arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1202.3863cond-mat.mes-hall
收藏

拓扑绝缘体边缘态的连续统理论:变分原理和边界条件

Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions

Amal Medhi, Vijay B. Shenoy

摘要:

我们发展了一个连续介质理论来模拟一般的四带时间反演不变的电子系统的边界的低能激发。我们提出了一个变分能量泛函的波函数,使我们能够推导出自然的边界条件,有效的这样的系统。我们的配方是特别适合于开发一个连续理论的保护边缘/表面的拓扑绝缘体的激发在二维和三维。通过与Bernevig-Hughes-Zhang(BHZ)哈密顿量模拟的拓扑绝缘体带的紧束缚计算的详细比较,我们表明自然边界条件下的连续介质理论提供了一个合适的低能物理描述.作为一个自旋,我们发现,在一定的参数制度,在有限宽度的拓扑绝缘体带由于边缘状态从相对的边缘杂交产生的间隙,依赖于非单调的带宽,并可以几乎消失在某些“魔术宽度”。

英文摘要:

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural boundary conditions valid for such systems. Our formulation is particularly suited to develop a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modeled by the Bernevig-Hughes-Zhang (BHZ) hamiltonian, we show that the continuum theory with the natural boundary condition provides an appropriate description of the low energy physics. As a spin-off, we find that in a certain parameter regime, the gap that arises in topological insulator ribbons of finite width due to the hybridization of edges states from opposite edges, depends non-monotonically on the ribbon width and can nearly vanish at certain "magic widths".

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑