Green's functions of electrons in group-VI dichalcogenides in a magnetic field

Closed expression for the Green's function of the stationary two-dimensional Schrodinger equation for an electron in group-VI dichalcogenides in the presence of a magnetic field is obtained in terms of the Whittaker functions. The resulting Green's function operator is a~$8 \times 8$ matrix consisting of four block-diagonal~$2\times 2$ matrices, each of them characterized by different values of valley index and electron spin. The obtained results are used to calculate local density of states induced by a neutral delta-like impurity in the presence of a magnetic field within the lowest Born approximation. The spatial electron density experiences either the Friedel-like oscillations or an exponential decay as a function of the distance from the impurity.