Extinction of quasiparticle interference in underdoped cuprates with coexisting order

Abstract

Scanning tunneling spectroscopy (STS) measurements [Y. Kohsaka et al., Nature (London) 454, 1072 (2008)] have shown that dispersing quasiparticle interference (QPI) peaks in Fourier-transformed conductance maps disappear as the bias voltage exceeds a certain threshold corresponding to the coincidence of the contour of constant quasiparticle energy with the period-doubled (e.g., antiferromagnetic) zone boundary. Here we show that this may be caused by coexisting order present in the $d$-wave superconducting phase. We show explicitly how QPI peaks are extinguished in the situation with coexisting long-range spin-density wave order and discuss the connection with the more realistic case where short-range order is created by quenched disorder. Since it is the localized QPI peaks rather than the underlying antinodal states themselves which are destroyed at a critical bias, our proposal resolves a conflict between STS and photoemission spectroscopy regarding the nature of these states. We also study the momentum-summed density of states in the coexisting phase and show how the competing order produces a kink inside the ``V''-shaped $d$-wave superconducting gap in agreement with recent STS measurements [J. W. Alldredge et al., Nat. Phys. 4, 319 (2008)].