The Energy-dependent Checkerboard Patterns in Cuprate Superconductors

TL;DR

This paper explains the energy-dependent checkerboard patterns observed in cuprate superconductors' local density of states as quasiparticle interference effects caused by weak disorder, aligning with recent STM experimental findings.

Contribution

It provides a theoretical interpretation of STM-observed checkerboard patterns as quasiparticle interference effects in a d-wave superconductor, matching experimental energy-dependent orientation changes.

Findings

Checkerboard patterns arise from quasiparticle interference due to disorder.

Pattern orientation changes from 45° to parallel with Cu-O bonds at higher energies.

Theoretical results agree with recent STM experimental observations.

Abstract

Motivated by the recent scanning tunneling microscopy (STM) experiments [J. E. Hoffman {\it et al.}, Science {\bf 297}, 1148 (2002); K. McElroy {\it et al.}, Nature (to be published)], we investigate the real space local density of states (LDOS) induced by weak disorder in a d-wave superconductor. We first present the energy dependent LDOS images around a single weak defect at several energies, and then point out that the experimentally observed checkerboard pattern in the LDOS could be understood as a result of quasiparticle interferences by randomly distributed defects. It is also shown that the checkerboard pattern oriented along $45^0$ to the Cu-O bonds at low energies would transform to that oriented parallel to the Cu-O bonds at higher energies. This result is consistent with the experiments.