Band bending at the surface of Bi$_2$Se$_3$ studied from first principles

TL;DR

This study uses first-principles calculations to analyze band bending effects on Bi$_2$Se$_3$ surface states, revealing that surface doping can tune the Dirac point without bending the surface spectrum, aligning with experimental observations.

Contribution

It demonstrates that surface states in Bi$_2$Se$_3$ are not bent by doping, and provides insights into charge density oscillations and limitations of effective models.

Findings

Surface states are not bent at the surface despite doping.

Surface dopants can tune the Dirac point energy.

Charge density oscillations are suppressed beneath dopants.

Abstract

The band bending (BB) effect on the surface of the second-generation topological insulators implies a serious challenge to design transport devices. The BB is triggered by the effective electric field generated by charged impurities close to the surface and by the inhomogeneous charge distribution of the occupied surface states. Our self-consistent calculations in the Korringa-Kohn-Rostoker framework showed that in contrast to the bulk bands, the spectrum of the surface states is not bent at the surface. In turn, it is possible to tune the energy level of the Dirac point via the deposited surface dopants. In addition, the electrostatic modifications induced by the charged impurities on the surface induce long range oscillations in the charge density. For dopants located beneath the surface, however, these oscillations become highly suppressed. Our findings are in good agreement with recent experiments, however, our results indicate that the concentration of the surface doping cannot be estimated from the energy shift of the Dirac cone within the scope of the effective continuous model for the protected surface states.