real-complex-imaginary or real-complex transition as the nonreciprocity varies. Moreover, the skin effect exhibits phase transitions depending on the period of the mosaic nonreci…
Non-Hermiticity greatly expands existing physical laws beyond the Hermitian framework, revealing various novel phenomena with unique properties. Up to now, most exotic nonHermitian effects, such as exceptional points and non-Hermitian skin effects, are discovered in single-particle systems. The interplay between non-Hermitian and manybody correlation is expected to be a more fascinating but much less explored area. Due to the complexity of the problem, current researches in this field mainly stay at the theoretical level. The experimental observation of predicted non-Hermitian manybody phases …
A prominent feature of some one-dimensional non-Hermitian systems is that all right-eigenstates of the non-Hermitian Hamiltonian are localized in one end of the chain. The topological and trivial phases are distinguished by the emergence of zero-energy modes within the skin states in the presence of the chiral symmetry. Skin states are formed when the system is nonreciprocal, where it is said nonreciprocal if the absolute values of the right- and left-going hoppings amplitudes are different. Indeed, the zero-energy edge modes emerge at both edges in the topological phase of the reciprocal non-…
The pursuit of the non-Hermitian skin effect (NHSE) in various physical systems is of great research interest. Compared with recent progress in non-electronic systems, the implementation of the NHSE in condensed matter physics remains elusive. Here, we show that the NHSE can be engineered in the mesoscopic heterojunctions (system plus reservoir) in which electrons in two channels of the system moving towards each other have asymmetric coupling to those of the reservoir. This makes electrons in the system moving forward and in the opposite direction have unequal lifetimes, and so gives rise to …
A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero …
We study nonreciprocal nonlinear Schrödinger systems. As a prototype we analyze the Hatano-Nelson model together with a typical nonlinear term introduced and its generalization to two dimensions. We employ the quench dynamics, where a pulse is given to one site and its time evolution is analyzed. It is found that the skin state is always formed due to the nonreciprocal hopping and hence that the system is topological. However, the structure of the skin state is essentially modified by the nonlinear interaction because it favors a self-trapping. Four typically different states emerge as an inte…
Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Research Institute of Future Technology, South China Normal University（华南师范大学未来技术研究院）；State Key Laboratory of Luminescent Materials and Devices and Institute of Optical Communication Materials, South China University of Technology（华南理工大学发光材料与器件国家重点实验室及光通信材料研究所）；Center for Quantum Computing, RIKEN（理研量子计算中心）；Department of Physics, University of Michigan（密歇根大学物理系）
Based on a general transport theory for non-reciprocal non-Hermitian systems and a topological model that encompasses a wide range of previously studied models, we (i) provide conditions for effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption, (ii) identify which effects are compatible and linked with each other, and (iii) determine by which levers they can be tuned independently. For instance, the directed amplification inherent in the non-Hermitian skin effect does not enter the spectral conditions for reflectionless transport, lasing, or coheren…
Non-Hermitian skin effect and electronic nonlocal transport
Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所（ICMM），西班牙科学研究委员会）；Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子设备中心）
We study interaction-induced Mott insulators, and their topological properties in a 1D non-Hermitian strongly-correlated spinful fermionic superlattice system with either nonreciprocal hopping or complex-valued interaction. For the nonreciprocal hopping case, the low-energy neutral excitation spectrum is sensitive to boundary conditions, which is a manifestation of the non-Hermitian skin effect. However, unlike the single-particle case, particle density of strongly correlated system does not suffer from the non-Hermitian skin effect due to the Pauli exclusion principle and repulsive interactio…
Non-Hermitian skin effect (NHSE) is a unique phenomenon studied intensively in non-Hermitian systems during the past few years. In this work, we discuss the energy dependence of NHSE by introducing nonreciprocity beyond the nearest-neighboring hopping in the one-dimensional lattices. The direction of NHSE reverses as the eigenenergy of the system under open boundary conditions (OBCs) sweeps across some critical energies. To characterize such a phenomenon, we introduce the concept of non-Hermitian skin effect edges, which separate the eigenstates localized at opposite ends of the lattice in the…
Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Department of Physics, Sophia University（上智大学物理系）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）
Observation of Erratic Non-Hermitian Skin Effect in Phononic Crystals
Institute of Acoustics, School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院声学研究所）；School of Advanced Manufacturing Engineering, Nanjing University（南京大学先进制造工程学院）
Localization in microcavities revealed by phase-space non-Hermitian skin effect
Institute for Basic Science (IBS)（基础科学研究院）；Korea University of Science and Technology (UST)（韩国科学技术院）；Kyungpook National University（庆北国立大学）；Pukyong National University（釜庆国立大学）；Hanyang University（汉阳大学）；Technische Universität Chemnitz（开姆尼茨工业大学）
We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum anomaly and non-Hermitian skin effects, in which the bulk spectra extremely depend on the boundary conditions. In this context, the fact that the intrinsic higher-dimensional skin effects under the full open boundary condition need the presence of the topological defects is understood in terms of the anomalous fermion production such as the Rubakov-Callan effe…
$\mathcal{PT}$ and anti-$\mathcal{PT}$ phase transitions in a trimerized Su--Schrieffer--Heeger chain with nonreciprocal Rashba spin-orbit coupling
University of Rostock（罗斯托克大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Ocean University of China（中国海洋大学）；University of Zanjan（赞詹大学）
The bulk-boundary or bulk-edge correspondence is a principle relating surface confined states to the topological classification of the bulk. By combining non-Hermitian ingredients in terms of gain or loss with media that violate reciprocity, an unconventional non-Bloch bulk-boundary correspondence leads to unusual localization of bulk states at boundaries$-$a phenomenon coined non-Hermitian skin effect. Here we \textcolor{black}{numerically} employ the acoustoelectric effect in electrically biased and layered piezophononic media as a solid framework for non-Hermitian and nonreciprocal topologi…
Competing skin effect and quasiperiodic localization in the non-Hermitian Su-Schrieffer-Heeger chain: Reentrant delocalization, spectral topology destruction, and entanglement suppression
Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Physics, National Taiwan Normal University（台湾师范大学物理系）；Department of Applied Physics, Tokyo University of Science（东京理科大学应用物理系）；Department of Basic Sciences, Kyushu Institute of Technology（九州工业大学基础科学系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
