Induced charge generated by a Coulomb impurity in transition metal dichalcogenides

TL;DR

This paper analytically calculates the induced charge density near a Coulomb impurity in transition metal dichalcogenides, revealing subcritical behavior for single charge impurities and potential supercriticality for higher charges, akin to graphene.

Contribution

It provides an exact analytical derivation of the small-distance charge density asymptotics in transition metal dichalcogenides, highlighting critical charge thresholds.

Findings

Single charge impurities remain subcritical at all coupling strengths.

Higher charge impurities can become supercritical at certain coupling constants.

The behavior is similar to that observed in graphene.

Abstract

We calculate analytically the charge density $\rho_{\text{ind}}(\boldsymbol{r})$ at small distances induced by a Coulomb impurity in two-dimensional transition metal dichalcogenides. The calculations were performed exactly in the coupling constant. We found the first three leading terms of the charge density asymptotics at small distances. Using this result, we demonstrate that the impurity with charge number $Z=1$ remains subcritical at any value of the coupling constant, whereas impurities with higher charge number could become supercritical at certain coupling constant values. Such a behavior is similar to that in graphene.