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arXiv 1409.3944cond-mat.supr-conhep-ph
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从粒子物理的标准模型到室温超导

From Standard Model of particle physics to room-temperature superconductivity

G. E. Volovik

摘要:

拓扑介质是有隙或无隙的费米子系统,其性质受到拓扑的保护,因此对系统参数的变形具有鲁棒性和通用性。我们讨论了一类无隙拓扑介质,它包含了标准模型的量子真空在其对称相,和凝聚态系统的零的能量谱,形成费米面,外尔和狄拉克点,狄拉克线,Khodel-Shaginyan平坦带等。一些零是拓扑保护,其特征在于拓扑不变量,表示在格林函数。为了稳定的其他${\bf p}$ -空间拓扑必须伴随着对称性。带有外尔点的费米子可以作为低能时出现的有效相对论量子场的来源:手征费米子、有效规范场和四维引力在外尔点附近同时出现。伴随的手征反常效应、电弱重子产生效应和手征涡旋效应都用对称性保护的${\bf p}$ -空间不变量表示。无间隙拓扑介质表现出体-面和体-涡的对应关系,特别是这种对应关系可能导致系统表面或核内的拓扑缺陷出现平带。在体相、表面或位错内部具有平带的材料具有奇异态密度,这对材料的超导转变临界温度有着重要的影响。虽然在所有已知的超导体中,转变温度作为对相互作用的函数被指数抑制,但在平坦带中,转变温度与对相互作用成比例,并且可以基本上更高。${\bf p}$ -空间拓扑可以为我们提供寻找或人工制造室温超导体的一般方法。

英文摘要:

Topological media are gapped or gapless fermionic systems, whose properties are protected by topology, and thus are robust to deformations of parameters of the system and generic. We discuss the class of gapless topological media, which contains the quantum vacuum of Standard Model in its symmetric phase, and condensed matter systems with zeroes in the energy spectrum, which form Fermi surfaces, Weyl and Dirac points, Dirac lines, Khodel-Shaginyan flat bands, etc. Some zeroes are topologically protected, being characterized by topological invariants, expressed in terms of Green's function. For stability of the others the ${\bf p}$-space topology must be accompanied by symmetry. Vacua with Weyl points serve as a source of effective relativistic quantum fields emerging at low energy: chiral fermions, effective gauge fields and tetrad gravity emerge together in the vicinity of a Weyl point. The accompanying effects, such as chiral anomaly, electroweak baryo-production and chiral vortical effect, are expressed via the symmetry protected ${\bf p}$-space invariants. The gapless topological media exhibit the bulk-surface and bulk-vortex correspondence: which in particular may lead to the flat band on the surface of the system or in the core of topological defects. The materials with flat band in bulk, on the surface or within the dislocations have singular density of states, which crucially influences the critical temperature of the superconducting transition in such media. While in all the known superconductors the transition temperature is exponentially suppressed as a function of the pairing interaction, in the flat band the transition temperature is proportional to the pairing interaction, and can be essentially higher. The ${\bf p}$-space topology may give us the general recipe for search or artificial fabrication of the room-temperature superconductors.

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