Atomic collapse in gapped graphene: lattice and valley effects

TL;DR

This paper investigates atomic collapse phenomena in gapped graphene, revealing how Coulomb impurity states evolve into resonances, with valley-dependent effects and orbital splitting, enriching understanding of impurity-induced states in two-dimensional materials.

Contribution

It provides a detailed analysis of atomic collapse in gapped graphene, highlighting valley effects, LDOS characteristics, and orbital splitting, which are novel insights into impurity states in this material.

Findings

Atomic collapse resonances appear as charge exceeds critical Z_c.

LDOS peaks are valley-dependent, showing pseudospin polarization.

Splitting of p orbital states into two distinct lobes in the plane.

Abstract

We study the atomic collapse phenomenon in $K$ and $K'$ valley of gapped graphene. Bound states induced by Coulomb impurity in the gap turn into atomic collapse resonances as the charge increases beyond the supercritical charge $Z_c$. $Z_c$ increases sublinear with the band gap $\Delta$. The atomic collapse resonances result in peaks in the LDOS at the same energies in $K$ and $K'$ valley, but the strong (weak) LDOS peaks in $K$ valley are weak (strong) LDOS peaks in $K'$ valley reminiscent of pseudospin polarization phenomenon. From a spatial LDOS analysis of the atomic collapse resonance states, we assign specific atomic orbitals to the atomic collapse resonances. Remarkably, the two $p$ atomic orbital atomic collapse states are no longer degenerate and splits into two having lobes in different directions in the graphene plane.