Berry Phase and Topological Response in Interacting Quantum Systems: from Weyl Semimetals to Chiral Superconductors

Abstract

Topological responses rooted in the Berry phase play an important role in modern condensed matter physics. However, in interacting quantum systems, the robustness and observability of such responses require careful analysis and examination. This dissertation comprises two studies on how topological phenomena, namely the chiral anomaly and the anomalous Hall effect, emerge and are (un)renormalized in interacting quantum systems.The first part investigates the robustness of the chiral anomaly in interacting systems through a mixed anomaly framework. The chiral anomaly is one of the robust quantum effects in relativistic field theories with chiral symmetry, where charges in the chiral sectors appear to be separately conserved. The chiral anomaly, which is often associated with a renormalization-invariant topological term, is a violation of this conservation law because of quantum effects. In condensed matter systems like Weyl semimetals, analogous phenomena emerge as charge pumping between Fermi pockets under electromagnetic fields. However, because the chiral charge is defined in terms of low energy quasiparticles, most studies of the chiral anomaly in condensed matter apply to effectively non-interacting systems. We apply an approach in which the chiral symmetry in solid materials is viewed as a so-called emanant symmetry of the underlying space translation symmetry, a mixed anomaly between the charge $U(1)$ and space translation. In this framework, the chiral charge is associated with total momentum, and we show that the corresponding chiral anomaly remains unrenormalized by interactions in contrast to other chiral charges in $(1+1)$D whose renormalization is dependent on regularization. In $(3+1)$D, is equivalent to the charge transferred between Fermi surfaces which can be measured through changes in Fermi-surface-enclosed volume. To measure this effect, we propose a pump-probe technique. The second part turns to another Berry-phase-related response, the anomalous Hall effect in the phase-disordered regime of chiral superconductors. Motivated by recent experiments showing evidence for chiral superconductivity in an anomalous Hall phase of tetralayer graphene, we study the relationship between the normal state anomalous Hall conductivity and that in the phase-disordered state slightly above the critical temperature of the superconductor. Numerical simulations show that the Berry phase on the Fermi surface determines the charge asymmetry between vortices and antivortices, resulting in a nonzero Hall response that is close to the normal-state anomalous Hall response. However, using a gauge-invariant superconducting response framework, we find that while the vortex charge is screened by interactions, the screening charge, after a time delay, reappears in the longitudinal current. Thus, in this phase, the dc Hall conductivity aligns with the ac Hall conductance of the superconducting and normal phases, rather than with the screened vortex charge.