LAUSR

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain nonlinear optical responses elegantly and transparently. We devise a kinetic theory applicable to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of nonlinear optical currents arising from the interference of interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report four findings. (i) The Fermi Golden Rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (non-resonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. As an illustration, we compute the nonlinear response of topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals dominated by interband coherence effects. We find that the nonlinear response of CuMnAs is responsive to the direction of finite magnetization field and choice of the polarization angle of the beam, while Weyl semimetal only to tilt.