ELFT HÍRADÓ

[Mihaly Gyorgy <mihaly AT szfki.hu>]

(Szeminarium tajekoztato ismetlese szelesebb korben is olvashato formaban)

           Berry-fazis elmelet Bloch elektronokra
      anomalis Hall effektus, polarizacios aramok

Eloado Dr. Ken-Ichiro Imura (RIKEN, Wako, Japan)
Idopont 2005. május 5. 10 ora
Helyszin BME, Fizika Tanszek
XI. ker., Budafoki ut 8., F epulet III. lepcsohaz 2. em. 13-as terem


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 reconsidered the
problem of adiabatic motion of a wave packet of Bloch functions,
under a perturbation varying slowly and incommensurately to the
lattice structure [1]. We showed using only the fundamental
principles of quantum mechanics that the effective wave-packet
dynamics of Bloch electrons is conveniently described by a set
of equations of motion (EOM) in which a nonabelian Berry phase
associated with the internal degree of freedom appears.

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Our EOM can be viewed as a generalization of the standard
Ehrenfest's theorem, and their derivation was asymptotically exact
in the framework of linear response theory. Our analysis is entirely
based on the concept of local Bloch bands, a good starting point
for describing the adiabatic motion of a wave packet. One of the
advantages of our approach is that the various types of gauge fields
were classified into two categories by their different physical origin
(1) projection onto specific bands, (2) time-dependent local Bloch basis.
Using those gauge fields, we write our EOM in a covariant form,
whereas the gauge-invariant field strength stems from the noncommutativity
of covariant derivatives along different axes of the reciprocal parameter
space. On the other hand, the degeneracy of Bloch bands makes the
gauge field nonabelian.

For the purpose of applying our wave-packet dynamics to the analyses
on transport phenomena in the context of Berry phase engineering,
we focused on the Hall-type and polarization currents. Our formulation
 turned out to be useful for investigating and classifying various types
of topological current on the same footing. We highlighted their
symmetries, in particular, their behavior under time reversal
($T$) and space inversion ($I$). The result of these analyses was
summarized as a set of cancellation rules. We also introduced the
concept of parity polarization current, which may embody the physics
of orbital current. Together with charge/spin Hall/polarization currents,
this type of orbital current is expected to be a potential probe for
detecting and controlling Berry phase.


[1] Ryuichi Shindou, Ken-Ichiro Imura, cond-mat/0411105.




G. Mihaly
Department of Physics
Budapest University of Technology and Economics
http://dept.phy.bme.hu/