TY - JOUR

T1 - Topological insulators avoid the parity anomaly

AU - Mulligan, Michael

AU - Burnell, F. J.

PY - 2013/8/5

Y1 - 2013/8/5

N2 - The surface of a 3topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2 system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here, we explain why such a state can exist on the boundary of a 3 system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional space-time. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.

AB - The surface of a 3topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2 system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here, we explain why such a state can exist on the boundary of a 3 system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional space-time. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.

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U2 - 10.1103/PhysRevB.88.085104

DO - 10.1103/PhysRevB.88.085104

M3 - Article

AN - SCOPUS:84884578754

VL - 88

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 8

M1 - 085104

ER -