Electrical Magnetochiral current in Tellurium

We have studied theoretically the effect of Electrical Magneto-Chiral Anisotropy (eMChA) in $p$-type tellurium crystals. It is shown that the terms $k_i B_j$ in the hole Hamiltonian, linear both in the wave vector ${\mathbf k}$ and the magnetic field ${\mathbf B}$, do not lead to the eMChA and one needs to include the higher-order terms like $k_i^3 B_j$. Two microscopic mechanisms of the effect are considered. In the first one only elastic scattering of holes by impurities or imperfections are taken into consideration only. In the second mechanism, besides the elastic scattering processes the hole gas heating and its energy relaxation are taken into account. It is demonstrated that he both contributions to the magneto-induced rectification are comparable in magnitude. The calculation is performed by using two independent approaches, namely, in the time relaxation approximation and in the limit of of small chiral band parameter $\beta$. A bridge is thrown between the eMChA and magneto-induced photogalvanic effects.