Coexistence and competition of nematic and gapped states in bilayer graphene

TL;DR

This paper explores the complex phase diagram of bilayer graphene, revealing how strain and gate voltage influence the coexistence and competition between nematic and gapped states, including phase transitions and critical points.

Contribution

The study provides a detailed theoretical analysis of the phase diagram in bilayer graphene considering strain and gate voltage, identifying hybrid phases and critical phenomena.

Findings

Existence of hybrid spin-valley symmetry-broken phases.

Identification of first- and second-order phase transition lines.

Prediction of a critical end point in the phase diagram.

Abstract

In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term, ${\cal N}_{0}$, and a top-bottom gates voltage imbalance, $U_{0}$, is obtained by solving the gap equation in the random-phase approximation. At nonzero ${\cal N}_0$ and $U_0$, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of ${\cal N}_0$, respectively. The existence of a critical end point, where the line of first-order phase transitions terminates, is predicted. For ${\cal N}_0=0$, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As ${\cal N}_{0}$ increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For $U_{0}=0$, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero $U_{0}$ suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.