Farajollahpour Tohid, Phirouznia Arash
Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran.
Condensed Matter Computational Research Lab., Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran.
Sci Rep. 2017 Dec 19;7(1):17878. doi: 10.1038/s41598-017-18238-5.
Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points (K and K') of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points. In other words each of these gauges alone could not induce any topological valley-polarized current in the system at zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as a result of the external strain even at zero magnetic field. In the context of Berry curvature within the linear response regime the valley polarization (both magnetic free polarization, Π, and field dependent response function, χ ) in different values of gauge fields of lattice deformation has been obtained.
人们已经对石墨烯蜂窝晶格中的真实磁规范场和晶格变形规范场进行了研究。这两种规范场的共存将导致系统的两个谷点（K点和K'点）之间出现能隙差异。这种能隙差异使我们能够研究石墨烯片中可能存在的拓扑谷霍尔电流和谷极化。在没有磁场的情况下，当费米能恰好与狄拉克点重合时，仅应变无法产生谷极化。因为在这种情况下，谷点的粒子数没有任何不平衡。换句话说，在零费米能时，这些规范场中的任何一个都无法在系统中诱导出任何拓扑谷极化电流。同时，在非零费米能下，即使在零磁场中，外部应变也会导致粒子数不平衡。在线性响应范围内的贝里曲率背景下，已经得到了晶格变形规范场不同值下的谷极化（包括无磁极化Π和场依赖响应函数χ）。
