Udupa Adithi, Banerjee Abhishek, Sengupta K, Sen Diptiman
Center for High Energy Physics, Indian Institute of Science, Bengaluru 560012, India.
Center for Quantum Devices and Microsoft Quantum Lab Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark.
J Phys Condens Matter. 2021 Feb 5;33(14). doi: 10.1088/1361-648X/abdd63.
Motivated by the spin-momentum locking of electrons at the boundaries of certain topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons with-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, and we take these to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two-wave superconductors with different phases of the pairing, with a-function potential barrier lying at the junction of the two superconductors. Remarkably, we find that the system has aAndreev bound state (ABS) which is localized at the junction. When the pairing phase difference crosses a multiple of 2, an ABS touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constantand a term which oscillates with a frequency. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency= 2/is a rational fraction of. We discuss experiments which can realize such junctions.
受某些拓扑绝缘体边界处电子的自旋动量锁定的启发，我们研究了一个具有s波超导配对的自旋轨道耦合无质量狄拉克电子的一维系统。由于自旋轨道耦合，我们的模型只有两种线性色散模式，我们将其取为向右移动的自旋向上和向左移动的自旋向下。我们研究了晶格模型和连续介质模型。在晶格模型中，我们发现，只要s波配对具有扩展形式，即最近邻配对大于在位配对，则在有限系统的每一端都会出现一个马约拉纳零能模。我们通过计算缠绕数在数值和解析上都证实了这一点。我们发现连续介质模型也有零能端模。接下来，我们研究了一个同时包含薛定谔项和类狄拉克项的模型的晶格版本，发现该模型根据薛定谔项和狄拉克项的相对强度在拓扑平凡相和非平凡相之间存在拓扑转变。然后，我们研究了一个由具有不同配对相位的两个s波超导体组成的连续介质系统，在两个超导体的交界处有一个δ函数势垒。值得注意的是，我们发现该系统有一个局域在交界处的安德列夫束缚态（ABS）。当配对相位差跨越2的倍数时，一个ABS接触到超导能隙的顶部并消失，并且从能隙底部出现一个不同的状态。我们还研究了在这样一个具有恒定电压偏置和一个随频率振荡项的结中的交流约瑟夫森效应。我们发现，与标准约瑟夫森结不同，当约瑟夫森频率ω = 2eV/ħ是ħω0的有理分数时会出现夏皮罗平台。我们讨论了可以实现这种结的实验。
