标题： 金属中的环形、反磁性和非中心对称序 显示英文标题

标题： Toroid, Altermagnetic and Noncentrosymmetric ordering in metals

摘要： 本文献旨在庆祝兰道理论物理研究所成立60周年，综述了环形、交替磁性和非中心对称金属的正常和超导性质。具有环形序的金属是那些在空间和时间反演操作下不具备对称性但在这两种操作的乘积下对称的化合物。在这些材料的样品中传播的电流会导致其磁化。环形金属中的超导状态是单态和三态的混合。即使在理想的无杂质晶体中，超导性也是无能隙的。交替磁铁是具有特定电子能带自旋分裂的反铁磁金属，这种分裂由时间反演与晶体点阵旋转和反射的组合决定。在对称性不包括空间反演操作的金属中也会发生类似的分裂。这两种类型的材料都表现出异常的霍尔效应。在非中心对称金属中传播的电流会导致磁化，但在交替磁铁中则不会。另一方面，在交替磁铁中有特定的压磁霍尔效应。非中心对称金属中的超导配对发生在占据同一能区内的电子之间，而在交替磁铁中则是跨能区配对，这对形成超导态不利。 显示英文摘要

摘要： The article is dedicated to the 60-th anniversary of the Landau Institute for Theoretical Physics and presents a review of normal and superconducting properties of toroidal, altermagnetic and noncentrosymmetric metals. Metals with toroidal order are compounds not possessing symmetry in respect of space and time inversion but symmetric in respect of product of these operations. An electric current propagating through samples of such a material causes its magnetisation. Superconducting states in toroidal metals are a mixture of singlet and triplet states. Superconductivity is gapless even in ideal crystals without impurities. Altermegnets are antiferromagnetic metals that have a specific spin splitting of electron bands determined by time inversion in combinations with rotations and reflections of crystal lattice. Similar splitting takes place in metals whose symmetry does not have a spatial inversion operation. Both of these types materials have an anomalous Hall effect. A current propagating through a noncentrosymmetric metal causes magnetization, but this is not the case in altermagnets. On the other hand, in altermagnets there is a specific piezomagnetic Hall effect. Superconducting pairing in non-centrosymmetric metals occurs between electrons occupying states in one zone, whereas in altermagnets we are dealing with interband pairing, which is unfavorable for the formation of a superconducting state.