Geometric aspects of nonlinear and nonequilibrium phenomena

Abstract

We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet theory for periodically driven systems. Then we review recent attempts to engineer topological phases in nonequilibrium matters such as graphene, magnets, and superconductors irradiated with circularly polarized light. We next review a bulk photovoltaic effect of inversion broken materials focusing on the shift current response. The shift current is described with Berry connections and has a close relationship to the modern theory of polarization. We further review recent extensions of the shift current to correlated electron systems. Finally, we explain the geometric diabatic time evolution in the Zener tunneling process and its consequences on nonreciprocal transport.

arXiv comment22 pages, 13 figures; a review paper submitted to J. Phys. Soc. Jpn

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• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Large shift current via in-gap and charge-neutral exciton excitations in BN nanotubes and single BN layer
• Quantum geometry encoded to pair potentials
• Quantum Geometry and the Hidden Scales in Materials
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Direct current generation by dielectric loss in ferroelectrics
• Nonlinear optical responses in multi-orbital topological superconductors
• Diverging shift current responses in the gapless limit of two-dimensional systems
• Unexpected linear conductivity in Landau-Zener model: limitations and improvements of the relaxation time approximation in the quantum master equation
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Phase shifts, band geometry and responses in triple-Q charge and spin density waves
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals
• Theory of Photocurrent and High-Harmonic Generation with Chiral Fermions
• Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses
• Role of Ward-Takahashi identity in an electron-phonon coupled system -- Revisiting phonon shift current
• Formulation of the orbital magnetic moment in multiorbital tight-binding models: Application to the inverse Faraday effect
• Giant Shift Current in Electrically-Tunable Superlattice Bilayer Graphene
• Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses
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• Time-dependent Gutzwiller simulation of Floquet topological superconductivity
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Tangent equations of motion for nonlinear response functions
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
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• Axion dark matter detection via shift current
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective