2022/06/21 by Tyner, Alexander C., Goswami, Pallab
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2206.10636
The non-trivial third homotopy class of three-dimensional topological insulators leads to quantized, magneto-electric coefficient or axion angle θ= n π, with n ∈ ℤ. In Part I, we developed tools for computing n from a staggered symmetry-indicator κAF,j and Wilson loops of non-Abelian, Berry connection in momentum-space, which clearly distinguished between magneto-electrically trivial (n=0), and non-trivial (n=2s) topological crystalline insulators. In this work, we perform ℤ-classification of real-space, topological response or θ by carrying out thought experiments with magnetic, Dirac monopoles. We demonstrate this for non-magnetic and magnetic topological insulators by computing induced electric charge on monopoles or Witten effect. We show that both first- and higher- order topological insulators can exhibit quantized, magneto-electric response, irrespective of the presence of gapless surface-states, and corner-states. Special attention is paid to the response of octupolar higher-order topological insulator, which was originally predicted to be magneto-electrically trivial. The important roles of fermion zero-modes, CP, and flavor symmetries are critically addressed. Our work outlines a unified theoretical framework for addressing dc topological response and topological quantum phase transitions, which cannot be reliably predicted by symmetry-based classification scheme.