Английская Википедия:Dresselhaus effect
Шаблон:Short description Шаблон:More citations needed The Dresselhaus effect is a phenomenon in solid-state physics in which spin–orbit interaction causes energy bands to split. It is usually present in crystal systems lacking inversion symmetry. The effect is named after Gene Dresselhaus, who discovered this splitting in 1955.[1]
Spin–orbit interaction is a relativistic coupling between the electric field produced by an ion-core and the resulting dipole moment arising from the relative motion of the electron, and its intrinsic magnetic dipole proportional to the electron spin. 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 crystalline material, the motion of the conduction electrons in the lattice can be altered by a complementary effect due to the coupling between the potential of the lattice and the electron spin. If the crystalline material is not centro-symmetric, the asymmetry in the potential can favour one spin orientation over the opposite and split the energy bands into spin aligned and anti-aligned subbands.
The Rashba spin–orbit coupling has a similar energy band splitting, but the asymmetry comes either from the bulk asymmetry of uniaxial crystals (e.g. of wurtzite type[2]) or the spatial inhomogeneity of an interface or surface. Dresselhaus and Rashba effects are often of similar strength in the band splitting of GaAs nanostructures.[3]
Zincblende Hamiltonian
Materials with zincblende structure are non-centrosymmetric (i.e., they lack inversion symmetry). This bulk inversion asymmetry (BIA) forces the perturbative Hamiltonian to contain only odd powers of the linear momentum. The bulk Dresselhaus Hamiltonian or BIA term is usually written in this form:
- <math>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,</math>
where <math display="inline">\sigma_x</math>, <math display="inline">\sigma_y</math> and <math display="inline">\sigma_z</math> are the Pauli matrices related to the spin <math display="inline">\mathbf{S}</math> of the electrons as <math display="inline">\mathbf{S}=\tfrac{1}{2}\hbar\sigma</math> (here <math display="inline">\hbar</math> is the reduced Planck constant), and <math display="inline">p_x</math>, <math display="inline">p_y</math> and <math display="inline">p_z</math> are the components of the momentum in the crystallographic directions [100], [010] and [001], respectively.[4]
When treating 2D nanostructures where the width direction <math display="inline">z</math> or [001] is finite, the Dresselhaus Hamiltonian can be separated into a linear and a cubic term. The linear Dresselhaus Hamiltonian <math display="inline">H_{\rm D}^{(1)}</math> is usually written as
- <math>H_{\rm D}^{(1)}=\frac{\beta}{\hbar}(\sigma_xp_x-\sigma_yp_y),</math>
where <math display="inline">\beta</math> is a coupling constant.
The cubic Dresselhaus term <math display="inline">H_{\rm D}^{(3)}</math> is written as
- <math>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),</math>
where <math display="inline">d</math> is the width of the material.
The Hamiltonian is generally derived using a combination of the k·p perturbation theory alongside the Kane model.
See also
References
- ↑ Шаблон:Cite journal
- ↑ E. 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
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite book
