Sensitivity of $T_{\mathrm{c}}$ to pressure and magnetic field in the cuprate superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$: Evidence of charge-order suppression by pressure

Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping $p\simeq 0.12$. Here we show that in the archetypal cuprate ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) pressure suppresses charge order but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at $T^{*}$ is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magnetic field shift the superconducting transition temperature $T_{\mathrm{c}}$ of YBCO in the same way as a function of doping—but in opposite directions—and most effectively at $p\simeq 0.12$. This shows that the competition between superconductivity and CDW order can be tuned in two ways, either by suppressing superconductivity with field or suppressing CDW order by pressure. Based on existing high-pressure data and our own work, we observe that when CDW order is fully suppressed at high pressure, the so-called “1/8 anomaly” in the superconducting dome vanishes, revealing a smooth $T_{\mathrm{c}}$ dome which now peaks at $p\simeq 0.13$. We propose that this $T_{\mathrm{c}}$ dome is shaped by the competing effects of the pseudogap phase below its critical point $p^{★}\sim 0.19$ and spin order at low doping.

Figure 1

Temperature-doping phase diagram of YBCO, showing the superconducting phase below $T_{\mathrm{c}}$ (black dots [19]) and the onset of charge order seen by NMR, above a threshold magnetic field, below $T_{\mathrm{NMR}}$ (green squares [12]). CDW modulations are detected by x-ray diffraction below $T_{\mathrm{XRD}}$ (up triangles [10]; down triangles [11]). The Fermi surface undergoes a reconstruction seen as a downturn in the Hall coefficient below $T_{\max }$ (red dots [16]). $T^{★}$ marks the onset of the pseudogap phase (dashed line [20, 21]). Full lines are guides to the eye.

Figure 2

$a$-axis electrical resistivity ${\rho }_{\mathrm{a}}\left(T\right)$ of YBCO as a function of temperature at dopings and pressures as indicated. The top panels show the ${\rho }_{\mathrm{a}}\left(T\right)$ [or the resistance $R\left(T\right)$ for panel (g)]. The bottom panels show ${\rho }_{\mathrm{a}}\left(T\right) \left[R\right(T\left)\right]$ normalized by its value at $T=275$ K. The data in panels (g) and (h) are reproduced from Ref. [22], on ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ with $p=0.14$ ($T_{\mathrm{c}}=80$ K), which is stoichiometric with perfect oxygen order. In panels (d) and (f), the straight line is a linear fit to the data at high temperature. The pseudogap temperature $T^{★}$ (arrow) is defined as the temperature below which ${\rho }_{\mathrm{a}}\left(T\right)$ deviates from its linear dependence at high temperature [20, 21]. Note that $T^{★}>300\mathrm{K}$ for $p=0.090$ [20]. The absence of linearity in ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ [panels (g) and (h)] may come from measurements on a twinned sample with randomly oriented domains. The important aspect is that there is no change in the functional form of $R\left(T\right)$ in ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ up to 10 GPa. $T_{\mathrm{XRD}}$ marks the onset of CDW modulations seen in x-ray diffraction at the corresponding doping (see Fig. 1). The normalized resistivity is affected by pressure only below $T_{\mathrm{XRD}}$.

Figure 3

Hall coefficient $R_{\mathrm{H}}$ of YBCO at dopings and pressures as indicated. In panels (a), (c) we show $R_{\mathrm{H}}$ as a function of field at temperatures as indicated. In panels (b), (d) we show $R_{\mathrm{H}}$ as a function of temperature from our data at $H=34$ T. In all panels the full lines are data at ambient pressure and dashed lines are data at 1.8 GPa. Note that the slight upturn at $10\mathrm{K}$ and $p=0.120$ (d) is an artefact caused by superconductivity, as $R_{\mathrm{H}}$ has not fully transitioned (saturated) to the normal state value at $34\mathrm{T}$ [red dashed line in (c)].

Figure 4

(a) Superconducting $T_{\mathrm{c}}$ of our YBCO samples with dopings as indicated as a function of pressure (applied at room temperature). $T_{\mathrm{c}}$ is obtained from the resistivity data in Fig. 2. (b) Sensitivity of $T_{\mathrm{c}}$ to pressure $P$ in YBCO, defined as $d{T}_{\mathrm{c}}/dP$, the initial slope in the $T_{\mathrm{c}}$ vs $P$ dependence, as a function of doping $p$. The data points come from the literature (blue circles and dots; see Table 2 and references therein) and from our own measurements [red circles and dots; data from panel (a)]. Two quantities are plotted: (1) the measured values of $d{T}_{\mathrm{c}}/dP$ [labeled ${(d{T}_{\mathrm{c}}/dP)}_{\mathrm{meas}}$; open circles]; (2) the corrected values [labeled ${(d{T}_{\mathrm{c}}/dP)}_{\mathrm{corr}}$; full dots]. The corrected data are obtained via ${(d{T}_{\mathrm{c}}/dP)}_{\mathrm{corr}}={\left(\partial T_{\mathrm{c}}/\partial P\right)}_p={(d{T}_{\mathrm{c}}/dP)}_{\mathrm{meas}}-0.01p(d{T}_{\mathrm{c}}/dp)$ (see Table 2 and Sec. 3d). The red line is the magnitude of the correction, with ${\left(\partial T_{\mathrm{c}}/\partial p\right)}_P$ being the derivative of the $T_{\mathrm{c}}$ vs $p$ curve (black line; right axis). The horizontal dashed line marks ${(d{T}_{\mathrm{c}}/dP)}_{\mathrm{corr}}=0$.

Figure 5

Electrical resistance of YBCO with oxygen contents $y$ as indicated, in $H=15$ T, plotted versus $T-T_{\mathrm{c}}$, where $T_{\mathrm{c}}$=$T_{\mathrm{c}}$(0) is the zero-field superconducting transition temperature. The shift in $T_{\mathrm{c}}$ caused by the field, $\mathrm{\Delta }{T}_{\mathrm{c}}=T_{\mathrm{c}}$(0)$-T_{\mathrm{c}}$(15 T), is marked by a short vertical line and is a measure of the sensitivity to field, defined as $-d{T}_{\mathrm{c}}/dH$=$\mathrm{\Delta }{T}_{\mathrm{c}}$/15 T. All values of $T_{\mathrm{c}}$(0), $T_{\mathrm{c}}$(15 T), and $\mathrm{\Delta }{T}_{\mathrm{c}}$/15 T are listed in Table 1.

Figure 6

Nernst effect of YBCO for six of the samples whose resistance data are shown in Fig. 5, in $H=15$ T, plotted versus $T-T_{\mathrm{c}}$. $T_{\mathrm{c}}$(15 T) is defined as the point where $N=0$, indicated by the linear extrapolations (dashed lines). The corresponding values are listed in Table 1. Details on Nernst effect measurements can be found in Ref. [21].

Figure 7

Sensitivity of $T_{\mathrm{c}}$ to pressure and magnetic field in YBCO as a function of doping. The sensitivity to pressure is defined as the positive change $d{T}_{\mathrm{c}}$ induced by a small pressure $dP$ (at constant $p$), plotted as $(\partial T_{\mathrm{c}}/{\partial P)}_p$ vs $p$ (blue dots, right axis; see Table 2 in the Appendix). Open circles with error bars are from our own data [see Fig. 4]; full circles are from published data (Fig. 4 and Table 2 in the Appendix). To get $(\partial T_{\mathrm{c}}/{\partial P)}_p$, a small doping-dependent correction is applied to the measured $d{T}_{\mathrm{c}}/dP$, that accounts for the increase in doping, and hence in $T_{\mathrm{c}}$, due to pressure (see Sec. 3d). The dashed line marks $(\partial T_{\mathrm{c}}/{\partial P)}_p=0$. The sensitivity to field is defined as the negative shift $d{T}_{\mathrm{c}}$ in $T_{\mathrm{c}}$ in 15 T: $-d{T}_{\mathrm{c}}/dH$=$[T_{\mathrm{c}}(H=0)-T_{\mathrm{c}}(H=15$ T)]/15 T (red squares, left axis; Table 1 in the Appendix).

Figure 8

Superconducting $T_{\mathrm{c}}$ versus pressure in YBCO for dopings as indicated, reproduced from Ref. [29]. Note that to avoid relaxation effects due to oxygen ordering, the pressure was applied at low temperature. Full lines are a guide to the eye. We extract the values of $T_{\mathrm{c}}$ at $P=2$ and 7.5 GPa by taking cuts, and at $P=15$ GPa (vertical dashed line) by extrapolating the data (dotted lines). The values of $T_{\mathrm{c}}$ thus obtained are plotted in Fig. 9, with the doping adjusted to account for pressure effects. The zero-pressure values of $T_{\mathrm{c}}$ are (from bottom to top): $T_{\mathrm{c}}\left(0\right)=14.2$ (yellow), 17.5 (green), 34.1 (blue), 63.7 (red), and 92.3 K (black) [29].

Figure 9

Superconducting phase diagram of YBCO, showing $T_{\mathrm{c}}$ at $P=0$ (dashed blue line; same as Fig. 1 [19]), $P=2$ GPa [green open circles, from our data in Fig. 4; green dots, from Ref. [29] (see Fig. 8)] and $P=7.5$ GPa [purple dots, from Ref. [29] (see Fig. 8)]. $T_{\mathrm{c}}$ measured at, or extrapolated to, $P=15$ GPa is shown as red dots [from Ref. [29] (see Fig. 8)]. The doping values have been adjusted to include the effect of pressure (see Sec. 3d). The green, purple, and red lines are guides to the eye.