Zener - bloch oscillations

ZENER - BLOCH OSCILLATIONS

Definition

It denotes the oscillation of a particle (e.g. an electron) confined in a periodic potential when a constant force is acting on it.

This was first pointed out by Bloch and Zener while studying the electrical properties of crystals. In particular, they predicted that the motion of electrons in a perfect crystal under the action of a constant electrical field is oscillatory instead of uniform.

While in natural crystals this phenomenon is extremely hard to observe due to the scattering of electrons by lattice defects.

Zener-Bloch oscillation is observed in semiconductor superlattices (multiple quantum well structure) and in different physical systems such as cold atoms in an optical potential and ultrasmall Josephson junctions.

Derivation

Zener Bloch oscillation of the particle is derived by considering the one-dimensional equation of motion for an electron in constant electric field E

Substituting (2) in (1)

On infegration of the equation (3) we get,

The velocity v of the electron is given by

where ɛ (k) denotes the energy band.

Suppose that the energy band has the (tight-binding) form 

ɛ (k) = A cosak

where a - lattice parameter

A - constant.

Then, v (k) is given by

The electron position x is given by

This shows that the electron oscillates in real space. The angular frequency of the oscillation is given by

Discovery and Experimental Realizations

Bloch oscillations were predicted by Nobel laureate Leo Easaki in 1970. However, they were not experimentally observed for a long time, because in natural solid-state bodies, not large enough to allow for full oscillations of the charge carriers within the diffraction and tunneling times, due to relatively small lattice periods.

The development in semiconductor technology has recently led to the fabrication of structures with super lattice periods that are now sufficiently large, based on artificial semiconductors.

The oscillation period in those structures is smaller than the diffraction time of the electrons, hence more oscillations can be observed in a time window below the diffraction time.

For the first time, the experimental observation of Bloch oscillations in such super lattices at very low temperatures was shown by Jochen Feldmann and Karl Leo in 1992.