According to the standard theory of superconductivity, the origin of superconductivity is electron pairing. The induced current by a magnetic field is calculated by the linear response to the vector potential, and the supercurrent is identified as the dissipationless flow of the paired electrons, while single electrons flow with dissipation. This supercurrent description suffers from the following serious problems: (1) it contradicts the reversible superconducting-normal phase transition in a magnetic field observed in type I superconductors; (2) the gauge invariance of the supercurrent induced by a magnetic field requires the breakdown of the global [Formula: see text] gauge invariance, or the nonconservation of the particle number; and (3) the explanation of the ac Josephson effect is based on the boundary condition that is different from the real experimental one.We will show that above problems are resolved if the supercurrent is attributed to the collective mode arising from the Berry connection for many-body wavefunctions. Problem (1) is resolved by attributing the appearance and disappearance of the supercurrent to the abrupt appearance and disappearance of topologically protected loop currents produced by the Berry connection; problem (2) is resolved by assigning the non-conserved number to that for the particle number participating in the collective mode produced by the Berry connection; and problem (3) is resolved by identifying the relevant phase in the Josephson effect is that arising from the Berry connection, and using the modified Bogoliubov transformation that conserves the particle number.We argue that the required Berry connection arises from spin-twisting itinerant motion of electrons. For this motion to happen, the Rashba spin–orbit interaction has to be added to the Hamiltonian for superconducting systems. The collective mode from the Berry connections is stabilized by the pairing interaction that changes the number of particles participating in it; thus, the superconducting transition temperatures for some superconductors is given by the pairing energy gap formation temperature as explained in the BCS theory. The topologically protected loop currents in this case are generated as cyclotron motion of electrons that is quantized by the Berry connection even without an external magnetic field.We also explain a way to obtain the Berry connection from spin-twisting itinerant motion of electrons for a two-dimensional model where the on-site Coulomb repulsion is large and doped holes form small polarons. In this model, the electron pairing is not required for the stabilization of the collective mode, and the supercurrent is given as topologically protected spin-vortex-induced loop currents (SVILCs).

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超导体中的超电流理论

根据超导的标准理论，超导的起源是电子对。磁场的感应电流是通过对矢量势的线性响应来计算的，超电流被识别为成对电子的无耗散流动，而单电子则有耗散流动。这种超电流描述存在以下严重问题：（1）它与在 I 型超导体中观察到的磁场中的可逆超导-正常相变相矛盾；(2) 磁场感应的超电流的规范不变性要求打破全局[公式：见正文]规范不变性，或粒子数不守恒；(3) 交流约瑟夫森效应的解释是基于与实际实验不同的边界条件。我们将证明，如果超电流归因于由贝里连接引起的集体模式，上述问题得到解决。 -体波函数。问题 (1) 通过将超电流的出现和消失归因于 Berry 连接产生的拓扑保护回路电流的突然出现和消失来解决；问题 (2) 通过将非守恒数分配给参与由 Berry 连接产生的集体模式的粒子数来解决；问题 (3) 通过确定约瑟夫森效应中的相关相位是由贝里连接产生的相位来解决，并使用保留粒子数的改进的 Bogoliubov 变换。我们认为所需的 Berry 连接来自电子的自旋扭曲巡回运动。为了使这种运动发生，必须将 Rashba 自旋轨道相互作用添加到超导系统的哈密顿量中。来自 Berry 连接的集体模式通过改变参与其中的粒子数量的配对相互作用来稳定；因此，一些超导体的超导转变温度由 BCS 理论中解释的配对能隙形成温度给出。在这种情况下，拓扑保护的回路电流是作为电子的回旋加速运动产生的，即使没有外部磁场，也可以通过 Berry 连接进行量化。我们还解释了一种从电子的自旋扭曲巡回运动获得贝里连接的方法，用于二维模型，其中现场库仑斥力很大，掺杂空穴形成小极化子。在该模型中，集体模式的稳定不需要电子配对，并且超电流以拓扑保护的自旋涡旋感应回路电流 (SVILC) 的形式给出。