Dipoles in Graphene Have Infinitely Many Bound States

Abstract

We show that in graphene charge distributions with non-vanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power.

References in corpus (3)

• Gauge fields in graphene
• Electric dipole induced universality for Dirac fermions in graphene
• Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices

Cited by in corpus (11)

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• Inverse scattering for Schrödinger operators on perturbed lattices
• Decoupling of Deficiency Indices and Applications to Schrödinger-Type Operators with Possibly Strongly Singular Potentials
• Continuum limit for lattice Schrödinger operators
• Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene
• Schrodinger Equation for Non-Pure Dipole Potential in 2D Systems
• Accumulation Rate of Bound States of Dipoles in Graphene
• Accumulation Rate of Bound States of Dipoles Generated by Point Charges in Strained Graphene
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors