Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session R46: Non-Hermitian TopologyLive
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Sponsoring Units: DCMP Chair: Xiaoqi Sun |
Thursday, March 18, 2021 8:00AM - 8:12AM Live |
R46.00001: Exceptional Topological Insulators Michael Denner, Anastasiia Skurativska, Frank Schindler, Mark Fischer, Ronny Thomale, Tomas Bzdusek, Titus Neupert Since their theoretical conception and experimental discovery, 3-dimensional topological insulators (3D TIs) have become the focal point for research on topological quantum matter. Their key feature is a single Dirac electron on the surface, representing an anomaly: in purely 2D such a state can neither be regularized on a lattice nor in the continuum. In this work we search for a non-Hermitian analogue of the 3D TI: what could the anomalous non-Hermitian surface states be which necessitate a 3D topological bulk embedding? As an answer to this question, we introduce exceptional topological insulators (ETIs), a non-Hermitian topological state of matter that features exotic surface states. We show how this phase can evolve from a Weyl semimetal or Hermitian 3D TI close to the topological transition point when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter. |
Thursday, March 18, 2021 8:12AM - 8:24AM Live |
R46.00002: Exceptional topological insulators with crystal symmetries Titus Neupert, Frank Schindler, Michael Denner, Marta Brzezinska, Pascal Vecsei, Anar Bold, Tomas Bzdusek Exceptional topological insulators are a non-Hermitian three-dimensional phase of matter with nontrivial point-gap topology. Their topological index, a 3D winding number, is well-defined without any symmetries, and implies that the surface of the open system hosts anomalous topologically protected modes. I will explain how this non-Hermitian topological phase can be inferred using symmetry-indicators of the bulk Hamiltonian. Furthermore, I will demonstrate how exceptional topological insulators represent a pumping between a two-dimensional phase with a higher-order non-Hermitian skin effect and a trivial two-dimensional phase. This implies an anomalous localization of the surface states of an exceptional topological insulator. |
Thursday, March 18, 2021 8:24AM - 8:36AM Live |
R46.00003: Entanglement properties in topological non-Hermitian systems and non-unitary conformal field theories Po-Yao Chang We compute the entanglement properties in non-Hermitian systems by use of a biorthogonal basis. For the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT-symmetry), we find the entanglement entropy scaling at the critical point has a logarithmic scaling with corresponding central charge c=-2. This critical point is the first free-fermion lattice realization of the non-unitary conformal field theory. In addition, we use the existence of the mid-gap states in the entanglement spectrum to characterize the topological properties in both the non-Hermitian SSH model and the non-hermitian Chern insulators. |
Thursday, March 18, 2021 8:36AM - 8:48AM Live |
R46.00004: Generalized Brillouin zone of non-Hermitian continuum systems Yu-Min Hu, Yin-Quan Huang, Wen-Tan Xue, Zhong Wang Recently, it has been found that the principle of bulk-boundary correspondence is dramatically revised in non-Hermitian systems. According to the conventional bulk-boundary correspondence, the topological boundary modes of a Hermitian band insulator are generally determined by topological invariants defined in the Brillouin zone; the non-Hermitian bulk-boundary correspondence, however, relies on topological invariants defined in the generalized Brillouin zone (GBZ). While the GBZ has been successfully applied to characterize various non-Hermitian lattice models, its formulation and significance in non-Hermitian continuum systems have been unclear so far. Here, we generalize the GBZ theory to continuum systems and demonstrate its applications. As an illustration, we show an efficient GBZ-based calculation of the band gaps. |
Thursday, March 18, 2021 8:48AM - 9:00AM Live |
R46.00005: Non-Bloch PT symmetry breaking in two-dimensional non-Hermitian bands Fei Song, Hongyi Wang, Zhong Wang Recent studies of non-Hermitian topology have uncovered unique phenomena such as the non-Hermitian skin effect. From a topological perspective, the non-Bloch band theory has been introduced to predict non-Hermitian topological edge states. Nevertheless, it is unclear to what extent the non-Bloch bands may manifest themselves in the bulk physics. Here, we show that non-Hermitian skin effect and non-Bloch bands cause a thresholdless PT symmetry breaking in two-dimensional non-Hermitian systems. Our work highlights an intriguing interplay among non-Bloch band, PT symmetry, and spatial dimensions. |
Thursday, March 18, 2021 9:00AM - 9:12AM Live |
R46.00006: Non-Hermitian SSH3 model in 1D and Hopf model in 3D Chih-Chun Chien, Yan He We present non-Hermitian generalizations of the SSH3 model with period-3 patterns of the hopping coefficients in 1D and the two-band Hopf model in 3D. The Hermitian SSH3 model does not have a well-defined winding number, despite its resemblance to the SSH model with alternating hopping coefficient. Adding non-Hermitian terms to the SSH3 model leads to a well-defined winding number due to its complex-valued spectrum. Moreover, we found two types of localized states associated with a special symmetry. The Hermitian 3D two-band Hopf model, on the other hand, is a topological insulator but does not fall into the standard classification. The modulus of the Hopf index remains quantized in the non-Hermitian generalizations. Depending on the types of non-Hermitian terms, the non-Hermitian Hopf insulator exhibits complex-valued spectra with a bulk-boundary correspondence or non-Hermitian skin effect with skewed profiles of the bulk states. |
Thursday, March 18, 2021 9:12AM - 9:24AM Live |
R46.00007: Exceptional non-Hermitian topological edge mode and its application to active matter Kazuki Sone, Yuto Ashida, Takahiro Sagawa Bulk band topology is recently much studied in non-Hermitian physics, while its correspondence to the existence of edge modes is more subtle than the Hermitian case. Here, we reveal that gapless edge modes can be protected by topology and symmetry of the band structure of edge modes themselves around the branchpoint singularity of exceptional points [1]. Such gapless edge modes, which we termed as exceptional edge modes, are robust independently of the bulk topology, thus implying the breakdown of the bulk-edge correspondence in non-Hermitian systems. We numerically confirm the emergence and robustness of exceptional edge modes in a simple model with topologically trivial bulk. We also propose the applications of exceptional edge modes to a topological insulator laser and chiral active matter. |
Thursday, March 18, 2021 9:24AM - 9:36AM Live |
R46.00008: Topological Duality in Floquet and Non-Hermitian Dynamical Anomalies: Extended Nielsen-Ninomiya Theorem and Chiral Magnetic Effect Takumi Bessho, Masatoshi Sato According to conventional theory, bulk anomalous gapless states are prohibited in lattices. However, Floquet and non-Hermitian systems may dynamically realize such quantum anomalies in the bulk. Here, we present an extension of the Nielsen-Ninomiya theorem that is valid even in the presence of the bulk quantum anomaly. Particularly, the extended theorem establishes the exact |
Thursday, March 18, 2021 9:36AM - 9:48AM Live |
R46.00009: Driving topological insulators out of equilibrium: deviations from periodicity Ranjani Seshadri, Tami Pereg-Barnea The behaviour of topological systems driven out of equilibrium has been |
Thursday, March 18, 2021 9:48AM - 10:00AM Live |
R46.00010: Direction Depended Transport in a Hamiltonian Ratchet induced by a time-Dependent Dissipative Impurity Zlata Fedorova, Christoph Dauer, Anna Sidorenko, Sebastian Eggert, Johann Kroha, Stefan Linden Ratchets are known to induce directed transport, but in hermitean systems transport strongly depends on the initial conditions which can reduce the ratchet effect dramatically. In this work we both theoretically and experimentally study directed transport in a fast Hamilton ratchet and show that a time-depended dissipative impurity can be used as a direction depended filter. We calculate asymmetric transmission coefficients using Floquet-S-matrix theory and find parameter regions where we the efficiency of the filter is almost ideal. |
Thursday, March 18, 2021 10:00AM - 10:12AM Live |
R46.00011: Z2 topological quench dynamics Pok-Man Chiu, Po-Yao Chang We study a quantum quench protocol with Z2 topology in 3+1 dimensions. The Z2 feature is classified by the homotopy group Pi4(SU(2)) and the Z2 topological invariant is constructed from the dimensional reduction method. Furthermore, we show that the entanglement spectra can identify the Z2 signature. Finally, we discuss the possible realization in cold-atom systems and quantum optics. |
Thursday, March 18, 2021 10:12AM - 10:24AM Live |
R46.00012: Topological delocalization in two-dimensional quantum walks Janos Asboth, Arindam Mallick Quantum walks spread faster than classical random walks, which makes them interesting for quantum information applications. However, they are more sensitive to spatial disorder: they can undergo Anderson localization, which stops them from spreading off to infinity. We show that in two-dimensional discrete-time quantum walks with two internal states, increasing the disorder to the maximum possible value, i.e., using position-dependent rotation operators selected randomly and Haar uniformly, does not lead to Anderson localization, but rather, to a critical dynamical system where the quantum walk spreads diffusively. The reason behind this has to do with the topological invariants of the quantum walk: maximal disorder tunes the quantum walk to a critical point between phases with different topological invariants. We calculate these invariants by detecting edge states. We characterize the critical state of the quantum walk, by numerical calculation of the critical exponent η in three different ways, obtaining η=0.52 as in the integer quantum Hall effect. |
Thursday, March 18, 2021 10:24AM - 10:36AM Live |
R46.00013: Non-Hermitian fractional quantum Hall states in open quantum systems Yoshida Tsuneya, Koji Kudo, Hosho Katsura, Yasuhiro Hatsugai We report that open quantum systems with two-body loss host non-Hermitian fractional quantum Hall states (nHFQH) with 1/3 filling when the jump term is negligible[1]. The characterization of nHFQH states is accomplished by observing topological degeneracy and by computing the Chern number for the non-Hermitian Hamiltonian. |
Thursday, March 18, 2021 10:36AM - 10:48AM Live |
R46.00014: Open and closed boundary correspondence in non-reciprocal metamaterials Ananya Ghatak, Corentin Coulais, Jasper Van Wezel Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, skin effect and novel topological phases that can only exist in non-Hermitian systems have been introduced. In all these phenomena the critical relation in open and closed boundary condition for non-Hermitian one-dimensional chain is still under speculation with immense curiosity. We will discuss the theoretical inventories of such correspondences and demonstrate their experimental realizations in non-Hermitian metamaterials. With quantum-to-classical analogy we create mechanical metamaterials with non-reciprocal interactions to mimic non-Hermiticity, in which our predicted open-closed or bulk-boundary correspondence has been observed experimentally. It shows for a topological chain, a change in the bulk corresponds to a change of localization of the topological edge mode. Such unfamiliar bulk boundary correspondence has also been manifested in the metamaterial to manipulate waves in unprecedented fashions. These techniques are useful to engineer wave properties, steering waves on demand, in sensing and energy harvesting. |
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