Dr. Manabu Machida (Institute of Industrial Science, University of Tokyo)
"Temporal Oscillation of Conductivities in Quantum Hall Effect of Bloch Electrons"
We obtain time-varying conductivities of 2D Bloch electrons in a
periodic potential under a perpendicular magnetic field [1].
If we apply an electric field suddenly at time t=0,
The Hall and longitudinal conductivities oscillate in time with
very large frequencies by quantum fluctuation.
We obtain expressions of the conductivities and
numerically demonstrate the conductivities as a function of time.
Two years after the discovery of the quantum Hall effect
by von Klitzing and Kawaji in 1980,
Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) theoretically
studied the quantum Hall effect in two-dimensional electrons with
a periodic potential.
Using the Kubo formula, they expressed the Hall conductivity
as an integer multiplied by e2/h.
The integer is a topological invariant called the Chern number.
Recently, such a system has been experimentally realized as
a superlattice structure in a semiconductor heterojunction.
We consider the conductivities of the same system as TKNN.
Although we also assume linear response as in TKNN,
unlike the Kubo formula, we take into account
the conductivities of finite Fourier components.
As a result, we obtain the conductivity for arbitrary time-dependent
electric fields. In particular, we show that both Hall and
longitudinal conductivities vary in time for the electric field
suddenly switched on at t=0. We estimate that the oscillation period
is of the order of 100ps to 1ns for a 2D surface in a semiconductor.
[1] M. Machida, N. Hatano, and J. Goryo, J. Phys. Soc. Jpn. 75 (2006)
063704.