Mixed state of a lattice d-wave superconductor

TL;DR

This paper investigates the low-energy quasiparticle spectrum in a lattice d-wave superconductor's mixed state, revealing oscillatory behaviors influenced by nodal interference and vortex effects, with implications for tunneling experiments in high-Tc cuprates.

Contribution

It provides a detailed analysis of the oscillatory quasiparticle spectrum and vortex effects in a lattice d-wave superconductor, extending understanding of mixed state phenomena.

Findings

Spectrum exhibits oscillatory behavior with respect to k_D and magnetic length l.

Inter-nodal interference enhances oscillations near vortices.

Periodic energy oscillations double when a vortex pierces a superconducting grain.

Abstract

We study the mixed state in an extreme type-II lattice d-wave superconductor in the regime of intermediate magnetic fields H_{c1} << H << H_{c2}. We analyze the low energy spectrum of the problem dominated by nodal Dirac-like quasiparticles with momenta near k_F=(\pm k_D,\pm k_D) and find that the spectrum exhibits characteristic oscillatory behavior with respect to the product of k_D 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 1/l dependence as its monotonous ``envelope'' part. The oscillatory behavior of the spectrum is due to the inter-nodal interference enhanced by the singular nature of the low energy eigenfunctions near vortices. We also study a separate problem of a single vortex piercing an isolated superconducting grain of size L by L. Here we find that the periodicity of the quasiparticle energy oscillations with respect to k_D L 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 1/L. Finally, we review the overall features of the tunneling conductance experiments in YBCO and BSCCO, and suggest an interpretation of the peaks at 5-20 meV observed in the tunneling local density of states in these materials.