Quantum Transport in Transition
Metal Oxides
Anomalous transport properties in transition
metal oxides have been a focus of attention incondensed matter physics since the discovery ofhigh-Tc superconducting materials in cuprates. In
these compounds, low-lying excited states aremostly governed by spin degrees of freedom andthere are indications to show that the groundstate must be a non-Fermi liquid due to strong
correlation. Another aspect of the transition-metaloxides, in particular in manganese and rutheniumoxides, is that they are equipped with orbital
degrees of freedom; thus, the total internal
degrees of freedom consist of both spin andorbital degrees.
In this situation, electronic motion is far fromtrivial due to complexity of the band dispersion
curves even in a simple picture of the band
electron; there are numerous crossings and also
sensitively affected with spatial arrangements of
the internal degrees of freedom, which is very
likely to be coupled with lattice distortions throughvibronic effects. Even in the cuprate case, thespin band is not simple; on the contrary, one with
non-trivial flux is speculated for a certain range ofparameters [1].

the band theory, we have recently reinvestigatedthe velocity formula for Bloch electrons. Usually
the formula is given byk as is derivedn (k ) /in textbooks. In magnetic materials, however, it
has been known that it is not valid; instead, afictitious magnetic field Bnk has to be included:
1 n k
k B nk ;kA nk , Ank i unk

B nkkunk ,where Ank is the gauge potential (Berry phaseconnection) associated with the Bloch electron[2],giving rise to non-trivial geometric phase effects
when the crossings of bands exist, or when either
time-reversal or inversion symmetry is broken[3].
According to our recent reinvestigation [4], theabove formula has to be further modified; anadditional term is found in the fundamental
expression for the electron velocity. By employing
a path-integral representation for the propagatorof a Bloch electron, the formula is obtained as

1n kk

Enk k Bnk ; EnkA nk .
tIn developing the conventional Fermi-liquid
theory, the second and third terms (GeometricPhase current) in this velocity formula are notusually taken into account. Thus a further work iscalled for to elucidate the consequence of theseterms, especially in the transition-metalcompounds. Note that the second term, which isproduced by the fictitious electric field Enk,
explains the adiabatic charge transport processes,
which may be relevant in explaining the recently
observed anomalous acoustoelectric effect in thefilm of La0.67Ca0.33MnO3[5].

References[1] I. Affleck and J. B. Marston, Phys. Rev. B 37,3774 (1988).
[2] J. Zak, Phys. Rev. Lett. 62, 2747 (1989).
[3] M. -C. Chang and Q. Niu, Phys. Rev. Lett. 75,1348 (1995).
[4] H. Koizumi and Y. Takada, Phys. Rev. B 65,153104 (2002).
[5] Y. Ilisavskii et al., Phys. Rev. Lett. 87, 146602(2001).
Figure 1: Conically intersecting bands for the flux
state in the 2D Hubbard model [1]. The conicalintersections are located at ( /2, /2). They are thesources of a gauge potential Ank. Its
time-dependence, which may be produced by anadiabatic deformation of the lattice, is predicted toproduce a geometric phase current in our paper [4].

In order to understand the anomalous current intransition-metal compounds from a viewpoint ofAuthors

H. Koizumi, Faculty of Science, Himeji Institute ofTechnology.
Y. Takada, ISSP.