Nonuniform Electron–Hole Pairing in Graphene Bilayer

Abstract

Electron–hole (e–h) pairing caused by Coulomb interaction in the system of independently gated graphene layers is considered. The influence of the mismatch of concentrations of e and h and trigonal warping of their spectrum on critical temperature is studied. We predict the appearance of the state with finite value of Cooper pair momentum–Larkin–Ovchinnikov–Fulde–Ferrell-like (LOFF) state at mismatch of the concentrations of e and above the critical value. Internal Josephson effect in LOFF-like state caused by interlayer tunneling of e and h is considered. We suggest a new phase-sensitive experiment based on the internal Josephson effect for probing spatial structure of order parameter in a LOFF-like state.

Keywords:

• Graphene
• bilayer
• nonuniform superconductivity
• Josephson effect

Acknowledgments

The work was supported by the Russian Foundation for Basic Research (10-02-92607-Ko a) and by the grant of the president of the Russian Federation (MK-5288.2011.2). One of the authors (DKE) acknowledges support from the Dynasty Foundation.