Berry Fermi Liquid Theory

Abstract

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current-current correlator exactly matches with the result obtained from the kinetic theory.

arXiv commentv2: typos fixed, v3: some issues clarified, typos fixed, v4: an error fixed; 46 pages

References in corpus (15)

• Berry Phase Effects on Electronic Properties
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Renormalization Group Approach to Interacting Fermions
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Berry phase correction to electron density of states in solids
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Chiral Kinetic Theory
• Kinetic theory with Berry curvature from quantum field theories
• Lorentz Invariance in Chiral Kinetic Theory
• Berry phase correction to electron density in solids and "exotic" dynamics
• Non-analytic corrections to the Fermi-liquid behavior
• Singular perturbation theory for interacting fermions in two dimensions
• Gradient expansion approach to multiple-band Fermi liquids

Cited by in corpus (18)

• Quantum Nanophotonics in Two-Dimensional Materials
• Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• Photonic Berry curvature in double liquid crystal microcavities with broken inversion symmetry
• The universal shear conductivity of Fermi liquids and spinon Fermi surface states and its detection via spin qubit noise magnetometry
• A topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking
• 2D-Dirac surface states and bulk gap probed via quantum capacitance in a 3D topological insulator
• Chiral pair of Fermi arcs, anomaly cancelation, and spin or valley Hall effects in inversion symmetry-broken Weyl metals
• Spin-valley collective modes of the electron liquid in graphene
• Effective field theory of Berry Fermi liquid from the coadjoint orbit method
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Fermi-liquid corrections to the intrinsic anomalous Hall conductivity of topological metals
• Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids
• Static Magnetic Response of Non-Fermi Liquid Density
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Collective dynamics of Fermi-surface fluctuations in an interacting Weyl metal phase
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons