Dresselhaus effect

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:

${\displaystyle H_{\rm {D}}\propto p_{x}(p_{y}^{2}-p_{z}^{2})\sigma _{x}+p_{y}(p_{z}^{2}-p_{x}^{2})\sigma _{y}+p_{z}(p_{x}^{2}-p_{y}^{2})\sigma _{z},}$

where ${\textstyle \sigma _{x}}$, ${\textstyle \sigma _{y}}$ and ${\textstyle \sigma _{z}}$ are the Pauli matrices related to the spin ${\textstyle \mathbf {S} }$ of the electrons as ${\textstyle \mathbf {S} ={\tfrac {1}{2}}\hbar \sigma }$ (here ${\textstyle \hbar }$ is the reduced Planck constant), and ${\textstyle p_{x}}$, ${\textstyle p_{y}}$ and ${\textstyle p_{z}}$ are the components of the momentum in the crystallographic directions [100], [010] and [001], respectively.[4]

When treating 2D nanostructures where the width direction ${\textstyle z}$ or [001] is finite, the Dresselhaus Hamiltonian can be separated into a linear and a cubic term. The linear Dresselhaus Hamiltonian ${\textstyle H_{\rm {D}}^{(1)}}$ is usually written as

${\displaystyle H_{\rm {D}}^{(1)}={\frac {\beta }{\hbar }}(\sigma _{x}p_{x}-\sigma _{y}p_{y}),}$

where ${\textstyle \beta }$ is a coupling constant.

The cubic Dresselhaus term ${\textstyle H_{\rm {D}}^{(3)}}$ is written as

${\displaystyle H_{\rm {D}}^{(3)}=-{\frac {\beta }{\hbar ^{3}}}\left({\frac {d}{\pi }}\right)^{2}p_{x}p_{y}(p_{y}\sigma _{x}-p_{x}\sigma _{y}),}$

where ${\textstyle d}$ is the width of the material.

The Hamiltonian is generally derived using a combination of the k·p perturbation theory alongside the Kane model.

• Fine electronic structure
• Electric dipole spin resonance
• Spin–orbit interaction