Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

@article{Shindou2005NoncommutativeGA,
  title={Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons},
  author={Ryuichi Shindou and Ken-Ichiro Imura},
  journal={Nuclear Physics},
  year={2005},
  volume={720},
  pages={399-435}
}
Abstract Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion… Expand

Tables from this paper

Multiband effects in equations of motion of observables beyond the semiclassical approach
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separatedExpand
Non-Abelian properties of electron wave packets in the Dirac semimetals A3Bi (A=Na, K,Rb)
The motion of electron wave packets in the Dirac semimetals A$_3$Bi (A=Na,K,Rb) is studied in a semiclassical approximation. Because of the two-fold degeneracy of the Dirac points and aExpand
Berry connection induced anomalous drift velocity in non-Hermitian systems
Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems,Expand
Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields
Berry curvature and orbital moment of the Bloch state are two basic ingredients, in addition to the band energy, that must be included in the formulation of semiclassical dynamics of electrons inExpand
Coherent wave-packet evolution in coupled bands
We develop a formalism for treating coherent wave-packet dynamics of charge and spin carriers in degenerate and nearly degenerate bands. We consider the two-band case carefully in view of spintronicsExpand
Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections
Abstract.It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible forExpand
Topological currents in ferromagnets and related systems – from the viewpoint of wave‐packet dynamics
We reconsider the problem of the adiabatic motion of a wave packet of Bloch electrons, under a perturbation that is incommensurate with the lattice structure and varies slowly in time. Its effectiveExpand
Phase-space curvature in spin-orbit-coupled ultracold atomic systems
We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles withExpand
Spin dynamics with non-Abelian Berry gauge fields as a semiclassical constrained Hamiltonian system
The dynamics of observables which are matrices depending on and taking values in classical phase-space is defined by retaining the terms up to the first order in of the Moyal bracket. Within thisExpand
Coriolis force, geometric phase, and spin-electric coupling in semiconductors
We consider the response of the effective spin of a charge carrier in semiconducting systems to an adiabatic rotation of its crystal momentum induced by an electric field. We demonstrate that theExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 117 REFERENCES
Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first-orderExpand
monopole and Berry phase in momentum space in noncommutative quantum mechanics
To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter $\ensuremath{\theta}$ to a field operator,Expand
String theory and noncommutative geometry
We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimallyExpand
Spontaneous Hall effect in a chiral p-wave superconductor
In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiralExpand
Berry phase, hyperorbits, and the Hofstadter spectrum.
  • Chang, Niu
  • Physics, Medicine
  • Physical review letters
  • 1995
TLDR
A semiclassical theory for the dynamics of electrons in a magnetic Bloch band, where the Berry phase plays an important role is developed, and an Onsager-like formula for the quantization of cyclotron orbits is derived. Expand
The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect
This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. We first illustrate some simpleExpand
SU (2) non-Abelian holonomy and dissipationless spin current in semiconductors
Following our previous work [S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003)] on the dissipationless quantum spin current, we present an exact quantum-mechanical calculation ofExpand
Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands.
  • Chang, Niu
  • Physics, Medicine
  • Physical review. B, Condensed matter
  • 1996
TLDR
Based on a set of semiclassical equations for electrons in magnetic Bloch bands, the pattern of band splitting, the distribution of Hall conductivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture. Expand
Quantal phase factors accompanying adiabatic changes
  • M. Berry
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1984
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiarExpand
Effective-field-theory model for the fractional quantum Hall effect.
TLDR
A field-theory model for the fractional quantum Hall effect and an approximate coarse-grained version of the same model are derived, and a Landau-Ginzburg theory similar to that of Girvin is constructed. Expand
...
1
2
3
4
5
...