Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants

TL;DR

This paper introduces a new bulk-corner correspondence for time-reversal symmetric insulators, revealing boundary fractional charges through novel real-space invariants that extend beyond traditional Berry phase and symmetry indicators.

Contribution

It develops partial real-space invariants that identify fractional corner charges and detect all fragile topological phases in time-reversal symmetric insulators.

Findings

Partial real-space invariants govern fractional corner charges.

These invariants detect all fragile topological phases.

The approach applies to both isolated structures and heterostructures.

Abstract

The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To so do we develop "partial" real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These new crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.