Second-order dc conductivity in the velocity-gauge Keldysh formalism: gauge-invariant decomposition into nonlinear Drude, Berry-curvature-dipole, and quantum-metric responses

Junya Shibata

We derive a gauge-invariant clean-limit decomposition of the second-order dc nonlinear conductivity in multiband tight-binding systems within the velocity-gauge Keldysh Green's fun…