Theory of Orbital Magnetic Quadrupole Moment and Nonlinear Anomalous Thermoelectric Transport

Abstract

We present a microscopic theory of the magnetic quadrupole moment density ${\mathcal{Q}}_{ij}$ in periodic crystals with combined time reversal ($\mathcal{T}$) and inversion ($\mathcal{I}$) symmetry. We obtain a gauge-invariant expression with clear physical interpretation and demonstrate the typical behaviour of ${\mathcal{Q}}_{ij}$ in a minimal two-band model that hosts a tilted Dirac cone. We then show that ${\mathcal{Q}}_{ij}$ leads to an intrinsic nonlinear anomalous thermoelectric current. As an example, we calculate the nonlinear Nernst and Hall current in the loop-current model for cuprate superconductors, and demonstrate their unique behaviour and capability of indicating $\mathcal{TI}$-invariance.

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• Berry phase effect in anomalous thermoelectric transport
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• A global inversion-symmetry-broken phase inside the pseudogap region of YBa${}_2$Cu${}_3$O${}_y$
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• Time-reversal symmetry breaking hidden order in Sr${}_2$(Ir,Rh)O${}_4$
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