紧束缚模型下单层石墨烯电子输运性质的Monte-Carlo研究
Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
摘要：
我们研究了载流子之间的库仑相互作用对石墨烯单层性质的影响，假设相互作用的强度由石墨烯层放置在其上的衬底的介电常数控制。为此，我们考虑耦合到非紧规范场的六角晶格上的紧束缚模型。后者的行动也离散上的六方格子。用混合蒙特卡罗算法得到了规范场组态的平衡系综。我们的数值计算结果表明，在足够强的耦合下，也就是在足够小的衬底介电常数e<4和足够小的温度T<10^4 K时，六方晶格的简单子晶格之间的对称性自发地破坏，低频电导率逐渐下降到其弱耦合值的20-30%。另一方面，在弱耦合区（e>4），电导率实际上不依赖于e，接近普适值s=1/4。
英文摘要：
We study the effect of Coulomb interaction between charge carriers on the properties of graphene monolayer, assuming that the strength of the interaction is controlled by the dielectric permittivity of the substrate on which the graphene layer is placed. To this end we consider the tight-binding model on the hexagonal lattice coupled to the non-compact gauge field. The action of the latter is also discretized on the hexagonal lattice. Equilibrium ensembles of gauge field configurations are obtained using the Hybrid Monte-Carlo algorithm. Our numerical results indicate that at sufficiently strong coupling, that is, at sufficiently small substrate dielectric permittivities e<4, and at sufficiently small temperatures T<10^4 K the symmetry between simple sublattices of hexagonal lattice breaks down spontaneously and the low-frequency conductivity gradually decreases down to 20-30% of its weak-coupling value. On the other hand, in the weak-coupling regime (with e>4) the conductivity practically does not depend on e and is close to the universal value s=1/4.
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