Shubnikov-De Haas effect
Encyclopedia
An oscillation in the conductivity of a material that occurs at low temperatures in the presence of very intense magnetic fields, the Shubnikov–de Haas effect (ShdH) is a macroscopic manifestation of the inherent quantum mechanical nature of matter. It is often used to determine the effective mass
of charge carriers (electron
s and electron hole
s), allowing investigators to distinguish among majority and minority carrier populations.
, semimetal, or narrow band gap
semiconductor
will behave like simple harmonic oscillators. When the magnetic field strength is changed, the oscillation period of the simple harmonic oscillators changes proportionally. The resulting energy spectrum is made up of Landau levels
separated by the cyclotron
energy. These Landau levels are further split by the Zeeman energy
. In each Landau level the cyclotron and Zeeman energies and the number of electron states (eB/h) all increase linearly with increasing magnetic field. Thus, as the magnetic field increases, the spin-split Landau levels move to higher energy. As each energy level passes through the Fermi energy
, it depopulates as the electrons become free to flow as current. This causes the material's transport and thermodynamic properties to oscillate periodically, producing a measurable oscillation in the material's conductivity. Since the transition across the Fermi 'edge' spans a small range of energies, the waveform is square rather than sinusoidal, with the shape becoming ever more square as the temperature is lowered.
when plotted as a function of inverse magnetic field. The "frequency
" of the magnetoresistance
oscillations indicate areas of the extremal Fermi surface
. The area of the Fermi surface is expressed in teslas.
The effect is named after Wander Johannes de Haas
and Lev Shubnikov
.
Effective mass
In solid state physics, a particle's effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. It can be shown that electrons and holes in a crystal respond to electric and magnetic fields almost as if they were particles with a mass dependence in their...
of charge carriers (electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s and electron hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
s), allowing investigators to distinguish among majority and minority carrier populations.
Physical process
At sufficiently low temperatures and high magnetic fields, the free electrons in the conduction band of a metalMetal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
, semimetal, or narrow band gap
Band gap
In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the...
semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
will behave like simple harmonic oscillators. When the magnetic field strength is changed, the oscillation period of the simple harmonic oscillators changes proportionally. The resulting energy spectrum is made up of Landau levels
Landau quantization
Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields. As a result, the charged particles can only occupy orbits with discrete energy values, called Landau levels. The Landau levels are degenerate, with the number of electrons...
separated by the cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...
energy. These Landau levels are further split by the Zeeman energy
Zeeman effect
The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...
. In each Landau level the cyclotron and Zeeman energies and the number of electron states (eB/h) all increase linearly with increasing magnetic field. Thus, as the magnetic field increases, the spin-split Landau levels move to higher energy. As each energy level passes through the Fermi energy
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
, it depopulates as the electrons become free to flow as current. This causes the material's transport and thermodynamic properties to oscillate periodically, producing a measurable oscillation in the material's conductivity. Since the transition across the Fermi 'edge' spans a small range of energies, the waveform is square rather than sinusoidal, with the shape becoming ever more square as the temperature is lowered.
Related physical process
The effect is related to the de Haas–van Alphen effect, which is the name given to the corresponding oscillations in magnetization. The signature of each effect is a periodic waveformWaveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
when plotted as a function of inverse magnetic field. The "frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
" of the magnetoresistance
Magnetoresistance
Magnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. The effect was first discovered by William Thomson in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. This...
oscillations indicate areas of the extremal Fermi surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
. The area of the Fermi surface is expressed in teslas.
The effect is named after Wander Johannes de Haas
Wander Johannes de Haas
Wander Johannes de Haas was a Dutch physicist and mathematician. He is best known for the Shubnikov–de Haas effect, the de Haas–van Alphen effect and the Einstein–de Haas effect.-Personal life:...
and Lev Shubnikov
Lev Shubnikov
Lev Vasilyevich Shubnikov was a Soviet experimental physicist who worked in the Netherlands and USSR....
.
External links
- The article uses text from Shubnikov effect on Lang.gov that is a Public Domain as a work of a US government agency.
- Material behavior in strong magnetic fields