Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session W55: Non-Hermitian Topological Phases |
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Sponsoring Units: DCMP Room: Mile High Ballroom 2B |
Friday, March 6, 2020 8:00AM - 8:12AM |
W55.00001: Homotopical classification of non-Hermitian band structures Zhi Li, Roger Mong We proposed a framework towards the topological classification of non-Hermitian band structures. Different from previous K-theoretical approaches, our approach is homotopical, which enables us to see more topological invariants. Specifically, we considered the classification of non-Hermitian systems with separable band structures. We found that the whole classification set is decomposed into several sectors, based on the braiding of energy levels. Each sector can be further classified based on the topology of eigenstates (wave functions). Due to the interplay between energy level braiding and eigenstates topology, we found some torsion invariants, which only appear in the non-Hermitian world. We further proved that these new topological invariants are unstable, in the sense that adding more bands will trivialize these invariants. |
Friday, March 6, 2020 8:12AM - 8:24AM |
W55.00002: Doubling theorem for Fermi points, degenerate points, and exceptional points in 2D non-Hermitian systems Ching-Kai Chiu, Zhesen Yang, Andreas P Schnyder Fermion doubling theorem, which is known as Nielsen-Ninomiya theorem, states that once a Weyl node with a non-zero topological charge is present in the 3D Brillouin zone, the node must be accompanied by at least one Weyl node to neutralize the total topological charge in the entire Brillouin zone. In 2D non-Hermitian systems, Fermi points, degeneracy points, and exceptional points can be protected by non-zero topological invariants in the absence of symmetries. We show that these three types of protected points obey the doubling theorem in the 2D Brillouin Zone in this talk. |
Friday, March 6, 2020 8:24AM - 8:36AM |
W55.00003: Non-Hermitian exceptional Landau quantization in electric circuits Xiao-Xiao Zhang, Marcel Franz Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian quantum systems. We propose here a realization of a time-reversal invariant pseudo-magnetic field, enabling the exploration of non-Hermitian physics under external magnetic field. Based on circuit realizations of non-Hermitian Dirac and Weyl systems under magnetic field, we identify the low-energy physics with a generic real energy spectrum from the non-Hermitian relativistic Landau quantization of exceptional points and rings, avoiding the non-Hermitian skin effect and providing a physical example of quasiparticles moving in the complex plane. Realistic detection schemes are designed that can be used to probe the flat energy bands, sublattice polarization, edge states protected by a non-Hermitian sublattice symmetry, and a characteristic nodeless probability distribution. |
Friday, March 6, 2020 8:36AM - 8:48AM |
W55.00004: Topological invariants for non-Hermitian chiral-symmetric systems Timo Hyart, Wojciech Brzezicki We show that the topology of one-dimensional chiral-symmetric non-Hermitian systems is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian H_{eff}(k,η), where k is the momentum and η is the imaginary part of the energy [1]. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram and calculate the end states originating from the hidden Chern number. We discuss various generalizations and realizations of this model, and the corresponding topological invariants. |
Friday, March 6, 2020 8:48AM - 9:00AM |
W55.00005: Non-Hermitian band theory of directional amplification Wentan Xue, Ming-Rui Li, Fei Song, Yu-Min Hu, Zhong Wang Owing to its open-system nature, amplification of electromagnetic and other signals is naturally described in terms of non-Hermitian operators. Recently, it has been shown that the non-Hermitian band theory is dramatically shaped by the non-Hermitian skin effect (NHSE), namely the exponential accumulation of eigenstates to the boundary of the system. In view of the NHSE, non-Bloch band theory based on the generalized Brillouin zone has been formulated to predict the topological edge modes. Here, we show that the non-Bloch band theory provides a natural framework for the intriguing phenomenon of directional amplification (or nonreciprocal amplification) that is useful in many applications. The magnitude of directional amplification is expressed in terms of the quantities of the generalized Brillouin zone. Our results provide a natural and quantitative theoretical formulation for the directional amplification. |
Friday, March 6, 2020 9:00AM - 9:12AM |
W55.00006: Non-Hermitian skin effect and chiral damping in open quantum systems Fei Song, Shunyu Yao, Zhong Wang One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. The non-Hermitian skin effect plays a crucial role in the non-Hermitian topology and bulk-boundary correspondence. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. |
Friday, March 6, 2020 9:12AM - 9:24AM |
W55.00007: Observation of non-Hermitian topology and its bulk-edge correspondence Ananya Ghatak, Martin Brandenbourger, Jasper van Wezel, Corentin Coulais Topological edge modes and the bulk-edge correspondence has enabled the creation of robust electronic, electromagnetic and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter and geophysical flows. Recently, in the advent of non-Hermitian topological systems novel topological phases have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we discover and observe a novel form of bulk-edge correspondence for non-Hermitian topological phases. We find that a change in the bulk non-Hermitian topological invariant corresponds to a change of localization of the topological edge mode. Using a quantum-to-classical analogy, we create a mechanical metamaterial with non-reciprocal interactions, in which we observe experimentally the predicted bulk-edge correspondence, demonstrating its robustness. Our results have a major impact on the field of non-Hermitian topology and boost metamaterials by opening new avenues to manipulate waves in unprecedented fashions. |
Friday, March 6, 2020 9:24AM - 9:36AM |
W55.00008: Symmetry and Topology in Non-Hermitian Physics Kohei Kawabata, Ken Shiozaki, Masahito Ueda, Masatoshi Sato Non-Hermiticity enriches topological phases beyond the existing framework for Hermitian topological phases. Here, we develop a general theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies and unifies the celebrated Altland-Zirnbauer symmetry for insulators and superconductors, leading to 38-fold symmetry instead of the 10-fold one. Moreover, we reveal that two types of energy gaps are relevant for non-Hermitian systems because of the complex-valued nature of energy spectra, both of which constitute non-Hermitian topology. Based on these fundamental insights in non-Hermitian physics, we completely classify topological phases of non-Hermitian insulators and superconductors, as well as semimetals that support exceptional points. Our work paves the way toward unique phenomena and functionalities due to the interplay of non-Hermiticity and topology, such as symmetry-protected topological lasers and dissipative topological quantum computation. |
Friday, March 6, 2020 9:36AM - 9:48AM |
W55.00009: Classification of Exceptional Points and Non-Hermitian Topological Semimetals Takumi Bessho, Kohei Kawabata, Masatoshi Sato Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas the past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbell of exceptional points in three dimensions is constructed as an illustration. Our work paves the way towards richer phenomena and functionalities of exceptional points and non-Hermitian topological semimetals. |
Friday, March 6, 2020 9:48AM - 10:00AM |
W55.00010: Non-Hermitian physical aspects in disordered Weyl/Dirac semimetals Taiki Matsushita, Yuki Nagai, Satoshi Fujimoto Recently, the platform of non-Hermitian physics is extended to many-body or disordered systems where quasiparticles possess a finite lifetime. The realization of non-Hermitian topological defects in equilibrium systems attracts great interests because non-Hermiticitian nature makes topological classification very rich. For example, non-Hermitian perturbations in Weyl Hamiltonian lead to the realization of Weyl exceptional rings and flat bands. |
Friday, March 6, 2020 10:00AM - 10:12AM |
W55.00011: Non-Hermitian fractional quantum Hall states with 1/3 filling Yoshida Tsuneya, Koji Kudo, Yasuhiro Hatsugai We elucidate the emergence of non-Hermitian fractional quantum Hall states (nHFQH) with 1/3 filling for cold atoms with two-body loss. We characterize the nHFQH states with the topological degeneracy under the periodic boundary condition and the total Chern number Ctot=1 for the ground state triplet. Furthermore, we point out that nHFQH states emerge even when the interaction is purely dissipative. |
Friday, March 6, 2020 10:12AM - 10:24AM |
W55.00012: Appearance of a topological semimetal phase in 1D non-Hermitian systems Kazuki Yokomizo, Shuichi Murakami In our previous work, we establish a non-Bloch band theory in one-dimensional (1D) tight-binding non-Hermitian systems [1]. We show how to determine the generalized Brillouin zone C_{β} for the complex Bloch wave number β=e^{ik}, k∈C. In contrast to Hermitian cases, where C_{β} is always a unit circle, in non-Hermitian systems C_{β} is a closed curve, not necessarily a unit circle. Furthermore, we find that C_{β} can have cusps, and its shape depends on system parameters. A byproduct of our theory is that one can prove the bulk-edge correspondence between the winding number defined from C_{β} and existence of topological edge states. |
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