Making Sense of Topological Solid-State Materials with Concepts from Quantum Field Theory: Axion Electrodynamics and Beyond (groupe de travail Quantique)

Benjamin Wieder

IPhT

Tue, May. 30th 2023, 14:00-15:00

Pièce 50, Bât. 774, Orme des Merisiers

Just over 15 years ago, researchers discovered that readily accessible solid-state insulators can host seemingly exotic, symmetry-protected 3D generalizations of quantum Hall states. However this past year, high-throughput first-principles (DFT) calculations revealed that symmetry-protected topological insulating (TI) and topological crystalline insulating (TCI) states are not rare, but rather occur in thousands of known materials [1]. This raised a concerning question: if topological materials are everywhere, then is topology an inessential detail in describing materials, or are we just not applying the correct experimental probes? This question can partially be answered by recognizing that unlike quantum Hall states and 3D TIs, 3D TCI states in nonmagnetic materials are featureless from the perspective of the bulk and surface electromagnetic response. Furthermore, for TCIs without gapless surface states, which have become known as higher-order TCIs (HOTIs), photoemission signatures of surface Dirac cones also cannot be employed to infer the bulk topology. Nevertheless, we expect 3D HOTI states to carry properties that are just as robust to interactions, disorder, and sample details as other, better-understood, crystal-symmetry-protected topological phases of matter. Drawing on quantities from quantum field theory that are quantifiably robust to interactions and disorder, including boundary anomalies and axion (theta) angles, we have developed gauge-invariant numerical tools for extracting previously-unknown bulk and surface properties of TCIs and HOTIs [2]. Combining the theoretical and numerical methods of sector- (spin-) resolution, layer constructions, Wilson loops, position-space Chern markers, and magnetic flux insertion, we demonstrate that nonmagnetic HOTIs can be characterized by bulk nontrivial “partial” axion angles that give rise to half-quantized surface 2D TI states originating from a “partial” parity anomaly. We have applied our methods to the DFT-obtained electronic structures of candidate HOTIs including MoTe2 and BiBr to deduce associated experimental observables, finding in particular that a novel, spin-charge-separated variant of axion electrodynamics provides a topological contribution to the bulk spin-electromagnetic response of BiBr [3].
[1] M. G. Vergniory*, B. J. Wieder*, L. Elcoro, S. S. P. Parkin, C. Felser, B. A. Bernevig, and N. Regnault, Science (2022)
[2] F. Schindler, S. S. Tsirkin, T. Neupert, B. A. Bernevig, and B. J. Wieder, Nature Communications (2022)
[3] K.-S. Lin, G. Palumbo, Z. Guo, J. Blackburn, D. P. Shoemaker, F. Mahmood, Z. Wang, G. A. Fiete, B. J. Wieder, and B. Bradlyn, arXiv:2207.10099 (2022)

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