【摘要】 根据平庸与非平庸拓扑区域以能带的能隙关闭为界的拓扑理论,研究了具有自旋轨道耦合的二维晶格模型拓扑结构.文章首先将KITAEV的Majorana拓扑数M(H)推广到二维情况,在动量空间计算了二维晶格的Majorana拓扑数和相图.由M(H)=-1确定的非平庸拓扑区与用TKNN宇称确定的非平庸拓扑区完全一致,证明Majorana拓扑数与TKNN宇称是一致的.但Majorana拓扑数比TKNN宇称的计算简单.文章还计算了有限宽无穷长带的能带和波函数.如果参数取在非平庸参数区(kx=π)则长带的能带显示Majorana零能模,而且波函数分布在长带的边界上;如果参数取在平庸参数区,则能带不受拓扑保护,系统不出现零能态,或者出现偶数个零能态.更多还原

【Abstract】 The topological structure of a two dimensional topological superconductor with a spin-orbital coupling is studied. Trivial and non-trivial topological regions are separated by the curves where the band gap closes. The Majorana topological number M( H) proposed by Kitaev for one dimensional quantum wires is expanded to the two dimensional case. The Majorana topological number of the above superconductor is calculated and three topological phase diagrams are determined. These diagrams are fully in accordance with those given by TKNN parity. The method of the former is much simpler. A two dimensional and infinite slice with a width of 24 lattice sites is calculated to show the Majorana zero modes. Using a set of parameters inside the non-trivial topological regions of the phase diagrams a zero energy appears at kx= π and has a wave function near the edges of the slice( Majorana zero mode). For parameters outside the non-trivial topological regions,however,the band has either no zero mode or two zero modes,which are not topologically stable.更多还原