Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session S65: Quantum Hall Effect: Field Responses and FluctuationsRecordings Available

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Chair: Darya Aleinikava, Benedictine University Room: Hyatt Regency Hotel Grant Park C 
Thursday, March 17, 2022 8:00AM  8:12AM 
S65.00001: Accelerated Discovery of the ValleyPolarized Quantum Anomalous Hall Effect in MXenes Ranjan K Barik The topological phase preserved by spontaneous magnetization in noncentrosymmetric twodimensional systems leads to valleypolarized quantum anomalous Hall (VPQAH) insulators. Because of these strict criteria, the VPQAH effect has been observed in a very few materials. We applied a highthroughput firstprinciples approach, wherein the magnetic and topological properties of inversion symmetrybroken 2D MXenes are screened, systematically. We find 14 MXenes having the outofplane ferromagnetic ground state in the presence of spin−orbit coupling. The nontrivial Berry curvature and chiral edge states confirm the VPQAH effect in these MXenes. Furthermore, using basic elemental features, we have developed a machinelearningbased magnetic nodal line semimetal classification model and a regression model, which accurately predict both the nodal positions. Our study provides a robust platform to incorporate valley and topological physics, which would accelerate the search for promising VPQAH materials. 
Thursday, March 17, 2022 8:12AM  8:24AM 
S65.00002: On the Road to Connect Nonlinear Charged and Orbital Effects. Diego García A few years ago, it was theoretically proposed and experimentally demonstrated that nonmagnetic materials with nontrivial band topology support anomalous Hall effect at the second order in the electric field and in the absence of magnetic field. This nonlinear anomalous Hall effect emerges in noncentrosymmetric materials and was connected to the Berry curvature dipole of the ground state. In fact, the absence of a symmetry center in such materials unlocks the generation of nonequilibrium orbital magnetization, linear in the electric field. This effect is tagged the gyrotropic Edelstein effect. In this presentation, we investigate the intimate relation between the nonlinear anomalous Hall effect mechanism and gyrotropic Edelstein. As a matter of fact, these two effects are governed by the same crystalline symmetries and are both associated with the Berry curvature dipole. In this sense, the mathematical structure of these two quantities suggests that they are connected between each other, and must be a nontrivial function of the chemical potential. We address their corresponding behaviours in two different multiband model systems, remarking the fact that the spinorbit coupling is not a necessary condition on both nonlinear Hall effect and gyrotropic Edelstein effect. From a theoretical point a view, a formal relationship between the orbital and charge transports opens the possibility to unify the notions of the Berry curvature and the orbital moment, since in essence both objects are akin to an angular velocity of electrons in the adiabatic limit, when they are subjected to an external electric field. 
Thursday, March 17, 2022 8:24AM  8:36AM 
S65.00003: Electric polarization and magnetization in metals and topologically nontrivial matter Perry T Mahon, Jason Kattan, John E Sipe A feature of the modern theory of polarization is that metallic systems do not admit a welldefined electric polarization, P. This is predicated on the assumption that P is welldefined if and only if the electronic ground state is “localized”. If instead one takes the view that P is more fundamentally related to the general existence of a complete set of exponentially localized Wannier functions, which follows from topological considerations, a definition is always admitted. This is the perspective we have adopted in the unified theory of microscopic polarization and magnetization fields that we have previously developed. Interestingly, when the modern theory admits a welldefined P, in particular for “trivial” insulators, these philosophically different approaches agree. Comparison with the modern theory of magnetization is somewhat different; we find agreement for the orbital magnetization in “trivial” insulators and as well the predicted magnetoelectric effect, but disagree with later thermodynamic extensions to include metals and Chern insulators in that description. In addition to considering such quantities in metals and Chern insulators, we also provide a novel perspective on the distinct contributions to the electrical conductivity tensor in the longwavelength limit. 
Thursday, March 17, 2022 8:36AM  8:48AM 
S65.00004: Hofstadter Butterfly In Twisted Trilayer Graphene Muhammad Imran, Yafis Barlas The Morie lattice in twisted trilayer graphene(tTLG) exhibits magic angle flat band phenomena along with superconductivity. In this talk, we will discuss the energy dispersion of tTLG and Hofstadter butterfly patterns at high magnetic field, as a function of the displacement field and twist angle. We show that for zero displacement field tTLG exhibits mirror symmetry, with even parity twisted bilayer graphene Hofstadter bands and odd parity Dirac Landau levels. We calculate the Chern numbers associated with the energy gaps in of tTLG at high magnetic field. We also show that as the displacement field is increased, the Hofstadter bands hybridize with the relativistic Landau levels and identify and characterize topological transition as a function of the displacement field and twist angle. 
Thursday, March 17, 2022 8:48AM  9:00AM 
S65.00005: Fractional Mutual Statistics on Integer Quantum Hall Edges JuneYoung M Lee, Cheolhee Han, H.S. Sim Fractional charge and statistics are hallmarks of lowdimensional interacting systems such as fractional quantum Hall (QH) systems, but the detection of the fractional statistics is a challenging task due to their strongly interacting nature. Integer QH systems are regarded noninteracting, yet they can have fractional charge excitations when they couple to another interacting system or timedependent voltages. The integer QH systems provide good experimental controllability. 
Thursday, March 17, 2022 9:00AM  9:12AM 
S65.00006: Geometric logarithmic negativity in integer quantum Hall states* ChiaChuan Liu, Juliette Geoffrion, William WitczakKrempa We study the quantum entanglement structure of integer quantum Hall (IQH) states via the logarithmic negativity (LN), and the mutual information for various fillings. Unlike the entanglement entropy, the LN provides an accurate measure of quantum entanglement even for mixed states, which enables us to study the quantum entanglement encoded in various tripartite geometries. Working at zero temperature, we focus on an important class of regions that contain corners, leading to a geometric angledependent contribution to the LN at different fillings. We find surprising relations of these corner terms by comparing them at different fillings, and with the mutual information, as well as charge fluctuations. In a followup talk by Juliette Geoffrion, the finite temperature properties will be discussed. 
Thursday, March 17, 2022 9:12AM  9:24AM 
S65.00007: Logarithmic negativity in the integer quantum Hall effect at finite temperature Juliette Geoffrion, ChiaChuan Liu, William WitczakKrempa We study the entanglement structure of integer quantum Hall states at finite temperature obtained by numerically computing the logarithmic negativity (LN). The LN is well suited to measure the entanglement content of mixed states. We work with various subregions including ones with corners, in order to study the geometric contribution of the LN. We compare results at different fillings, draw connections to finite temperature charge fluctuations, and discuss the relevant physics in the different temperature regimes. In particular, a rapid drop of the LN is observed with increasing temperature. This complements the zerotemperature results presented in the talk by ChiaChuan Liu et al. 
Thursday, March 17, 2022 9:24AM  9:36AM 
S65.00008: Local density of states of the HarperHofstadter model with random disorder. Chakradhar Rangi, Juana Moreno, KaMing Tam Anderson localization plays a crucial role in the integer quantum hall systems. The degenerated Landau level is split by random disorder and the increase of disorder strength leads to the localization of the states in the tails of the Landau level. The recently developed ClusterTypical Medium Theory (ClusterTMT) can be modified to study lattice models for the integer quantum effect, in particular the HarperHofstadter model with local random disorder. The clusterTMT method is successful in reproducing the full phase diagram of the three dimensional Anderson model. Its success is hinted by the observation that the local density of states of the localized phase follows a lognormal distribution. We investigate the statistics of the local density of states of the HarperHofstadter model with local random potential. We find that the local density of states changes very closely from normal to lognormal distribution as the disorder strength increases. This provides support on the validity of the clusterTMT when applied to the integer quantum hall systems. 
Thursday, March 17, 2022 9:36AM  9:48AM 
S65.00009: Boundary effects of Hall viscosity Pranav Rao, Barry Bradlyn In this talk, we examine in detail the ambiguity of viscosity coefficients in two dimensions, where different components of the dissipative and nondissipative viscosity tensor correspond to physically identical effects in the bulk—redundant viscosities give rise to the same bulk viscous force and can be shifted into one another by adding divergenceless "contact terms" to the stress tensor of the system. Considering fluid flow in systems with a boundary, we are able to distinguish between the redundant viscosity components, and interpret the contact terms as a specific choice of stress boundary conditions. We examine the waves on the surface of a chiral fluid to probe this phenomenon, finding that the dispersion of these surface waves is sensitive to the contact terms, and contextualize our results with recent experiments on chiral active fluids. Lastly, we interpret the quantum Hall fluid through the lens of our framework, showing that the boundary term one adds to the WenZee action to render it gauge invariant on systems with a boundary can be interpreted as a contact term (or as modified stress boundary conditions). 
Thursday, March 17, 2022 9:48AM  10:00AM 
S65.00010: Observation of Quantum Hall Effect and Charge Density Wave in CaCu_{4}As_{2} single crystal SOUVIK SASMAL, VIKAS SAINI, Sitaram Ramakrishnan, Gourav Dwari, Bishal B Maity, Jinke Bao, Rajib Mondal, Vikram Tripathi, Bahadur Singh, A Thamizhavel Quantum Hall effect (QHE) is usually observed in 2D systems due to the quantization of electron gas at sufficiently large applied magnetic fields. Whereas, in a 3D system, the charge carriers are free to move in all special directions which essentially prevents the quantization of Hall conductance. In search of new materials, we have grown single crystals of CaCu_{4}As_{2} which crystallizes in the rhombohedral structure with three septuple layers in one unit cell. From thermal, electrical transport and temperature dependent single crystal xray diffraction measurements, we observe a transition at 52 K attributed to the structural and/or charge density wave (CDW) transition. The Shubnikovde Haas (SdH) oscillation reveals a unique frequency at 255 T, and the angular dependence of this frequency confirms the 2D nature of the charge carriers. The inverse Hall resistance vs 1/B plot exhibits clear steps like features. Our detailed analysis confirms that these steps are due to the QHE. Our experimental results indicate that the QHE may be originated from a large number of parallel conduction channels and CDW enhances the 2D nature of the charge carrier. Thus, CaCu_{4}As_{2} provides a new platform to understand the coexistence of both CDW and QHE in a 3D system. 
Thursday, March 17, 2022 10:00AM  10:12AM 
S65.00011: Supermetalinsulator transition in a nonHermitian network model JhihShih You, Hui Liu, Shinsei Ryu, Ion C Fulga We study a nonHermitian and nonunitary version of the twodimensional ChalkerCoddington network model with balanced gain and loss. This model belongs to the class D^{†} with particlehole symmetry^{†} and hosts both the nonHermitian skin effect as well as exceptional points. By calculating its twoterminal transmission, we find a contact effect induced by the skin effect, which results in a nonquantized transmission for chiral edge states. In addition, the model exhibits an insulator to “supermetal” transition, across which the transmission changes from exponentially decaying with system size to exponentially growing with system size. In the clean system, the critical point separating insulator from supermetal is characterized by a nonHermitian Dirac point that produces a quantized critical transmission of 4, instead of the value of 1 expected in Hermitian systems. This change in critical transmission is a consequence of the balanced gain and loss. When adding disorder to the system, we find a critical exponent for the divergence of the localization length ν≈1, which is the same as that characterizing the universality class of twodimensional Hermitian systems in class D. Our work provides a way of exploring the localization behavior of nonHermitian systems, by using network models, which in the past proved versatile tools to describe Hermitian physics. 
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