Resonating valence bond pairing energy in graphene by quantum Monte Carlo

TL;DR

This study uses quantum Monte Carlo methods to analyze the resonating-valence-bond state in graphene, revealing a geometry-dependent electron pairing mechanism influenced by system size and energy gap conditions.

Contribution

It introduces a detailed quantum Monte Carlo analysis of RVB pairing energy in graphene, highlighting the role of geometry and finite energy gaps in stabilizing electron pairing.

Findings

Finite energy gaps stabilize electron pairing in graphene.

RVB pairing energy is approximately 0.48 mHa/atom at the thermodynamic limit.

System size and geometry critically influence the energy gap and pairing stability.

Abstract

We determine the resonating-valence-bond (RVB) state in graphene using real-space quantum Monte Carlo with correlated variational wave functions. Variational and diffusion quantum Monte Carlo (DMC) calculations with Jastrow-Slater-determinant and Jastrow-antisymmetrized-geminal-power ansatze are employed to evaluate the RVB pairing energy. Using a rectangular graphene sample that lacks $\pi/3$ rotational symmetry, we found that the single-particle energy gap near the Fermi level depends on the system size along the $x$-direction. The gap vanishes when the length satisfies $L_x=3n\sqrt{3}d$, where $n$ is an integer and $d$ is the carbon-carbon bond length, otherwise, the system, exhibits a finite gap. Our DMC results show no stable RVB pairing in the zero-gap case, whereas the opening of a finite gap near the Fermi level stabilizes the electron pairing. The DMC predicted absolute value of pairing energy at the thermodynamic limit for a finite-gap system is $\sim 0.48(1)$ mHa/atom. Our results reveal a feometry-driven electron pairing mechanism in the confined graphene nanostructure.