Berry Phase Correction to Electron Density in Solids and "Exotic" Dynamics

Duval, Christian; Horváth, Z.; Horváthy, P. A.; Martina, L.; Stichel, P.

doi:10.1142/s0217984906010573

Cited by 152 publications

(196 citation statements)

References 10 publications

(29 reference statements)

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“…Contrary to the work of [16], we show that the momentum also acquires a Berry-phase contribution leading to different semiclassical equations of motion. These last ones turn out to be those derived first in [8,9] (also Duval et al [14] in another context). Our rigorous approach has the merit to show without ambiguities that the equations of motion are indeed Hamiltonian in the standard sense.…”

supporting

confidence: 59%

Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach

et al. 2006

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By formally diagonalizing with accuracy the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase corrections, and therefore confirm the validity of the Liouville theorem. We show that both the position and momentum operators acquire a Berry-phase dependence, leading to a non-canonical Hamiltonian dynamics. The equations of motion turn out to be identical to the ones previously derived in the context of electron wave-packets dynamics. PACS numbers:The notion of Berry phase has found many applications in several branches of quantum physics, such as atomic and molecular physics, optic and gauge theories, and more recently, in spintronics, to cite just a few. Most studies focused on the geometric phase a wave function acquires when a quantum mechanical system has an adiabatic evolution. It is only recently that a possible influence of the Berry phase on semiclassical dynamics of several physical systems has been investigated. It was then shown that Berry phases modify semiclassical dynamics of spinning particles in electric [1] and magnetic fields [2], as well as in semiconductors [3]. In the above cited examples, a noncommutative geometry, originating from the presence of a Berry phase, which turns out to be a spin-orbit coupling, underlies the semiclassical dynamics. Also, spin-orbit contributions to the propagation of light have been the focus of several other works [1,4,5], and have led to a generalization of geometric optics called geometric spinoptics [6].Semiclassical methods in solid-state physics have also played an important role in studying the dynamics of electrons to account for the various properties of metals, semiconductors, and insulators [7]. In a series of papers [8,9] (see also [10]), the following new set of semiclassical equations with a Berry-phase correction was proposed to account for the semiclassical dynamic of electrons in magnetic Bloch bands (in the usual one-band approximation)ṙwhere E and B are the electric and magnetic fields respectively and E(k) = E 0 (k)−m(k).B is the energy of the nth band with a correction due to the orbital magnetic moment [9]. The correction term to the velocity −k × Θ with Θ(k) the Berry curvature of electronic Bloch state in the nth band is known as the anomalous velocity predicted to give rise to a spontaneous Hall conductivity in ferromagnets [11]. For crystals with broken time-reversal symmetry or spatial inversion symmetry, the Berry curvature is nonzero [9]. Eqs.1 were derived by considering a wave packet in a band and using a time-dependent variational principle in a Lagrangian formulation. The derivation of a semiclassical Hamiltonian was shown to lead to difficulties in the presence of Berry-phase terms [9]. The apparent non-Hamiltonian character of Eqs.1 led the authors of [12] to conclude that the naive phase space volume is not conserved in the presence of a Berry phase, thus violating Liouville's theorem. To remedy this...

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supporting

confidence: 59%

Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach

et al. 2006

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“…In particular, the effects of the Berry curvature work oppositely between right-handed and left-handed chiral fermions. Let us now consider the action of a single quasiparticle in the presence of the electromagnetic fields and Berry curvature [32,33],…”

Section: A Berry Curvature and Poisson Bracketsmentioning

confidence: 99%

“…As we shall demonstrate in this paper, however, if one carefully integrates out ψ − degrees of freedom, Berry curvature corrections emerge in the kinetic theory from the mixing between ψ + and ψ − (or ψ − and ψ − ). The modification to Liouville's theorem on the phase space known in the condensed matter literature [32,33] and the modification to the current found in Ref. [4] can be naturally understood from this deliberate integrating out procedure [see Eqs.…”

Section: Introductionmentioning

confidence: 99%

Kinetic theory with Berry curvature from quantum field theories

2013

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A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.

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“…is also the prefactor which modifies the invariant phase space volume dpdx → D(B, Ω k )dpdx, giving rise to a non-commutative mechanical model 77 , because the Poisson brackets of coordinates is non-zero. For brevity of notation, we will sometimes omit showing the explicit dependence of D(B, Ω(k)) on B…”

Section: Boltzmann Formalism For Nernst Response In a Lattice Weymentioning

confidence: 99%

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

Sharma¹,

Goswami²,

Tewari³

2016

Phys. Rev. B

181

191

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Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a non-trivial Berry curvature. Using semiclassical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TR-broken WSM also has an anomalous Nernst response due to a non-vanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (∇T ⊥ B) and the longitudinal (∇T B) set-up and confirm from our lattice model that in the parallel set-up, the Wiedemann-Franz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.

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Berry Phase Correction to Electron Density in Solids and "Exotic" Dynamics

Cited by 152 publications

References 10 publications

Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach

Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach

Kinetic theory with Berry curvature from quantum field theories

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

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