Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model

M. Iskin

doi:10.1103/physrevb.107.224505

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arXiv · 2304.03613

Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model

M. Iskin

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Abstract

We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider time-reversal-symmetric systems with uniform (i.e., at both low-momentum and low-frequency) pairing fluctuations in a unit cell, and derive the corresponding time-dependent Ginzburg-Landau (TDGL) equation. In addition to the conventional intraband contribution that depends on the derivatives of the Bloch bands, we show that the kinetic coefficients of the TDGL equation have a geometric contribution that is controlled by both the quantum-metric tensor of the underlying Bloch states and their band-resolved quantum-metric tensors. Furthermore we show that thermodynamic properties such as London penetration depth, GL coherence length, GL parameter and upper critical magnetic field have an explicit dependence on quantum geometry.

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M. Iskin. 2023-04-07. Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model. https://doi.org/10.1103/physrevb.107.224505

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