Bloch oscillations

As Bloch oscillations (after Felix Bloch ) is defined as the oscillation of charge carriers in solids under the action of a static electric field . The cause is the relationship between the effective mass of a charge carrier and the dispersion relation in a periodic potential .

Mathematical description

The effective mass of charge carriers in crystalline solids is essentially dependent on the periodic properties of the lattice. The direction ( anisotropy ) and amount ( dispersion ) of the charge carrier speed relative to the crystal lattice also have an influence on the effective mass. For the simple approximation of an anisotropic solid, the effective mass is inversely proportional to the curvature (i.e. to the second derivative) of the dispersion curve : ${\ displaystyle m ^ {*}}$

{\ displaystyle m ^ {*} = \ hbar ^ {2} \ cdot \ left [{\ frac {\ mathrm {d} ^ {2} \ varepsilon (k)} {\ mathrm {d} k ^ {2} }} \ right] ^ {- 1}}

With

the reduced Planck quantum of action ${\ displaystyle \ hbar}$
the circular wavenumber . ${\ displaystyle k}$

The effective mass can assume any real values, in particular it can also be negative .

An externally applied constant electric field now leads to an acceleration of the charge carriers: ${\ displaystyle E_ {0}}$ ${\ displaystyle a}$

{\ displaystyle a = {\ frac {e} {m ^ {*}}} \ cdot E_ {0}}

with the elementary charge . ${\ displaystyle e}$

If the impulse is so great that the effective mass becomes negative, then a further force does not lead to further acceleration, but to deceleration, followed by acceleration in the opposite direction. Since the dispersion relation is symmetrical with respect to positive and negative impulses, a reversal point is reached again in the case of a negative impulse, so there is an oscillation.

The oscillation frequency

{\ displaystyle \ omega _ {B} = {\ frac {e} {\ hbar}} \ cdot E_ {0} \ cdot d}

is proportional to the strength of the external field applied and to the grating period of the solid. This oscillation of electrical charge causes electromagnetic radiation , which in principle can be measured. ${\ displaystyle d}$

Discovery, observation, application

In natural solids, due to the relatively small lattice periods, even with very strong electric fields, it is not high enough for the charge carriers to perform complete oscillations within scattering and tunneling times. The experimental proof of Bloch oscillations could therefore not be provided for a long time since their theoretical prediction by Leo Esaki in 1970. Only the advances in semiconductor technology of recent years and decades made it possible to manufacture structures with sufficiently large superlattice periods using artificial semiconductors (semiconductor superlattices ). In such structures, the period of the oscillations is smaller than the scattering times of the electrons, so that several oscillations can be observed in a time-resolved experiment within the scattering time. The observation of Bloch oscillations in superlattices was possible for the first time at temperatures close to absolute zero ( Jochen Feldmann , 1992; Karl Leo , 1992). An important milestone was the observation of coherent terahertz radiation from Bloch oscillations ( Hartmut Roskos , 1993). Bloch oscillations could also be proven experimentally at room temperature ( Thomas Dekorsy , 1995). ${\ displaystyle \ omega _ {B}}$

Another system in which Bloch oscillations can be observed relatively easily are optical lattices for neutral atoms.

Bloch oscillations find potential application in electronic components for the generation of terahertz radiation . However, it has not yet been possible to implement such a component.

Individual evidence

↑ T. Dekorsy: Bloch oscillations at room temperature . In: Physical Review B . tape 51 , no. 23 , 1995, pp. 17275-17278 , doi : 10.1103 / PhysRevB.51.17275 .
↑ as an example of Bloch oscillations in a Bose-Einstein condensate, s. a .: Marco Fattori, C. D'Errico, G. Roati, M. Zaccanti, MJ Lasinio, M. Modugno, G. Modugno, and M. Inguscio: Atom Interferometry with a Weakly Interacting Bose Einstein Condensate . In: Laser Science XXIV, OSA Technical Digest (CD) . 2008.

literature

Jochen Feldmann u. a .: Optical Investigation of Bloch Oscillations in a Semiconductor Superlattice . In: Physical Review B / 3. Series , Vol. 46 (1992), 7252, ISSN 1098-0121
Karl Leo u. a .: Observation of Bloch Oscillations in a Semiconductor Superlattice . In: Solid State Communications. A condensed matter science journal , Vol. 84 (1992), 7252, ISSN 0038-1098 .
Christian Waschke u. a .: Coherent Submillimeter-Wave Emission from Bloch Oscillations in a Semiconductor Superlattice . In: Physical Review Letters , Vol. 70 (1993), 3319, ISSN 0031-9007 .
Thomas Dekorsy u. a .: Bloch Oscillations at Room-Temperature . In: The Physical Review , Vol. 51 (1995), 17275.

[1] T. Dekorsy: Bloch oscillations at room temperature . In: Physical Review B . tape 51 , no. 23 , 1995, pp. 17275-17278 , doi : 10.1103 / PhysRevB.51.17275 .

[2] s an example of Bloch oscillations in a Bose-Einstein condensate, s. a .: Marco Fattori, C. D'Errico, G. Roati, M. Zaccanti, MJ Lasinio, M. Modugno, G. Modugno, and M. Inguscio: Atom Interferometry with a Weakly Interacting Bose Einstein Condensate . In: Laser Science XXIV, OSA Technical Digest (CD) . 2008.