Superconducting Copper Pairs in AA Bilayer Graphene

Gholami, Rouhollah

doi:10.22055/jrmbs.2025.20196

Superconducting Copper Pairs in AA Bilayer Graphene

Document Type : Full length research Paper

Author

Rouhollah Gholami

Department of physics, Ilam university, Ilam, Iran

10.22055/jrmbs.2025.20196

Abstract

We use a multi-band extended Hubbard model to describe superconductivity in AA-bilayer graphene. In addition to the usual chirality of single-layer graphene that arises from the helicity of its massless quasiparticles, this system is described by an additional index called the "cone-index". This issue has been given very little attention in the literature, despite a few articles noting its prominent role in phenomena such as Klein tunneling and Andreev reflection. In this manuscript, it is shown that the cone-index is a consequence of mirror symmetry and is itself a new and distinct type of chirality from the helicity of massless quasiparticles, which we term “mirror-chirality”. Due to this mirror symmetry, the Hamiltonian of bilayer graphene is block-diagonalized by applying a unitary transformation. This process is mathematically analogous to the reduction of the Dirac equation in the 4-component Dirac representation to the chiral Weyl representation, which acts on left-handed and right-handed 2-component Weyl spinors. The method is extended to include the superconducting state. It is shown that four electrons in the upper and lower layers are coupled to form two kinds of superconducting Cooper pairs with an extra left/right-handed chiral character. Furthermore, inter-band Cooper pairing between quasiparticles with different mirror-chirality indices is forbidden. This naturally leads to a hidden double-gap superconductivity with new aspects.

Keywords

Superconductivity

AA bilayer graphene

Cooper pair

Prohibition rule

Weyl representation

chirality

Subjects

Condensed matter

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