Bound States in Graphene

Abstract

We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantized and is unbounded from below. The corresponding eigenstates are square-integrable at infinity and have a rapidly oscillatory behaviour in the short distance, which can be interpreted as a fall to the centre. Using a cutoff regularization, we show that the effective Coulomb interaction strength is driven to its critical value under the renormalization group flow. In the subcritical region, we find bound states with imaginary values of the energy for certain range of the system parameters. The physical significance of these bound states with imaginary eigenvalues is discussed.

6 pages, Latex file, minor typo in Eq. (21) corrected. Ref. [10] added, minor changes in the text

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• Zero-energy vortices in Dirac materials
• mKdV equation approach to zero energy states of graphene
• A Dirac type xp-Model and the Riemann Zeros
• Planar massless fermions in Coulomb and Aharonov-Bohm potentials
• Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene
• Orthogonality catastrophe and fractional exclusion statistics
• Bound and resonant impurity states in a narrow gaped armchair graphene nanoribbon
• Scattering in graphene with impurities : A low energy effective theory
• Impurity induced current in a Chern insulator
• Klein Bound States in Single-Layer Graphene
• Conformal quantum mechanics and holography in noncommutative space-time
• Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field
• SUSY design of smooth quantum rings in graphene