论文标题
扭曲双层石墨烯中超导性的对称限制：分数涡流，$ 4E $冷凝物或非独立配对
Symmetry constraints on superconductivity in twisted bilayer graphene: Fractional vortices, $4e$ condensates or non-unitary pairing
论文作者
论文摘要
当两个石墨烯片相对于彼此的角度扭曲时，增强的相关性导致超导性的起源仍在争论中。在这里，我们在扭曲的双层石墨烯（TBG）中得出了一些对超导性的一般限制，与其潜在机制无关。忽略山谷之间的弱耦合，除了山谷电荷旋转外，TBG的全局对称组还由每个山谷中的独立自旋旋转组成，$ {\ rm su}（2）（2）\ times {\ rm su}（\ rm su}（2）（2）\ times {\ times {\ rm u} _v（1）$。在理想化的手性限制中，此对称性进一步增强到了完整的$ {\ rm su}（4）$。在这两种情况下，我们都表明，任何费用$ 2E $配对都必须打破全球对称性。此外，如果配对是统一的，则产生的超导体会允许分数涡流。这导致了以下一般性陈述：任何一个对称类别中的任何超导式冷凝物都必须满足三种可能性之一：（i）超导配对是非自动的，（ii）超导式冷凝水的收费$ 2E $，但承认至少有一半的量子涡流，这些量子均含有$ h/4e $ $ $ $ $，$ $，$（iii $ $ $ $），或者（iii $ $ $ $）。 $ m> 1 $，带有$ h/2me $ flux的涡流。后一种可能性可以通过对称费用$ 4E $超导体（$ m = 2 $）来实现。在TBG中，在风味极化状态附近观察到的超导体中，TBG中有非自然的配对（I）。另一方面，在没有风味极化的情况下，例如在电荷中立的附近，预计两种外来的可能性（II）和（iii）之一。我们概述了如何在基于天际的强效性耦合理论中以不同的限制实现这三种情况。最后，我们讨论了降低各向异性的对称性和这些情况的实验意义的效果。
When two graphene sheets are twisted relative to each other by a small angle, enhanced correlations lead to superconductivity whose origin remains under debate. Here, we derive some general constraints on superconductivity in twisted bilayer graphene (TBG), independent of its underlying mechanism. Neglecting weak coupling between valleys, the global symmetry group of TBG consists of independent spin rotations in each valley in addition to valley charge rotations, $ {\rm SU}(2) \times {\rm SU}(2) \times {\rm U}_V(1) $. This symmetry is further enhanced to a full ${\rm SU}(4)$ in the idealized chiral limit. In both cases, we show that any charge $2e$ pairing must break the global symmetry. Additionally, if the pairing is unitary the resulting superconductor admits fractional vortices. This leads to the following general statement: Any superconducting condensate in either symmetry class has to satisfy one of three possibilities: (i) the superconducting pairing is non-unitary, (ii) the superconducting condensate has charge $2e$ but admits at least half quantum vortices which carry a flux of $h/4e$, or (iii) the superconducting condensate has charge $2me$, $m>1$, with vortices carrying $h/2me$ flux. The latter possibility can be realized by a symmetric charge $4e$ superconductor ($m=2$). Non-unitary pairing (i) is expected in TBG for superconductors observed in the vicinity of flavor polarized states. On the other hand, in the absence of flavor polarization, e.g. in the vicinity of charge neutrality, one of the two exotic possibilities (ii) and (iii) is expected. We sketch how all three scenarios can be realized in different limits within a strong coupling theory of superconductivity based on skyrmions. Finally we discuss the effect of symmetry lowering anisotropies and experimental implications of these scenarios.
