Friedel oscillations (FO) of electron density caused by a deltalike neutral impurity in two-dimensional (2D) systems in a magnetic field are calculated. Three 2D cases are considered: free electron gas, monolayer graphene, and group-VI dichalcogenides. An exact form of the renormalized Green's function is used in the calculations, as obtained by a summation of the infinite Dyson series and regularization procedure. Final results are valid for large ranges of potential strengths $V_0$, electron densities $n_e$, magnetic fields $B$, and distances from the impurity $r$. Realistic models for the impurities are used. The first FO of induced density in ${\mathrm{WS}}_2$ are described by the relation $\mathrm{\Delta }n\left(\mathit{r}\right)\propto sin(2\pi r/T_{\mathrm{FO}})/r^2$, where $T_{\mathrm{FO}}\propto 1/\sqrt{E_F}$. For weak impurity potentials, the amplitudes of FO are proportional to $V_0$. For attractive potentials and high fields, the total electron density remains positive for all $r$. On the other hand, for low fields, repulsive potentials and small $r$, the total electron density may become negative, so that many-body effects should be taken into account.

• Received 25 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.205410