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arXiv 2005.11557cond-mat.mes-hall
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具有量子自旋霍尔绝缘体边缘态的量子线及其结中的散射

Scattering in quantum wires and junctions of quantum wires with edge states of quantum spin Hall insulators

Abhiram Soori

摘要:

连续量子系统中散射理论计算的一个组成部分,除了写下正确的哈密顿量之外,还包括确定适当的边界条件。在一维晶格中最简单的散射问题中,由于原位势的散射和由于不等键的散射(在其他方面不变的晶格中)给出了散射振幅的不同结果。虽然散射问题的连续和晶格模型可以映射到另一个散射由于现场电位,等效连续模型的散射由于一个不平等的债券是失踪。我们引入了一个新的参数$c$的边界条件的连续模型,相当于散射由于一个不平等的键上的晶格。在此基础上,我们利用参数$c$研究了连续介质中普通金属量子线与量子自旋霍尔绝缘体(QSHI)的一维边之间的结。在一个正常的金属量子线和QSHI的边缘之间的结的情况下,我们确定的边界条件,允许最大的传输。此外,我们解决了量子线和QSHI使用晶格模型的结之间的散射问题,并将其映射到连续介质模型的结果。四通道自旋正常金属量子线和两通道QSHI边之间的输运问题还没有很好的定义。我们纠正这种情况,制定的半无限正常金属量子线与QSHI的无限边缘的交界处的散射问题,通过塞曼场的QSHI边缘的一个半无限部分,并在交界处施加适当的边界条件。我们解析地计算了散射振幅。

英文摘要:

An integral part of scattering theory calculations in continuum quantum systems involves identifying appropriate boundary conditions in addition to writing down the correct Hamiltonian. In the simplest problem of scattering in one dimensional lattice, scattering due to an on-site potential and scattering due to an unequal bond (in otherwise translationally invariant lattice) give different results for scattering amplitudes. While the scattering problems in the continuum and the lattice models can be mapped to one another for scattering due to on-site potential, the equivalent continuum model for scattering due to an unequal bond is missing. We introduce a new parameter $c$ in the boundary condition of the continuum model that is equivalent to scattering due to an unequal bond on the lattice. Further, we study a junction between a normal metal quantum wire and a one dimensional edge of quantum spin Hall insulator (QSHI) in continuum using the parameter $c$. In the case of a junction between a normal metal quantum wire and the edge of QSHI, we identify the boundary condition that permits maximum transmission. Further, we solve the scattering problem between the junction of quantum wire and QSHI using a lattice model and map it to continuum model results. The problem of transport between four channels of spinful normal metal quantum wire and two channels of QSHI edge is not well-defined. We rectify this situation by formulating the scattering problem in terms of a junction of a semi-infinite normal metal quantum wire with an infinite edge of QSHI, gapping out one semi-infinite section of the QSHI edge by a Zeeman field and applying an appropriate boundary condition at the junction. We calculate the scattering amplitudes analytically.

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。

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