Power-law spin correlations in a perturbed honeycomb spin model

We consider spin-$\frac{1}{2}$ model on the honeycomb lattice~\cite{Kitaev06} in presence of a weak magnetic field $h_{\alpha }\ll 1$. Such a perturbation destroys exact integrability of the model in terms of gapless fermions and \textit{static} $Z_{2}$ fluxes. We show that it results in appearance of a long-range tail in the irreducible dynamic spin correlation function: $\left\langle \left\langle s^{z}(t,r)s^{z}(0,0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,r)$, where $f(t,r)\propto \lbrack \max (t,r)]^{-4}$ is proportional to the density polarization function of fermions

Low-temperature electron mobility in doped semiconductors with high dielectric constant

We propose and study theoretically a new mechanism of electron-impurity scattering in doped seminconductors with large dielectric constant. It is based upon the idea of \textit{vector} character of deformations caused in the crystalline lattice by any point defects siting asymmetrically in the unit cell. In result, local lattice compression due to the elastic deformations decay as $1/r^2$ with distance from impurity. Electron scattering (due to standard deformation potential) on such defects leads to low-temperature mobility $\mu(n)$ scaling with electron density $n$ of the form $\mu(n) \propto n^{-2/3}$ that is close to experimental observations on a number of relevant materials.Comment: 6 pages, 4 figure