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The Z2-anomaly and boundaries of topological insulators · Around

2012

The Z2-anomaly and boundaries of topological insulators

Ringel, Zohar, Stern, Ady

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We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a novel Z2-anomaly associated with charge conservation.

The anomaly is manifested through a 2-point correlation function involving creation and annihilation operators on two decoupled boundaries.
Although charge conservation on each boundary requires this quantity to vanish, we find that it diverges.
A corollary result is that under an insertion of a flux quantum the ground state evolves to an exactly orthogonal state independent of the rate at which the flux is inserted.

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The determinant can be made well defined using a Pauli-Villars regulator [ 11 ] which generates a Π n [ λ n − i M ] \Pi_{n}[\lambda_{n}-iM] denominator

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