Quantum mechanics

Algorithm

Quantization (signal processing)

Energy (signal processing)

Physics

Mathematics

Topological insulator

Homogeneous space

Condensed matter physics

Geometry

Combinatorics

Charge (physics)

Electron

Topology (electrical circuits)

Physical review. B./Physical review. B

In the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required for charge neutrality. In this paper, we show that a filling anomaly can arise when corners are introduced in $C_n$-symmetric crystalline insulators with vanishing polarization, having as consequence the existence of corner-localized charges quantized in multiples of $\frac{e}{n}$. We characterize the existence of this charge systematically and build topological indices that relate the symmetry representations of the occupied energy bands of a crystal to the quanta of fractional charge robustly localized at its corners. When an additional chiral symmetry is present, $\frac{e}{2}$ corner charges are accompanied by zero-energy corner-localized states. We show the application of our indices in a number of atomic and fragile topological insulators and discuss the role of fractional charges bound to disclinations as bulk probes for these crystalline phases.

Quantization of fractional corner charge in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>C</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> -symmetric higher-order topological crystalline insulators

Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators