Faraei Zahra, Jafari Seyed Akbar
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran.
Sharif University of Technology, Department of Physics, Tehran, 11155-9161, Iran.
Sci Rep. 2023 Oct 20;13(1):17976. doi: 10.1038/s41598-023-44910-0.
We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions in systems with broken time reversal symmetry and inversion symmetry is of the [Formula: see text] where [Formula: see text] is the usual order parameter and [Formula: see text] is the pseudo-scalar order parameter. After factoring out the U(1) phase [Formula: see text], this form of superconductivity admits yet additional complex structure in the plane of [Formula: see text]. The polar angle [Formula: see text] in this plane, which we call the chiral angle, can be controlled by the external flux bias. We present a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes [Formula: see text] leads to [Formula: see text], where [Formula: see text] is the superconducting order parameter of the SC layers, and the chiral angle [Formula: see text] is directly given by the flux [Formula: see text] in units of the flux quantum [Formula: see text]. This can be used as a building block to construct a two-dimensional Josephson array. In this setup [Formula: see text] will be a background field defining a pseudoscalar [Formula: see text] that can be tuned to desired configuration. While in a uniform background field [Formula: see text] the dynamics of [Formula: see text] is given by standard XY model and its associated vortices, a staggered background [Formula: see text] (or equivalently [Formula: see text] and [Formula: see text] in alternating lattice sites) creates a new set of minima for the [Formula: see text] field that will support half-vortex excitations. An isolated single engineered "half-vortex" in the [Formula: see text] field in an otherwise uniform background will bind a [Formula: see text]-half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.
我们表明，在具有破缺时间反演对称性和空间反演对称性的系统中，手性费米子的自旋单重态超导序参量的最一般形式为[公式：见正文]，其中[公式：见正文]是通常的序参量，[公式：见正文]是赝标量序参量。在消除U(1)相位[公式：见正文]后，这种超导形式在[公式：见正文]平面中允许额外的复结构。我们将这个平面中的极角[公式：见正文]称为手性角，它可以通过外部磁通偏置来控制。我们提出了一种基于拓扑绝缘体（TI）和超导体（SC）堆叠的合成装置。或者，用磁通[公式：见正文]对超导体进行磁通偏置会导致[公式：见正文]，其中[公式：见正文]是SC层的超导序参量，手性角[公式：见正文]直接由磁通[公式：见正文]以磁通量子[公式：见正文]为单位给出。这可以用作构建二维约瑟夫森阵列的一个组件。在这个装置中，[公式：见正文]将是一个定义赝标量[公式：见正文]的背景场，该赝标量可以被调谐到所需配置。虽然在均匀背景场[公式：见正文]中，[公式：见正文]的动力学由标准XY模型及其相关涡旋给出，但交错背景[公式：见正文]（或者等效地，在交替晶格位点中的[公式：见正文]和[公式：见正文]）会为[公式：见正文]场创建一组新的极小值，这些极小值将支持半涡旋激发。在否则均匀的背景中，[公式：见正文]场中一个孤立的单个工程化“半涡旋”将束缚一个[公式：见正文]-半涡旋。这类似于p波超导涡旋核心束缚一个马约拉纳费米子的方式。
