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arXiv 0708.0394cond-mat.mes-hallcond-mat.str-elhep-ph
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面内磁场作用下石墨烯的自发对称性破缺

Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field

I. L. Aleiner, D. E. Kharzeev, A. M. Tsvelik

摘要:

施加平行于石墨烯片平面的磁场导致形成电子和空穴状费米表面。这种情况被证明是不稳定的激子凝聚体的形成,即使对于任意的弱磁场和相互作用强度。在低于平均场温度的温度下,形成序参量振幅。序参量本身是一个U(2)矩阵,允许自旋和谷空间中的组合旋转。这些旋转平滑地插入站点和键为中心的自旋密度波和自旋通量状态之间。三角形翘曲、短程相互作用和三粒子Umklapp过程在远小于平均场转变温度的温度下冻结了一些自由度,并使Berezinskiiii-Kosterlitz无涡旋(由涡旋或半涡旋驱动)或伊辛型转变成为可能。在单圈重整化群内计算了这些项的耦合常数在库仑作用下的强对数重整化。结果发现,在库仑相互作用的存在下,一些短程相互作用项变得比人们可能期望从天真的维数计数大得多。

英文摘要:

Application of the magnetic field parallel to the plane of the graphene sheet leads to the formation of electron- and hole-like Fermi surfaces. Such situation is shown to be unstable with respect to the formation of an excitonic condensate even for an arbitrary weak magnetic field and interaction strength. At temperatures lower than the mean-field temperature the order parameter amplitude is formed. The order parameter itself is a U(2) matrix allowing for the combined rotations in the spin and valley spaces. These rotations smoothly interpolate between site and bond centered spin density waves and spin flux states. The trigonal warping, short range interactions, and the three particle Umklapp processes freeze some degrees of freedom at temperatures much smaller than the mean-field transition temperature and make either Berezinskii-Kosterlitz-Thouless (driven either by vortices or half-vortices) or Ising type transitions possible. Strong logarithmic renormalization for the coupling constants of these terms by the Coulomb interaction are calculated within one-loop renormalization group. It is found that in the presence of the Coulomb interaction some short range interaction terms become much greater than one might expect from the naive dimensionality counting.

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