Theory of Scanning Tunneling Spectroscopy of Magnetic-Field-Induced Discrete Nodal States in a D-Wave Superconductor

TL;DR

This paper predicts discrete nodal states in a d-wave superconductor under magnetic fields, detectable via scanning tunneling microscopy, with characteristic energy peaks influenced by the superconductor's order parameter and vortex lattice structure.

Contribution

It introduces a theoretical framework for observing quantized nodal excitations in d-wave superconductors using local tunneling measurements.

Findings

Predicted peaks in tunneling conductance at ±√n energies near vortex lattice boundaries.

The n=0 peak appears only if the order parameter changes sign on the Fermi surface.

Each peak splits into four away from the boundary due to superfluid velocity effects.

Abstract

In the presence of an external magnetic field, the low lying elementary excitations of a d-wave superconductor have quantized energy and their momenta are locked near the node direction. It is argued that these discrete states can most likely be detected by a local probe, such as a scanning tunneling microscope. The low temperature local tunneling conductance on the Wigner-Seitz cell boundaries of the vortex lattice is predicted to show peaks spaced as $\pm \sqrt{n}, n ={0,1,2, ...}$. The $n=0$ peak is anomalous, and it is present only if the superconducting order parameter changes sign at certain points on the Fermi surface. Away from the cell boundary, where the superfluid velocity is nonzero, each peak splits, in general, into four peaks, corresponding to the number of nodes in the order parameter.