Fourier-Transformed Local Density of States and Tunneling into a $D$-Wave Superconductor with Bosonic Modes

TL;DR

This paper investigates how bosonic modes like phonons and spin resonances influence the local density of states in d-wave superconductors, revealing distinctive spectral features especially for the B1g phonon mode, and compares findings with STM experiments.

Contribution

It provides a detailed analysis of bosonic mode effects on LDOS in d-wave superconductors, highlighting the unique impact of the B1g phonon mode and contrasting it with other modes and no-coupling scenarios.

Findings

B1g phonon mode produces distinct spectral features at mode plus gap energy.

Coupling effects vary significantly among different bosonic modes.

Comparison with STM experiments supports the theoretical predictions.

Abstract

We analyze the effects of the electronic coupling to bosonic modes in a d-wave superconductor. The role of the scattering due to boson on the momentum transfer between electronic states in the Brilloine zone is addressed. We consider specific examples of $B_{1g}$ phonon, breathing mode phonon and spin resonance at $(\pi,\pi)$. The Fourier spectrum of the energy derivative local density of states (LDOS) is calculated. To properly calibrate the effects of different modes we fix the quasipartilce renormalization at specific momentum points. It is found that the $B_{1g}$ mode with highly anisotropic momentum-dependent coupling matrix element gives rise to well definded features in the Fourier spectrum, at the energy of mode plus gap, with a momentum transfer along the Cu-O bond direction of cuprates. This result is in a striking contrast to the cases of the coupling to other modes and also to the case of no mode coupling. The origin of this difference is explored in detail. A comparison with the recent STM experiments is briefly discussed.