Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa$_2$CuO$_{4+δ}$

TL;DR

The study demonstrates that uniaxial compression along the a-axis of underdoped HgBa2CuO4+δ induces a novel two-dimensional, nearly commensurate diffuse scattering feature with a wavevector near $q\approx(0.5,0,0)$ and a correlation length of about $\xi\approx4a$, saturating at $\sim0.2\%$ strain and showing little temperature dependence. Through X-ray diffraction, first-principles lattice-dynamics, and Raman spectroscopy, the authors characterize the lattice response (Poisson ratios $\nu_{ba}=0.16$, $\nu_{ca}=0.11$) and identify a significant Cu–O out-of-plane distance increase under strain, while no long-range CDW appears. The observed modulation is two-dimensional, unidirectional, and nearly commensurate, bearing resemblance to stripe-like charge correlations predicted in RVB-based spin-liquid models on a square lattice, suggesting a strain-engineered pathway to stabilize intrinsic electronic orders without competing with superconductivity. Hg1201’s simple tetragonal structure makes it an ideal platform to disentangle intrinsic electronic properties of doped CuO2 planes and to explore lattice-tuned electronic phases in high-$T_c$ superconductors.

Abstract

We investigate the strain response of underdoped HgBa$_2$CuO$_{4+δ}$ (Hg1201), by synchrotron X-ray diffraction and corresponding simulations of thermal diffuse scattering. The compression in the crystallographic $a$ direction leads to relatively small expansion in the $b$ and $c$ directions, with Poisson ratios $ν_{ba}$=0.16 and $ν_{ca}$=0.11, respectively. However, the Cu-O distance in the $c$ direction exhibits a notable 0.9% increase at 1.1% $a$-axis compression. We further find strain-induced diffuse scattering which corresponds to a new type of two-dimensional charge correlation. Interestingly, this signal is insensitive to the onset of superconductivity and instead corresponds to a short-range, nearly commensurate modulation with a wave vector close to (0.5, 0, 0) and a correlation length of approximately four unit cells. It closely resembles the charge order theoretically predicted in the phase diagram of the spin-liquid model with resonating valence bonds on a square lattice.

Figures (5)

• Figure 1: (a) Crystal structure of HgBa$_2$CuO$_{4+\delta}$. The doped oxygen atoms stay in the Hg layers. (b) The Razorbill CS200T strain cell used to apply strain to the sample.
• Figure 2: The strain-induced structural change in HgBa$_2$CuO$_{4+\delta}$ at $T_c$ = 78 K. (a) The shift of three representative Bragg reflections as a function of the a-axis compressive strain. The red, green, and blue colors represent 0.0%, 0.5%, and 1.1% strain, respectively. The dashed black lines tracks the shift of each Bragg reflection under strain. The intensity of the Bragg peaks is normalized with respect to the (0 0 -1) Bragg peak at zero strain. (b) The magnitude of expansive strain in the b ($\epsilon_{bb}$) and c ($\epsilon_{cc}$) directions as a function of the magnitude of compressive strain in the a direction ($-\epsilon_{aa}$). The strain values are determined from lattice parameters. The dashed lines are linear fits.
• Figure 3: The experimental X-ray diffraction patterns measured at $T_c$ = 78 K (shown in the right side of each panel, Exp.) compared with the calculated thermal diffuse scattering (shown in the left side of each panel, Calc.) for HgBa$_2$CuO$_{4+\delta}$. The three rows from top to bottom shows the results at zero strain, 1.1% strain, and their difference, respectively. The three panels to the left are in the (H 0 L) plane, whereas the three panels to the right are in the (HK 2) plane. The strain-induced diffuse scattering, which has strip shape in panel (e) and dot shape in panel (f), is labeled by blue arrows. The bow-tie-shaped lobes along the L direction is labeled by a green arrow and enlarged at bottom-right corner in panel (a).
• Figure 4: The line cuts along H direction across the (4 1 2) Bragg peak. (a) The strain dependence of the diffuse scattering at $T_c$ = 78 K. (b) The temperature dependence of the diffuse scattering under 1.1% strain. The dashed red curve show the fit to the 78 K spectrum. The (4 1 2) Bragg peak and the diffuse scattering associated with it are labeled by an red rectangle in the diffraction pattern shown at bottom-left corner.
• Figure 5: Strain dependence of Raman spectra measured in the aa polarization geometry at 30 K. The inset shows the shift of the A$_{1g}$-symmetry phonon at 592 cm$^{-1}$.