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arXiv 1504.07993cond-mat.supr-conhep-th
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三维拓扑超导体中的Higgs机制、相变和反常霍尔效应

Higgs Mechanism, Phase Transitions, and Anomalous Hall Effect in Three-Dimensional Topological Superconductors

Flavio S. Nogueira, Asle Sudbo, Ilya Eremin

摘要:

我们表明,希格斯机制在三维拓扑超导体具有独特的功能与实验观察到的后果。我们讨论的Higgs模型有两个超导分量和一个类轴子磁电项,超导序参量的相位差起着轴子场的作用。由于这个附加项,量子电磁和相位涨落导致了一个强大的拓扑非平凡状态,在存在相互作用的情况下也成立。在这个意义上,我们表明,重整化流的拓扑非平凡的阶段不能连续变形成一个拓扑非平凡的。我们对量子临界涨落的分析的一个结果是,在体相中有一级相变而在表面上有二级相变的可能性。我们还探讨了轴子希格斯电动力学的另一个结果,即反常的霍尔效应。在低频伦敦制度的异常霍尔效应是在平行于表面的电场的存在下诱导。这种反常的霍尔电流是由轴子项产生的类洛仑兹力引起的,它涉及超导组分的相对超流速度。反常霍尔电流有一个负号,这种情况使人联想到,但在物理起源上与在高$T_c$超导体中观察到的反常霍尔效应完全不同。与后者相反,拓扑超导体中的反常霍尔效应是非耗散的,并且在没有涡旋的情况下发生。

英文摘要:

We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axion-like magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically non-trivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically non-trivial one. One consequence of our analysis of quantum critical fluctuations, is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of, but quite distinct in physical origin from the anomalous Hall effect observed in high-$T_c$ superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is non-dissipative and occurs in the absence of vortices.

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