Quantum kinetic equation in phase-space textured multiband systems

In a three-dimensional Fermi liquid, quasiparticles near the the Fermi surface may possess Berry curvature. We show that if the Berry curvature has a nonvanishing flux through the Fermi surface, the particle number associated with this Fermi surface has a triangle anomaly in external electromagnetic fields. We show how Landau's Fermi liquid theory should be modified to take into account the Berry curvature. We show that the "chiral magnetic effect" also emerges from the Berry curvature flux.

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“…This is done by using a kinetic equation for quasiparticles; a more microscopic derivation of this equation [16,17] is desirable.…”

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confidence: 99%

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

2012

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“…A semi-classical kinetic equation has also been derived in an electron system with Berry curvature [5]. Chiral anomaly is an important quantum effect which is absent at the classical level.…”

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confidence: 99%

Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation

et al. 2013

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We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a 4-dimensional Euclidean Berry monopole which gives axial anomaly. By integrating out the zero-th component of the 4-momentum p, we reproduce the previous 3-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF. This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions. Introduction. -The Berry phase is a topological phase factor acquired by an eigen-energy state when it undergoes adiabatic evolution along a loop in parameter space [1]. It is in close analogy to the Aharonov-Bohm phase when a charged particle moves in a loop enclosing a magnetic flux, while the Berry curvature is like the magnetic field. The integral of the Berry curvature over a closed surface can be quantized as integers known as Chern-Simons numbers, which is similar to the Dirac magnetic monopole and has deep connection with the quantum Hall effect. The Berry phase is a beautiful, simple and universal structure in quantum physics and has many interesting applications, for a recent review of the Berry phase in condensed matter physics, see e.g. Ref.[2].

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“…The defining equations ofû, Eq. (2.6), become the following equations for the Wigner transform,ũ: 12) where matrix multiplication is implied and the star denotes the usual start product. We need to solve these equations order by order in .…”

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confidence: 99%

Derivation of one-particle semiclassical kinetic theory in the presence of non-Abelian Berry curvature

Bettelheim¹

2017

J. Phys. A: Math. Theor.

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In quantum mechanics it is often required to describe in a semiclassical approximation the motion of particles moving within a given energy band. Such a representation leads to the appearance of an analogues of fictitious forces in the semiclassical equations of motion associated with the Berry curvature. The purpose of this paper is to derive systematically the kinetic Boltzmann equations displaying these effects in the case that the band is degenerate, and as such the Berry curvature is non-Abelian. We use the formalism of phase-space quantum mechanics to derive the results.

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Quantum kinetic equation in phase-space textured multiband systems

Cited by 26 publications

References 43 publications

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation

Derivation of one-particle semiclassical kinetic theory in the presence of non-Abelian Berry curvature

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