Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

Abstract

Friedel oscillations (FO) of electron density caused by a delta-like 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 WS${}_2$ are described by the relation $\Delta n(\vec{r})\propto \sin (2\pi r/T_{FO})/r^2$, where $T_{FO}\propto 1/\sqrt{E_F}$. 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.

18 pages and 9 figures

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Cited by in corpus (4)

• Robust wavefront dislocations of Friedel oscillations in gapped graphene
• Friedel oscillations in two-dimensional materials with inverted bands and Mexican-hat dispersion
• Persistent Friedel oscillations in Graphene due to a weak magnetic field
• Exact Green's function approach to RKKY interactions