Weak-field Hall effect and static polarizability of Bloch electrons

Weak-field Hall effect and static polarizability of Bloch electrons

Temporal Oscillation of Conductances in Quantum Hall Effect of Bloch Electrons

Two years after the discovery of the quantum Hall effect,1,2 Thouless, Kohmoto, Nightingale and den Nijs (TKNN)3,4 theoretically studied the quantum Hall effect in two-dimensional electrons with a periodic potential. They expressed the Hall conductance as an integer multiplied by e2/h. The integer is a topological invariant called the Chern number. Such a system has been experimentally realized...

Temporal Oscillation of the Conductances in Quantum Hall Effect of Bloch Electrons

Two years after the discovery of the quantum Hall effect,1,2 Thouless, Kohmoto, Nightingale, and den Nijs (TKNN)3,4 theoretically studied the quantum Hall effect in two-dimensional electrons with a periodic potential. They expressed the Hall conductance in the form of an integer multiplied by e2/h. The integer is a topological invariant called the Chern number. Such a system has been experiment...

Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t.

Quantized Hall conductivity of Bloch electrons: Topology and the Dirac fermion.

We consider the Hall conductivity of two-dimensional non-interacting Bloch electrons when the magnetic flux per unit cell is a rational number p/q where p and q are mutually coprime. We present a counter-example for the naive expectation that the Hall conductivity carried by a band is given by treating gap minima as Dirac fermions. Instead of the above expectation, we show that the change of th...