Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold possibility of being applied diodes or high-frequency optical devices. are often closely related to multiband nature system which can be taken into account by geometric quantities such as Berry curvature shown nonlinear Hall effect. Theoretically, semi-classical Boltzmann treatment reduced density matrix method have been employed, effect dissipation is included through relaxation time approximation. In diagrammatic method, treated imaginary part self-energy Green function consequent broadening spectral for integration over real frequency. Therefore, poles do not play explicit pole when there finite dissipation. this paper, stark contrast conventional picture, we show that determine mostly response functions with dissipation, leads terms Fermi distribution complex argument results dissipation-induced term. We elucidate origin nonreciprocal conductivity, generalized higher derivative. Finally, derive analytical on conductivities type-I type-II Weyl Hamiltonian demonstrate their crucial roles.