Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Abstract

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

arXiv comment10 pages, 6 figures in the main text

References in corpus (39)

• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides
• Control over topological insulator photocurrents with light polarization
• Topological nature of nonlinear optical effects in solids
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Topological semi-metals with line nodes and drumhead surface states
• Design principles for shift current photovoltaics
• Intrinsic Superconducting Diode Effect
• Supercurrent diode effect and finite momentum superconductivity
• Photocurrents in Weyl semimetals
• A phenomenological theory of superconductor diodes
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAgX (X = P, As)
• Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• High-frequency rectification via chiral Bloch electrons
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Evidence of an odd-parity hidden order in a spin-orbit coupled correlated iridate
• Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity
• Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
• Quantum theory of the nonlinear Hall effect
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd${}_2$Re${}_2$O${}_7$
• Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal
• Gauge covariances and nonlinear optical responses
• Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
• Nonlinear optical responses of crystalline systems: Results from a velocity gauge analysis
• Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds
• Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems
• Nonreciprocal current from electron interactions in noncentrosymmetric crystals: roles of time reversal symmetry and dissipation
• Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals
• Longitudinal and anomalous Hall conductivity of a general two-band model
• Nonreciprocal optical response in parity-breaking superconductors
• Nonreciprocal Meissner response in parity-mixed superconductors
• Topological piezoelectric effect and parity anomaly in nodal line semimetals
• Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides

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