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Superconductivity in the twisted bilayer graphene: emergent mystery in the magic angle, the topological bosons and the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover
Philosophical Magazine ( IF 1.6 ) Pub Date : 2021-09-10 , DOI: 10.1080/14786435.2021.1970268
V. N. Davydov 1
Affiliation  

ABSTRACT

Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions.



中文翻译:

扭曲双层石墨烯中的超导性:魔角、拓扑玻色子和巴丁·库珀·施里弗 - 玻色爱因斯坦非常规交叉中的新兴奥秘

摘要

提出了扭曲双层石墨烯 (tBLG) 中的超导理论,其基础是狄拉克费米子配对产生拓扑玻色子,这是受拓扑保护的 Lifshitz 拓扑跃迁 (TPLTT) 的结果。我们已经证明在 tBLG 中以低扭转角实现了多个 TPLTT。在 TPLTT 中,Berry 相从双层石墨烯中的 2π 变为 tBLG 中的 π。当配对的吸引力相互作用主导排斥性屏蔽库仑相互作用时,有利于形成巴丁库珀施里弗-玻色爱因斯坦非常规交叉(BCS-BEUC)。该理论产生了 BCS-BEUC 的二阶相变,并计算了比热值和 Ginzburg-Landau 相干长度。解决了BCS-BEUC存在观测可能性的魔角中出现的神秘问题。当超导载流子的准波矢量从布里渊区移动到互易空间的其他单元时,该解决方案与 Umklapp 过程有关。该表给出了允许的魔角,其中包括配对狄拉克费米子的相应有效质量。

更新日期:2021-11-17
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