Deb Oindrila, Soori Abhiram, Sen Diptiman
Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India.
J Phys Condens Matter. 2014 Aug 6;26(31):315009. doi: 10.1088/0953-8984/26/31/315009. Epub 2014 Jul 14.
We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi(2) Se(3) to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.
我们使用诸如Bi(2)Se(3)这种三维拓扑绝缘体的体哈密顿量，来研究出现在其各种表面以及两个表面之间边缘处的态。我们既使用基于表面哈密顿量（由体哈密顿量导出）的解析方法，也使用基于体哈密顿量晶格离散化的数值方法。我们发现沿着边缘施加一个势垒会产生局域在该边缘的态。这些态具有不寻常的能量 - 动量色散，可通过沿着边缘施加一个势来控制；特别地，这些态的速度可以调至零。研究了穿过边缘的散射和电导作为边缘势的函数。我们表明在特定方向的磁场也会在某些边缘产生零能态。我们指出了寻找各种边缘态的可能实验方法。
