# Dresselhaus effect > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Dresselhaus_effect > Markdown URL: https://mediated.wiki/source/Dresselhaus_effect.md > Source: https://en.wikipedia.org/wiki/Dresselhaus_effect > Source revision: 1286909437 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Phenomenon in solid-state physics}} {{More citations needed|date=November 2017}} The '''Dresselhaus effect''' is a phenomenon in [solid-state physics](/source/solid-state_physics) in which [spin–orbit interaction](/source/spin%E2%80%93orbit_interaction) causes [energy band](/source/energy_band)s to split. It is usually present in [crystal](/source/crystal) systems lacking [inversion symmetry](/source/inversion_symmetry). The effect is named after [Gene Dresselhaus](/source/Gene_Dresselhaus), who discovered this splitting in 1955.{{Cite journal|last=Dresselhaus|first=G.|date=1955-10-15|title=Spin–Orbit Coupling Effects in Zinc Blende Structures|journal=Physical Review|volume=100|issue=2|pages=580–586|doi=10.1103/PhysRev.100.580|bibcode=1955PhRv..100..580D}} Spin–orbit interaction is a [relativistic](/source/Special_relativity) [coupling](/source/coupling) between the [electric field](/source/electric_field) produced by an [ion](/source/ion)-core and the resulting dipole moment arising from the relative motion of the [electron](/source/electron), and its intrinsic [magnetic dipole](/source/magnetic_dipole) proportional to the electron [spin](/source/Spin_(physics)). In an atom, the coupling weakly splits an orbital energy state into two states: one state with the spin aligned to the orbital field and one anti-aligned. In a solid [crystal](/source/crystal)line material, the motion of the conduction electrons in the lattice can be altered by a complementary effect due to the coupling between the [potential](/source/Potential_well) of the lattice and the electron spin. If the crystalline material is not [centro-symmetric](/source/Centrosymmetry), the asymmetry in the potential can favour one spin orientation over the opposite and split the [energy bands](/source/Valence_and_conduction_bands) into spin aligned and anti-aligned subbands. The [Rashba spin–orbit coupling](/source/Rashba_effect) has a similar energy band splitting, but the asymmetry comes either from the bulk asymmetry of [uniaxial crystal](/source/uniaxial_crystal)s (e.g. of [wurtzite](/source/Wurtzite_crystal_structure) typeE. I. Rashba and V. I. Sheka, Symmetry of Energy Bands in Crystals of Wurtzite Type II. Symmetry of Bands with Spin–Orbit Interaction Included, Fiz. Tverd. Tela: Collected Papers, v. 2, 162, 1959. English translation: http://iopscience.iop.org/1367-2630/17/5/050202/media/njp050202_suppdata.pdf) or the spatial inhomogeneity of an interface or surface. Dresselhaus and Rashba effects are often of similar strength in the band splitting of [GaAs](/source/Gallium_arsenide) [nanostructure](/source/nanostructure)s.{{cite journal|last1=Manchon|first1=A.|last2=Koo|first2=H. C.|last3=Nitta|first3=J.|last4=Frolov|first4=S. M.|last5=Duine|first5=R. A.|title=New perspectives for Rashba spin–orbit coupling|journal=Nature Materials|date=20 August 2015|volume=14|issue=9|pages=871–882|doi=10.1038/nmat4360|pmid=26288976|arxiv=1507.02408|bibcode=2015NatMa..14..871M|s2cid=24116488 }} == Zincblende Hamiltonian == Materials with [zincblende structure](/source/Cubic_crystal_system) are non-centrosymmetric (i.e., they lack inversion symmetry). This bulk inversion asymmetry (BIA) forces the [perturbative](/source/Perturbation_theory_(quantum_mechanics)) [Hamiltonian](/source/Hamiltonian_mechanics) to contain only odd powers of the [linear momentum](/source/Crystal_momentum). The bulk Dresselhaus Hamiltonian or BIA term is usually written in this form: :H_{\rm D}\propto p_x(p_y^2-p_z^2)\sigma_x + p_y(p_z^2-p_x^2)\sigma_y+p_z(p_x^2-p_y^2)\sigma_z, where \sigma_x, \sigma_y and \sigma_z are the [Pauli matrices](/source/Pauli_matrices) related to the spin \mathbf{S} of the electrons as \mathbf{S}=\tfrac{1}{2}\hbar\sigma (here \hbar is the reduced [Planck constant](/source/Planck_constant)), and p_x, p_y and p_z are the components of the momentum in the [crystallographic directions](/source/Miller_index) [100], [010] and [001], respectively.{{Cite book|title=Spin-orbit coupling effects in two-dimensional electron and hole systems|last=Roland|first=Winkler|date=2003|publisher=Springer|isbn=9783540366164|location=Berlin|oclc=56325471}} When treating 2D [nanostructure](/source/nanostructure)s where the width direction z or [001] is finite, the Dresselhaus Hamiltonian can be separated into a linear and a cubic term. The linear Dresselhaus Hamiltonian H_{\rm D}^{(1)} is usually written as :H_{\rm D}^{(1)}=\frac{\beta}{\hbar}(\sigma_xp_x-\sigma_yp_y), where \beta is a coupling constant. The cubic Dresselhaus term H_{\rm D}^{(3)} is written as :H_{\rm D}^{(3)}=-\frac{\beta}{\hbar^3}\left(\frac{d}{\pi}\right)^2 p_xp_y(p_y\sigma_x-p_x\sigma_y), where d is the width of the material. The Hamiltonian is generally derived using a combination of the ['''k·p''' perturbation theory](/source/K%C2%B7p_perturbation_theory) alongside the [Kane model](/source/Kane_model). == See also == *[Fine electronic structure](/source/Fine_electronic_structure) *[Electric dipole spin resonance](/source/Electric_dipole_spin_resonance) *[Spin–orbit interaction](/source/Spin%E2%80%93orbit_interaction) == References == Category:Semiconductors Category:Quantum magnetism Category:Spintronics Category:Physical phenomena --- Adapted from the Wikipedia article [Dresselhaus effect](https://en.wikipedia.org/wiki/Dresselhaus_effect) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Dresselhaus_effect?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.