Mixed state of a lattice d-wave superconductor

Abstract

We study the mixed state in an extreme type-II lattice dx2−y2-wave superconductor in the experimentally most relevant regime of intermediate magnetic fields Hc1⪡H⪡Hc2. We analyze the low energy spectrum of the problem, dominated by nodal Dirac-like quasiparticles with momenta near kF=(±kD,±kD), and find that the spectrum exhibits characteristic oscillatory behavior with respect to the product of kD and magnetic length l. The Simon-Lee scaling, predicted in this regime, is satisfied only on average, with the magnitude of the oscillatory part of the spectrum displaying the same l−1 dependence as its monotonous “envelope” part. In general, the spectrum obeys a scaling law Enk=(ℏvF∕l)En(kl,t∕Δ,kDl), where E is a dimensionless universal 2π-periodic function of kDl. The oscillatory behavior of the spectrum is due to the internodal interference enhanced by the singular nature of the low-energy eigenfunctions near vortices. Our results constitute an example of a finite size scaling of the Dirac-type quantum criticality. We also study a separate problem of a single vortex piercing an isolated superconducting grain of size L×L. Here we find that the periodicity of the quasiparticle energy oscillations with respect to kDL is doubled relative to the case where the field is zero and the vortex is absent, both such oscillatory behaviors being present at the leading order in L−1. Finally, we review the overall features of the tunneling conductance experiments in YBa2Cu3O7−δ (YBCO) and Bi2Sr2CaCu2O8+δ (BSCCO), and suggest an interpretation of the peaks at 5–20meV observed in the tunneling local density of states in these materials. We find that in the case of a pure d-wave superconducting order parameter with featureless vortex cores, the zero bias conductance peak (ZBCP) appears only on the sites that are the immediate nearest neighbors of vortex locations, while all the other sites in the close vicinity of vortices exhibit no such ZBCP and instead display pronounced peaks at subgap energies, typically at about a half or less of the coherence peak energy. Furthermore, we find that the on-site ZBCP can be strongly suppressed by enhanced local pairing near a vortex.

Source-reported materials — not catalogue approval

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