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arXiv · 2306.03946

Proof of Gauge-Invariance of Magnetic Susceptibility of Topologically Trivial Insulators in the Independent Particle Approximation

Alistair H. Duff·J. E. Sipe
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Abstract

We have derived an expression for the magnetic susceptibility of topologically trivial insulators, however an important consideration for any response tensor is whether it is gauge-invariant. By this we refer to the gauge-freedom in choosing the Bloch functions one uses in a computation since multiplication by an arbitrary $\textbf{k}$-dependent complex phase produces equally valid Bloch functions. Additionally Wannier functions, which can be constructed by a unitary mixing of the Bloch functions, are a useful basis for computation due to their localized properties, but are strongly non-unique. Therefore, we show that the theoretical expression we derived is independent of the choice of Bloch functions or Wannier functions used, and thus is gauge-invariant in this sense.

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Alistair H. Duff, J. E. Sipe. 2023-10-11. Proof of Gauge-Invariance of Magnetic Susceptibility of Topologically Trivial Insulators in the Independent Particle Approximation. https://arxiv.org/abs/2306.03946

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