= Rashba effect
{c}
{title2=$H_R=\lambda(k_x\sigma_y-k_y\sigma_x)$}
{wiki}
The <Rashba effect>, named for <Emmanuel Rashba>, is a <momentum>-dependent <spin-orbit interaction> associated with broken spatial <inversion symmetry>. In an isotropic two-dimensional model, choose $\lambda>0$ and write the <Hamiltonian> $H=\hbar^2k^2I/(2m)+\lambda(\hat{\mathbf z}\times\mathbf k)\cdot\boldsymbol\sigma$, where $I$ is the <identity matrix> and $\boldsymbol\sigma$ is the vector of <Pauli matrices>. The <eigenvalues> of the spin term give $E_\pm(k)=\hbar^2k^2/(2m)\pm\lambda k$. Define $k_R=m\lambda/\hbar^2$ and $E_R=\hbar^2k_R^2/(2m)$. The lower branch is $E_-(k)=\hbar^2(k-k_R)^2/(2m)-E_R$ and has a ring of <minima> at $k=k_R$. A negative $\lambda$ reverses the <spin> directions; ordering the two <energies> still uses $|\lambda|$. The alternative parameter $q_R=2k_R$ must not be mistaken for the minimum radius.
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