Vafek Oskar, Melikyan Ashot
Stanford University Institute for Theoretical Physics and Department of Physics, Stanford, California 94305, USA.
Phys Rev Lett. 2006 Apr 28;96(16):167005. doi: 10.1103/PhysRevLett.96.167005. Epub 2006 Apr 27.
We study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. For an inversion symmetric hc/2e vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero-energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of hc/e vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of Delta(0)/t in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin-Hall conductivity, which generally differs in the cases of the hc/2e and hc/e vortex lattices.
我们对处于涡旋晶格态的晶格d波超导体的低能谱进行了分析研究。对于具有反演对称性的hc/2e涡旋晶格且存在粒子-空穴对称性的情况，我们证明了一个指标定理，该定理对零能模的数量给出了一个下限。构建了一些一般情况，其中尽管具有相同的点群对称性，但这个下限超过了等效的hc/e涡旋晶格的零模数量。零模周围的准粒子谱是双重简并的，并且呈现出类似狄拉克的色散关系，在低磁场极限下，其速度成为Δ(0)/t的通用函数。对于弱粒子-空穴对称性破缺，能隙态可以由一个与自旋霍尔电导率相关的拓扑量子数来表征，这在hc/2e和hc/e涡旋晶格的情况下通常是不同的。
