Effect of pressure on the pseudogap and charge density wave phases of the cuprate Nd-LSCO probed by thermopower measurements

We report thermopower measurements under hydrostatic pressure on the cuprate superconductor ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (Nd-LSCO), at low temperature in the normal state accessed by suppressing superconductivity with a magnetic field up to $H=31\mathrm{T}$. Using an ac thermopower measurement technique suitable for high pressure and high field, we track the pressure evolution of the Seebeck coefficient $S$. At ambient pressure and low temperature, $S/T$ in Nd-LSCO was recently found to suddenly increase below the pseudogap critical doping $p^{★}=0.23$, consistent with a drop in carrier density $n$ from $n=1+p$ above $p^{★}$ to $n=p$ below. Under a pressure of 2.0 GPa, we observe that the large $S/T$ value just below $p^{★}$ is suppressed. This confirms a previous pressure study based on electrical resistivity and Hall effect, which found that pressure lowers $p^{★}$, thereby reinforcing the interpretation that this effect is driven by the pressure-induced shift of the van Hove point. It implies that the pseudogap only exists when the Fermi surface is hole-like, which puts strong constraints on theories of the pseudogap phase. We also report thermopower measurements on Nd-LSCO and ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ in the charge density wave phase near $p\sim 1/8$, which reveals a weakening of this phase under pressure.

Figure 1

(a) Temperature-doping phase diagram of Nd-LSCO showing the pseudogap temperature $T^{★}$ extracted from resistivity (red dots [4, 22, 28]) and ARPES measurements (red square, from Ref. [15]), the CDW ordering temperature $T_{\mathrm{CDW}}$ as seen in x-ray diffraction measurements (green squares [30, 31, 32]), the temperature $T_{\max }$ of the maximum in $S/T$ vs $T$ (blue dots [22]), and a schematic of the zero-field superconducting transition temperature $T_{\mathrm{c}}$ (black line). Corresponding values for $T_{\max }$ [25] and $T_{\mathrm{CDW}}$[33] in Eu-LSCO are shown as open symbols. The red and green full lines are guides to the eye. The red dashed line marks the end of the pseudogap phase, at the critical doping $p^{★}=0.23\pm 0.01$ [4]. The green dashed line is a linear extension of the full green line, extrapolating to $p=p_{\mathrm{CDW}}\simeq 0.19$ at $T=0$. (b) Illustration of our experimental setup, showing the piston-cylinder pressure cell and a zoom on the top view of our thermopower mount at the tip of the electrical feedthrough. The mount shows the sample (s; red to blue gradient), differential and absolute type E thermocouples (e,d; red), phosphor-bronze wires for $V_x$ pick-up (a; grey), strain gauge sample heater (f; yellow), and copper heat sink (c; brown). The entire setup is mounted on a small 2 mm × 2 mm G10 plate at the tip of our electrical feedthrough. Thermocouples are electrically insulated from the sample.

Figure 2

Isotherms of the Seebeck coefficient expressed as $S/T$ versus magnetic field $H$ in Nd-LSCO at $p=0.22$ [(a), (c)] and $p=0.24$ [(b), (d)], at temperatures and pressures as indicated. At near ambient pressure (0.1 GPa) [(a),(b)], $S/T$ changes by a factor of about 5 when going from $p=0.22<p^{★}$ to $p=0.24>p^{★}$, indicative of the sudden drop in carrier density at the onset of the pseudogap phase [22]. Under 2.0 GPa, $S/T$ at $p=0.22$ is heavily suppressed, signaling a lowering of $p^{★}$ with pressure. Dashed lines are linear fits to the isotherms at high field, whose back-extrapolation to $H=0$ yields the values of $S/T$ at $H\to 0$ (see text).

Figure 3

Pressure effects on the transport properties of Nd-LSCO near $p^{★}$. Top panels (ambient pressure): (a) Seebeck coefficient $S/T$, (b) electrical resistivity $\rho$, and (c) Hall coefficient $R_{\mathrm{H}}$ in Nd-LSCO at $p=0.22$ (blue) and 0.24 (red), in the field-induced normal state. Data for $S/T$ are from the present study (0.1 GPa; open circles) and from Ref. [22] (ambient; dots), in the $H\to 0$ limit obtained via back-extrapolations as shown in Fig. 2. Data for $\rho$ and $R_{\mathrm{H}}$ are reproduced from Ref. [4], and are respectively in zero-field (grey) and $H=16\mathrm{T}$ at high temperature, and $H=33\mathrm{T}$ at low temperature. In panel (b), we label the value of $\rho$ at $p=0.22$ and $H=33\mathrm{T}$, extrapolated to $T\to 0$, as $\rho \left(0\right)$, and the value obtained from a linear extrapolation of the high temperature $T$-linear regime as ${\rho }_0$. Bottom panels (2.0 GPa): data on Nd-LSCO at $p=0.22$ in 2.0 GPa, showing a clear suppression of the low-temperature upturns in $S/T$ (d), $\rho$ (e), and $R_{\mathrm{H}}$ (f). In panel (d) we also show $S/T$ for Nd-LSCO $p=0.24$ in 0.1 and 2.0 GPa. Data for $S/T$ are from the present study in $H=31\mathrm{T}$. Data for $\rho$ and $R_{\mathrm{H}}$ are reproduced from Ref. [14], in fields as indicated.

Figure 4

(a) Seebeck coefficient $S/T$ versus doping $p$ for Nd-LSCO, measured at $T=5\mathrm{K}$ in the $H\to 0$ limit. Data at ambient pressure (open circles) are reproduced from [22]. Data at $P=0.1\mathrm{GPa}$ (blue dots) and 2.0 GPa (red dots) are from the present study. The vertical blue dashed line indicates $p^{★}$ at ambient pressure, which coincides with the onset of the rise of $S/T$ caused by the drop in carrier density [4, 22]. Upon application of 2.0 GPa this rise in $S/T$ is fully suppressed at $p=0.22$, and $S/T$ now follows the doping evolution extrapolated from outside the pseudogap phase (red line). (b) Ratio $\rho \left(0\right)/{\rho }_0$ [see Fig. 3] as a function of doping, at ambient pressure (open circles [4]) and 2.0 GPa (red dots [14]), which puts $p^{★}$ in 2.0 GPa $p^{★}\simeq 0.21$ [14], as shown by the vertical red dashed line. The present data for $S/T$ are consistent with such a pressure-induced suppression of $p^{★}$.

Figure 5

Seebeck coefficient $S/T$ vs $T$ in the CDW phase, in (a) Nd-LSCO at $p=0.12$ and (b) Eu-LSCO at $p=0.125$, in the field-induced normal state at $H=18\mathrm{T}$ and at pressures as indicated. In Nd-LSCO $p=0.12$, x-ray diffraction measurements [30, 31] detect the onset of CDW order at $T_{\mathrm{CDW}}=70\mathrm{K}$, which coincides with the maximum in $S/T$ at $T_{\max }\simeq 70\mathrm{K}$. The step in the data is caused by the LTO-LTT structural transition at $T_{\mathrm{LTT}}\simeq 70\mathrm{K}$. In Eu-LSCO $p=0.125$, the CDW order occurs at $T_{\mathrm{CDW}}\simeq$ 80 K [33] while the structural transition is at $T_{\mathrm{LTT}}\simeq 130\mathrm{K}$ [46].