# Bound States and Supercriticality in Graphene-Based Topological Insulators

@article{Kloepfer2013BoundSA, title={Bound States and Supercriticality in Graphene-Based Topological Insulators}, author={Deborah Kelly Kloepfer and Alessandro De Martino and Reinhold Egger}, journal={arXiv: Mesoscale and Nanoscale Physics}, year={2013}, volume={3}, pages={14-27} }

We study the bound state spectrum and the conditions for entering a supercritical regime in graphene with strong intrinsic and Rashba spin-orbit interactions within the topological insulator phase. Explicit results are provided for a disk-shaped potential well and for the Coulomb center problem.

## 6 Citations

### The critical transition of Coulomb impurities in gapped graphene

- PhysicsJournal of High Energy Physics
- 2020

The effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can…

### Electric-dipole-induced universality for Dirac fermions in graphene.

- PhysicsPhysical review letters
- 2014

Electric dipole effects for massive Dirac fermions in graphene and related materials show a characteristic angular asymmetry, observable in tunnel spectroscopy, however, charge transport properties inferred from scattering states are highly isotropic.

### Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

- Physics
- 2014

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear…

### Weakly Bound States of Elementary Excitations in Graphene Superlattice in Quantizing Magnetic Field

- Physics
- 2015

The spectrum of allowed energy of electron in graphene superlattice in the quantizing magnetic field is investigated. Such spectrum consists of number of so-called magnetic minibands. The width of…

## References

SHOWING 1-10 OF 34 REFERENCES

### Stabilizing topological phases in graphene via random adsorption.

- PhysicsPhysical review letters
- 2012

It is shown that the randomization of adatom distribution greatly weakens the intervalley scattering, but plays a negligible role in spin-orbit couplings, which turns graphene from a trivial insulator into a topological state.

### Atomic collapse and quasi-Rydberg states in graphene.

- PhysicsPhysical review letters
- 2007

Charge impurities in graphene can host an infinite family of Rydberg-like resonance states of massless Dirac particles, described by Bohr-Sommerfeld quantization of collapsing classical trajectories that descend on point charge in analogy to the hydrogenic Ryd Berg states relation with planetary orbits.

### Quantum spin Hall effect in graphene.

- PhysicsPhysical review letters
- 2005

Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.

### Screening of a hypercritical charge in graphene

- Physics
- 2007

Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened…

### Intrinsic and Rashba spin-orbit interactions in graphene sheets

- Physics
- 2006

Starting from a microscopic tight-binding model and using second-order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the…

### Mapping Dirac quasiparticles near a single Coulomb impurity on graphene

- Physics
- 2012

In metals, the Coulomb potential of charged impurities is strongly screened, but in graphene, the potential charge of a few-atom cluster of cobalt can extend up to 10 nm. By measuring differences in…

### Magnetic field driven instability of a charged center in graphene

- Physics
- 2011

It is shown that a magnetic field dramatically affects the problem of supercritical charge in graphene making any charge in gapless theory supercritical. The cases of radially symmetric potential…

### Vacuum polarization and screening of supercritical impurities in graphene.

- PhysicsPhysical review letters
- 2007

Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem, showing the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances.

### Coulomb impurity problem in graphene.

- PhysicsPhysical review letters
- 2007

It is shown that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem and shows extra features that cannot be described by theDirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.

### Tunable thermopower in a graphene-based topological insulator

- Physics
- 2012

Gapped materials can possess unique topological properties and robust propagating states at their boundaries. The associated transport properties allow fascinating new electronic and spintronic…