Translational Symmetry Breaking in the Superconducting State of the Cuprates: Analysis of the Quasiparticle Density of States

TL;DR

This paper investigates how weak translational symmetry breaking affects the quasiparticle density of states in d-wave superconductors, proposing a formalism that explains recent STM experiments through periodic modulations in hopping or pairing amplitudes.

Contribution

It introduces a general formalism for analyzing the effects of weak translational symmetry breaking on quasiparticle spectra, emphasizing modulations in hopping or pairing rather than simple charge density waves.

Findings

STM data are consistent with periodic modulation in hopping or pairing amplitudes.

Charge density wave order alone cannot explain the experimental observations.

Impurity scattering and charge order pinning influence quasiparticle behavior.

Abstract

Motivated by the recent STM experiments of J.E. Hoffman et.al. and C. Howald et.al., we study the effects of weak translational symmetry breaking on the quasiparticle spectrum of a d-wave superconductor. We develop a general formalism to discuss periodic charge order, as well as quasiparticle scattering off localized defects. We argue that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained using a simple charge density wave order parameter, but are consistent with the presence of a periodic modulation in the electron hopping or pairing amplitude. We review the effects of randomness and pinning of the charge order and compare it to the impurity scattering of quasiparticles. We also discuss implications of weak translational symmetry breaking for ARPES experiments.