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: NonHermitian 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, 3dimensional 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 nonHermitian analogue of the 3D TI: what could the anomalous nonHermitian surface states be which necessitate a 3D topological bulk embedding? As an answer to this question, we introduce exceptional topological insulators (ETIs), a nonHermitian 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 solidstate systems, thereby setting a paradigm for nonHermitian 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 nonHermitian threedimensional phase of matter with nontrivial pointgap topology. Their topological index, a 3D winding number, is welldefined without any symmetries, and implies that the surface of the open system hosts anomalous topologically protected modes. I will explain how this nonHermitian topological phase can be inferred using symmetryindicators of the bulk Hamiltonian. Furthermore, I will demonstrate how exceptional topological insulators represent a pumping between a twodimensional phase with a higherorder nonHermitian skin effect and a trivial twodimensional 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 nonHermitian systems and nonunitary conformal field theories PoYao Chang We compute the entanglement properties in nonHermitian systems by use of a biorthogonal basis. For the nonHermitian SuSchriefferHeeger (SSH) model with parity and timereversal symmetry (PTsymmetry), 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 freefermion lattice realization of the nonunitary conformal field theory. In addition, we use the existence of the midgap states in the entanglement spectrum to characterize the topological properties in both the nonHermitian SSH model and the nonhermitian Chern insulators. 
Thursday, March 18, 2021 8:36AM  8:48AM Live 
R46.00004: Generalized Brillouin zone of nonHermitian continuum systems YuMin Hu, YinQuan Huang, WenTan Xue, Zhong Wang Recently, it has been found that the principle of bulkboundary correspondence is dramatically revised in nonHermitian systems. According to the conventional bulkboundary correspondence, the topological boundary modes of a Hermitian band insulator are generally determined by topological invariants defined in the Brillouin zone; the nonHermitian bulkboundary correspondence, however, relies on topological invariants defined in the generalized Brillouin zone (GBZ). While the GBZ has been successfully applied to characterize various nonHermitian lattice models, its formulation and significance in nonHermitian 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 GBZbased calculation of the band gaps. 
Thursday, March 18, 2021 8:48AM  9:00AM Live 
R46.00005: NonBloch PT symmetry breaking in twodimensional nonHermitian bands Fei Song, Hongyi Wang, Zhong Wang Recent studies of nonHermitian topology have uncovered unique phenomena such as the nonHermitian skin effect. From a topological perspective, the nonBloch band theory has been introduced to predict nonHermitian topological edge states. Nevertheless, it is unclear to what extent the nonBloch bands may manifest themselves in the bulk physics. Here, we show that nonHermitian skin effect and nonBloch bands cause a thresholdless PT symmetry breaking in twodimensional nonHermitian systems. Our work highlights an intriguing interplay among nonBloch band, PT symmetry, and spatial dimensions. 
Thursday, March 18, 2021 9:00AM  9:12AM Live 
R46.00006: NonHermitian SSH3 model in 1D and Hopf model in 3D ChihChun Chien, Yan He We present nonHermitian generalizations of the SSH3 model with period3 patterns of the hopping coefficients in 1D and the twoband Hopf model in 3D. The Hermitian SSH3 model does not have a welldefined winding number, despite its resemblance to the SSH model with alternating hopping coefficient. Adding nonHermitian terms to the SSH3 model leads to a welldefined winding number due to its complexvalued spectrum. Moreover, we found two types of localized states associated with a special symmetry. The Hermitian 3D twoband 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 nonHermitian generalizations. Depending on the types of nonHermitian terms, the nonHermitian Hopf insulator exhibits complexvalued spectra with a bulkboundary correspondence or nonHermitian skin effect with skewed profiles of the bulk states. 
Thursday, March 18, 2021 9:12AM  9:24AM Live 
R46.00007: Exceptional nonHermitian topological edge mode and its application to active matter Kazuki Sone, Yuto Ashida, Takahiro Sagawa Bulk band topology is recently much studied in nonHermitian 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 bulkedge correspondence in nonHermitian 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 NonHermitian Dynamical Anomalies: Extended NielsenNinomiya Theorem and Chiral Magnetic Effect Takumi Bessho, Masatoshi Sato According to conventional theory, bulk anomalous gapless states are prohibited in lattices. However, Floquet and nonHermitian systems may dynamically realize such quantum anomalies in the bulk. Here, we present an extension of the NielsenNinomiya 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 PeregBarnea 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 timeDependent 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 timedepended dissipative impurity can be used as a direction depended filter. We calculate asymmetric transmission coefficients using FloquetSmatrix 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 PokMan Chiu, PoYao 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 coldatom systems and quantum optics. 
Thursday, March 18, 2021 10:12AM  10:24AM Live 
R46.00012: Topological delocalization in twodimensional 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 twodimensional discretetime quantum walks with two internal states, increasing the disorder to the maximum possible value, i.e., using positiondependent 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: NonHermitian fractional quantum Hall states in open quantum systems Yoshida Tsuneya, Koji Kudo, Hosho Katsura, Yasuhiro Hatsugai We report that open quantum systems with twobody loss host nonHermitian 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 nonHermitian Hamiltonian. 
Thursday, March 18, 2021 10:36AM  10:48AM Live 
R46.00014: Open and closed boundary correspondence in nonreciprocal metamaterials Ananya Ghatak, Corentin Coulais, Jasper Van Wezel Recently, the advent of nonHermitian 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 nonHermitian systems have been introduced. In all these phenomena the critical relation in open and closed boundary condition for nonHermitian onedimensional chain is still under speculation with immense curiosity. We will discuss the theoretical inventories of such correspondences and demonstrate their experimental realizations in nonHermitian metamaterials. With quantumtoclassical analogy we create mechanical metamaterials with nonreciprocal interactions to mimic nonHermiticity, in which our predicted openclosed or bulkboundary 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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