一种适用于多探针系统输运的变转移矩阵方法
A variant transfer matrix method suitable for transport through multi-probe systems
摘要：
我们已经开发了一种变体的传输矩阵方法，适用于通过多探针系统的传输。利用这种方法，我们数值研究了二维石墨烯上的量子自旋霍尔效应（QSHE），同时考虑了内禀（Vso）和Rashba（Vr）自旋轨道（SO）耦合.在存在内禀SO相互作用的情况下，整数QSHE产生，并逐渐被Rashba SO相互作用和无序涨落破坏。我们用数值方法确定了分离整数QSHE和自旋Hall液体的相边界。我们发现，当V50> 0.2t时，当t为跳跃常数时，满足|E| <t的整数阶QSHE所需的能隙最大。对于较小的V50，能隙线性减小。在存在Rashba SO相互作用或无序时，能隙减小。在Rashba SO相互作用下，整数QSHE在能隙内的最大能量处是稳健的，而在能隙内的最小能量处，整数QSHE对无序不敏感。
英文摘要：
We have developed a variant transfer matrix method that is suitable for transport through multi-probe systems. Using this method, we have numerically studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic (Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the presence of intrinsic SO interaction and is gradually destroyed by the Rashba SO interaction and disorder fluctuation. We have numerically determined the phase boundaries separating integer QSHE and spin Hall liquid. We have found that when Vso> 0.2t with t the hopping constant the energy gap needed for the integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap decreases linearly. In the presence of Rashba SO interaction or disorders, the energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at the largest energy within the energy gap while at the smallest energy within the energy gap the integer QSHE is insensitive to the disorder.
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