Interaction-Driven Metal-Insulator Transition in Strained Graphene

Abstract

The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between π-electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that without strain, graphene remains metallic and changing the substrate from SiO2 to suspended samples hardly makes any difference. In contrast, applying a rather large -but experimentally realistic -uniform and isotropic strain of about 15% seems to be a promising route to making graphene an antiferromagnetic Mott insulator.PACS numbers: 71.27.+a,71.10.Fd,73.22.Pr,72.80.Vp Over the past decade graphene has established itself as a remarkable new material with superlative properties [1,2]. However, the early hopes to utilize it as a next generation transistor have been dashed mostly because graphene remains metallic -these prototypical Dirac fermions are immune to many of the conventional routes for driving two-dimensional electron gases into an insulating state, including, for example, Anderson localization and percolation transitions (see e.g. Ref.[3]). Other mechanisms for opening band-gaps including hydrogenation [4], application of uniaxial strain [5] and forming nanoribbons [6] severely degrade graphene's mobility. Very recently, moiré heterostuctures using graphene and hexagonal boron nitride have shown evidence of an insulating phase [7,8], although interpreting these results remains somewhat controversial [9][10][11][12].In this Letter, we explore a different avenue to make graphene insulating, namely, utilizing the electronelectron interactions. Despite much study on the effects of interactions in graphene [13] it is surprising how much still remains to be understood. While it is clear that without any electron-electron interactions, graphene should be a semi-metal (SM), and that for very strong interactions it should be an insulating anti-ferromagnet (AFM), it remains unclear what one should expect for the real graphene material. For example, there are distinct claims in the literature that suspended graphene should be insulating, strongly metallic and weakly metallic [14][15][16]. This discussion could have practical relevance as it could be the basis for a low power Mott-transistor [17].In this work we explore different ways of controlling the effective strength of electron-electron interactions in realistic graphene devices, and propose how one can move around its phase diagram. In particular (and in contrast to what is widely assumed to be true [2, 13]), we demonstrate that it is the non-universal, material-specific and short-range part of the electron-electron interactions that plays the dominant role in determining graphene's ground state. More interestingly, we conclude that application of isotropic strain is considerably more efficient in approaching the SM-AFM phase transition than substrate manipulation, providing a new route for...

Four-loop critical exponents for the Gross-Neveu-Yukawa models

“…One of the best candidates for an interaction-induced semimetal-insulator transition of the electronic quasiparticles in graphene (N ¼ 2) is the transition towards an antiferromagnetic spin-density wave (AF-SDW) state [12,14,15,[59][60][61][62] which has been suggested to be accessible by application of biaxial strain [63,64]. In the low-energy effective field-theoretical description this corresponds to a SU(2) symmetry breaking transition with a Heisenberg order parameter field ⃗ ϕ having three real components.…”

Excitonic mass gap in uniaxially strained graphene

“…More specifically our goal is to simplify the self-consistent mass gap equation as much as possible but use large scale numerical simulations to elucidate, under certain physical approximation, whether uniaxial strain enhances or suppresses the interaction-induced excitonic mass gap in freely suspended graphene 60,61 . The rest of the paper is organized as follows.…”

Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations

“…The way of transforming a quartic interaction term into a quadratic one via the Hubbard-Stratonovich transformation (HST) [22] is not unique and affects the efficiency of simulations [23][24][25][26][27][28]. Recently the popularity of this technique is substantially increased, because it has been realized that, with continuous auxiliary fields, one can treat interaction terms beyond the on-site Hubbard interaction, up to the complete treatment of the long-range Coulomb interaction [29][30][31][32][33], or of the long-range electron-phonon interaction [34], and even both of them on the same footing [35], without being vexed by the sign problem in a certain parameter region on bipartitle lattices. Interestingly, such a parameter region coincides with the one where rigorous statements on the ground state of an extended Hubbard-Holstein model are available [36,37].…”