Long before the discovery of its extraordinary properties, graphene - i.e., single sheet graphite - had long been the textbook exercise of a symmetry-induced semimetallic state of noninteracting electrons with nearest neighbor hopping t in the honeycomb lattice. Nowadays the accepted picture of correlated electrons in graphene comes from quantum Monte Carlo simulation of an idealized and simplified model on a lattice. In this model, by stretching graphene, namely by decreasing the hopping t between nearest neighbor carbons, the electronic system becomes an antiferromagnetic Mott insulator at a critical value of the ratio U/t = 3.84(1)[2, 3], where U is the Coulomb repulsion. It is therefore timely to investigate theoretically this interesting system by a more realistic simulation, also because, recently, it appears experimentally feasible to isotropically stretch graphene, overcoming its extremely large two-dimensional bulk modulus, originated in its harder-than-diamond sigma bonds.
In this paper, we study for the first time electronic and lattice structures of a single-layer graphene under isotropic stretching, by means of first-principles quantum Monte Carlo simulation. The competition between the totally symmetric state, the antiferromagnetic state, and a Peierls state with lattice distortion is explored by calculating the enthalpy as a function of tensile force at zero temperature. Preliminary results indicate that the antiferromagnetic state is less stable than the other states, while a transition between the totally symmetric state and the Peierls state is found at a certain strength of the tensile force.
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