ELFT HÍRADÓ

[Mihaly Gyorgy <mihaly AT szfki.hu>]

Berry-fázis elmélet Bloch elektronokra:
anomális Hall effektus, polarizációs áramok
(szeminárium)


Elõadó: Dr. Ken-Ichiro Imura (RIKEN, Wako, Japan)

Idõpont: 2005. május 5. 10⁰⁰

Helyszín: BME, Fizika Tanszék
XI. ker., Budafoki út 8., F épület III. lépcsõház 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/