Role of correlations in determining the Van Hove strain in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

Uniaxial pressure applied along a Ru-O-Ru bond direction induces an elliptical distortion of the largest Fermi surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report refined measurements of the strain at which this transition occurs, employing apparatus in which the stress on the sample is measured, and resonant ultrasound measurement of the low-temperature elastic moduli. The Lifshitz transition is found to occur at a longitudinal strain ${\varepsilon }_{xx}$ of $(-0.44\pm 0.06)\times {10}^{-2}$, which corresponds to a $B_{1g}$ strain ${\varepsilon }_{xx}-{\varepsilon }_{yy}$ of $(-0.66\pm 0.09)\times {10}^{-2}$. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory, we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is, furthermore, important to bring this critical strain close to the experimental number and thus well into the experimentally accessible range of strains.

Figure 1

(a) Schematic of the uniaxial stress cell incorporating both a displacement and force sensor. Both sensors are parallel-plate capacitors, placed underneath protective covers. (b) The resistivity of two different samples as a function of applied stress. For redundancy, two pairs of voltage contacts were attached to each sample; the letters a and b refer to pairs of voltage contacts on opposite sides of the same sample. (c) $T_{\text{c}}$ of the second sample, determined through magnetic susceptibility measurements and measured during the same cooldown as resistivity as a function of applied stress.

Figure 2

Band structure calculated within GGA [14] and $\text{GGA}+\text{SOC}$ for ${\varepsilon }_{xx}=-0.75$% using the full-potential WIEN2k code [15].

Figure 3

Energy of the $xy$ band at the $\mathrm{Y}$ point as a function of ${\varepsilon }_{xx}$, as obtained from various codes and approximations. Solid lines: GGA $+$ SOC; dashed lines: GGA [14]. The Van Hove strain ${\varepsilon }_{\text{VHS}}$ is the strain where $E_{xy}-E_{\text{F}}$ crosses zero.

Figure 4

Evolution of the correlated Fermi surface with $\alpha ,\beta$, and $\gamma$ sheets for the local Coulomb anisotropies $u=0.10$ eV (top) and $u=0.15$ eV (bottom) from zero strain to ${\varepsilon }_{xx}=-0.4\%$ and $-0.9\%$. Blue asterisks mark the experimental Fermi crossings along $\mathrm{\Gamma }\text{−}\mathrm{X}$ for the unstrained compound [29]. The strain-induced Lifshitz transition takes place close to the $\mathrm{Y}$ point in the Brillouin zone.