Density Wave Probes Cuprate Quantum Phase Transition

Abstract

In cuprates, the strong correlations in proximity to the antiferromagnetic Mott insulating state give rise to an array of unconventional phenomena beyond high temperature superconductivity. Developing a complete description of the ground state evolution is crucial to decoding the complex phase diagram. Here we use the structure of broken translational symmetry, namely d-form factor charge modulations in (Bi,Pb)2(Sr,La)2CuO 6+δ , as a probe of the ground state reorganization that occurs at the transition from truncated Fermi arcs to a large Fermi surface. We use real space imaging of nanoscale electronic inhomogeneity as a tool to access a range of dopings within each sample, and we definitively validate the spectral gap ∆ as a proxy for local hole doping. From the ∆-dependence of the charge modulation wavevector, we discover a commensurate to incommensurate transition that is coincident with the Fermi surface transition from arcs to large hole pocket, demonstrating the qualitatively distinct nature of the electronic correlations governing the two sides of this quantum phase transition. Furthermore, the doping dependence of the incommensurate wavevector on the overdoped side is at odds with a simple Fermi surface driven instability.

Evolution of Charge and Pair Density Modulations in Overdoped Bi2Sr2CuO6+δ

“…1(c) we plot the Fourier transform (FT) of the dI/dV map in Figs. 1(b), which was widely utilized to determine the modulation wavevector of charge orders in cuprates [5,7,23,36]. The Bragg peaks of the atomic lattice are marked by solid red circles in the FT map, whereas the broad peak circled in blue indicates the wavevector QCO  0.21 (2π/a0), corresponding to a wavelength CO  4.8 a0 of the long-range checkerboard charge order along the Cu-O direction.…”

“…Most previous STM studies on the charge order focused on underdoped and optimally doped cuprates with a well-defined pseudogap phase. It was found that the checkerboard pattern with 4 a0 periodicity (a0 is the lattice constant ~3.8 Å) is the first electronic order that emerges when doping holes into the parent Mott insulator [22], and it persists to hole density close to optimal doping [23]. With further doping into the overdoped regime, resonant x-ray scattering [9] and STM experiments [23] reported the persistence of checkerboard order with increasing wavelength up to 10 a0.…”

“…It was found that the checkerboard pattern with 4 a0 periodicity (a0 is the lattice constant ~3.8 Å) is the first electronic order that emerges when doping holes into the parent Mott insulator [22], and it persists to hole density close to optimal doping [23]. With further doping into the overdoped regime, resonant x-ray scattering [9] and STM experiments [23] reported the persistence of checkerboard order with increasing wavelength up to 10 a0. However, it remains unknown when and how the checkerboard order eventually vanishes in the strongly overdoped regime.…”

Locally commensurate charge-density wave with three-unit-cell periodicity in YBCO

“…• Scenario 2: q 0 locks to 1/4 in YBCO, the fundamental wave vector invoked for Bi-based cuprates [21][22][23], but in order to reach q 0.32, discommensurations are so frequent that the charge modulation is effectively best described as a period-3 CDW for π/2 DCs or a CDW with a period-6 motif for π DCs, as shown in Figs. 6c,e.…”

“…This view has been challenged by recent progress in the analysis of scanning tunnelling microscopy (STM) measurements in Bi-based cuprates revealing an extended doping range in which the local wave vector q 0 is 1/4 (in units of 2π a , with a being the crystal lattice parameter), equivalent to a local commensurate period λ = 4a [21][22][23][24][25]. Mesaros et al have taken this as evidence that there is a universal instability towards the formation of a period-four density wave, fundamentally rooted in strong-correlation physics [21].…”