Topological Dipole Insulator
arxiv(2024)
Abstract
We expand the concept of two-dimensional topological insulators to encompass
a novel category known as topological dipole insulators (TDIs), characterized
by conserved dipole moments along the x-direction in addition to charge
conservation. By generalizing Laughlin's flux insertion argument, we prove a
no-go theorem and predict possible edge patterns and anomalies in a TDI with
both charge U^e(1) and dipole U^d(1) symmetries. The edge of a TDI is
characterized as a quadrupolar channel that displays a dipole U^d(1) anomaly.
A quantized amount of dipole gets transferred between the edges under the
dipolar flux insertion, manifesting as `quantized quadrupolar Hall effect' in
TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed
by introducing a mutually commuting pair-hopping terms between wires to gap out
all the bulk modes while preserving the dipole moment. The effective action at
the quadrupolar edge can be derived from the wire model, with the corresponding
bulk dipolar Chern-Simons response theory delineating the topological
electromagnetic response in TDIs. Finally, we enrich our exploration of
topological dipole insulators to the spinful case and construct a dipolar
version of the quantum spin Hall effect, whose boundary evidences a mixed
anomaly between spin and dipole symmetry. Effective bulk and the edge action
for the dipolar quantum spin Hall insulator are constructed as well.
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