The role of electron-electron interactions in two-dimensional Dirac fermion systems remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator and a semimetallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. We predict that experimental realizations of Dirac fermions span this crossover and that this determines whether the Fermi velocity is increased or decreased by interactions. We explain several long-standing mysteries, including why the observed Fermi velocity in graphene is consistently about 20% larger than values obtained from ab initio calculations and why graphene on different substrates shows different behaviors.

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...

We use the Hirsch-Fye quantum Monte Carlo method to study the single magnetic impurity problem in a two-dimensional electron gas with Rashba spin-orbit coupling. We calculate the spin susceptibility for various values of spin-orbit coupling, Hubbard interaction, and chemical potential. The Kondo temperatures for different parameters are estimated by fitting the universal curves of spin susceptibility. We find that the Kondo temperature is almost a linear function of Rashba spin-orbit energy when the chemical potential is close to the edge of the conduction band. When the chemical potential is far away from the band edge, the Kondo temperature is independent of the spin-orbit coupling. These results demonstrate that, for single impurity problems in this system, the most important reason to change the Kondo temperature is the divergence of density of states near the band edge, and the divergence is induced by the Rashba spin-orbit coupling.

We investigate Rashba spin-orbit coupled Fermi gases in square optical lattice by using the determinant quantum Monte Carlo (DQMC) simulations which is free of the sign-problem. We show that the Berezinskii-Kosterlitz-Thoules phase transition temperature is firstly enhanced and then suppressed by spin-orbit coupling in the strong attraction region. In the intermediate attraction region, spin-orbit coupling always suppresses the transition temperature. We also show that the spin susceptibility becomes anisotropic and retains finite values at zero temperature. Introduction: Spin-orbit coupling (SOC), breaking the inversion symmetry, has attracted extensive attentions in condensed matter [1,2]. Recently, SOC in both the bosonic [3,4] and fermionic [5,6] systems has been realized in ultracold atomic experiments. These milestone breakthroughs have opened up an exciting route to study the novel phases [7][8][9][10][11][12][13][14][15] induced by SOC in these systems.By introducing SOC, two dimensional (2D) fermionic systems exhibit much more rich phenomena [16][17][18][19][20]. SOC can stabilize the topological nontrivial superfluid states [21][22][23][24]. Majorana zero mode exists in the vortices of these topological nontrivial phases and plays a crucial role in topological quantum computation [25]. It was found that SOC has nontrivial effect on pairing and superfluidity [22,26] in homogeneous systems. SOC enhances the pairing but suppresses the superfluidity. On lattice, SOC exhibits opposite filling-dependent behaviors for the superfluidity [27]. These interesting physics induced by SOC are all investigated by the Bogoliubovde Gennes (BdG) approach. Moreover, the study of the spin-orbit coupled Fermi gases in lattice at finite temperature is still waiting to be explored.Two effects are resulted by applying SOC in the Fermi Hubbard model. First, SOC enhances the effective hopping amplitude and enlarges the bandwidth. The other is that SOC flips the spin of the fermion which breaks the rotational symmetry of the spin and significantly changes the properties of the Fermi surface. When the system only contains the SOC, the ground state is semimetal near half-filling[27] with vanishingly small density of state(DOS)(ρ(E) ∼ |E|). In the strong attractive limit, the fermions are strongly bounded and the superfluid transition temperature is determined by the center-ofmass motion which is proportional to the inverse of the attraction. Therefore, our major concern here is to investigate what effects can be induced by the SOC on the pairing at finite temperature beyond the BdG approach.In this Letter we investigate the pairing of the attractive Fermi gases in 2D square optical lattice with SOC using both DQMC simulations [28][29][30][31][32] and mean field theory. To our knowledge, this is the first unbi-

Recent experimental (1) and numerical (2) evidence suggest an intriguing universal relationship between the Fermi surface anisotropy of the non-interacting parent two-dimensional electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed (3) nonperturbative and numerically-exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the ν = 1/2 composite Fermi liquid, this result is surprising since a Dirac fermion ground state (4) was only recently proposed as an alternative to the usual HLR state (5). The importance of the long-range interaction, expected for Dirac systems (6), is also consistent with recent transport measurements (7). Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators (8), organic conductors (9), and magic-angle twisted bilayer graphene (10). Dirac fermions | Fermi surface anisotropy | Composite fermions