Thermal Hall conductivity of electron-doped cuprates: Electrons and phonons

TL;DR

This work addresses the origin of the thermal Hall effect in cuprates by separating phonon- and electron-driven contributions to $\kappa_{xy}$ in electron-doped Nd$_{2-x}$Ce$_x$CuO$_4$. Using high-quality and dirtier crystals at $x=0.16$ and $0.17$, the authors measure $\kappa_{xx}$ and $\kappa_{xy}$ and perform quantum-oscillation tests to reveal Fermi-surface reconstruction and antiferromagnetic correlations. They find a sizable positive electronic $\kappa_{xy}$ in cleaner samples that competes with a largely doping-independent negative phonon $\kappa_{xy}$; in dirtier samples, phonons dominate and drive a negative $\kappa_{xy}$ across all temperatures. The results rule out skew scattering by charged impurities as the mechanism for phonon chirality and point to AF correlations or spin texture as a likely origin, with potential implications for the pseudogap phase in hole-doped cuprates and a unified view of phonon-mediated thermal transport in cuprates.

Abstract

It has recently become clear that phonons generate a sizable thermal Hall effect in cuprates, whether they are undoped, electron-doped or hole-doped (inside the pseudogap phase). At higher doping, where cuprates are reasonably good metals, mobile electrons also generate a thermal Hall effect, the thermal equivalent of the standard electrical Hall effect. Here we show that in the cleanest crystals of the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$, at high doping, the phonon and electron contributions to the thermal Hall conductivity $κ_{\rm {xy}}$ are of comparable magnitude, but of opposite sign. In samples of lower quality, phonons dominate $κ_{\rm {xy}}$, resulting in a negative $κ_{\rm {xy}}$ at all temperatures. The fact that the negative phononic $κ_{\rm {xy}}$ in the metallic state is similar in magnitude and temperature dependence to that found in the insulating state at lower doping rules out any mechanism based on skew scattering of phonons off charged impurities, since a local charge should be screened in the metallic regime. The phononic $κ_{\rm {xy}}$ is found to persist over the entire doping range where antiferromagnetic correlations are known to be significant, suggesting that such correlations may play a role in generating the phonon thermal Hall effect in electron-doped cuprates. If the same mechanism is also at play in hole-doped cuprates, the presence of a phononic $κ_{\rm {xy}}$ below (and only below) the critical doping $p^{\star}$ would be evidence that spin correlations are a property of the pseudogap phase.

Figures (6)

• Figure 1: Temperature-doping phase diagram of the electron-doped cuprate NCCO. The antiferromagnetic phase (AF) is bounded by the Néel temperature $T_{\mathrm{N}}$ (solid green line) and the superconducting phase (SC) by the zero-field critical temperature $T_{\mathrm{c}}$ (blue squares) Helm2010. The magnetic breakdown gap $\Delta_{\mathrm{MB}}$ (red circles), obtained in a prior study from quantum oscillations, is a measure of how strongly the Fermi surface of NCCO is reconstructed Helm2010. The doping dependence of $\Delta_{\mathrm{MB}}$ yields a critical doping $x^{\star}$$= 0.175$ (open red circle) above which the Fermi surface is not reconstructed. The solid blue line and red dashed line are guides to the eye. In our study, we investigated two samples of NCCO with nominal concentration $x = 0.16$ (red arrow) and one with $x = 0.17$ (blue arrow).
• Figure 2: (a) Temperature dependence of the thermal Hall conductivity for NCCO $x = 0.16$, sample 1 (circles) and $x = 0.17$ (squares), plotted as $\kappa_{\mathrm{xy}} / H$ vs $T$ for fields $H = 5$ T (green), 10 T (orange), and 15 T (blue). We observe two behaviors: the negative thermal Hall conductivity of phonons (very clear in the sample with $x = 0.17$ and also visible in the sample with $x = 0.16$) and the positive thermal Hall conductivity of electrons (visible only in the sample with $x=0.16$). (b) Thermal Hall conductivity of our three NCCO samples at $H = 15$ T, plotted as $\kappa_{\mathrm{xy}}$ vs $T$. At $x=0.16$, sample 1 is cleaner than sample 2, resulting in a larger positive electronic contribution in the former.
• Figure 3: (a) Thermal conductivity of NCCO $x=0.16$ (sample 1; red dots) at $H = 15$ T, plotted as $\kappa_{\mathrm{xx}} / T$ vs $T$. The dashed line is a linear fit to extract the residual term in the form $\kappa_{\mathrm{xx}}/T$$= \beta T^2 + \kappa_0/T$, with $\beta = 0.03$ mW/K$^4$cm and ${\kappa^0_{\mathrm{xx}}}/{T} = 9.1 \pm 0.1$ mW/K$^2$cm. Inset: Thermal conductivity for NCCO $x=0.16$ (red) and $x = 0.17$ (blue) at $H = 15$ T, plotted as $\kappa_{\mathrm{xx}} / T$ vs $T$, below 1 K. In both samples, we observe a downturn in $\kappa_{\mathrm{xx}} / T$ as $T\to 0$, characteristic of electron-phonon decoupling Smith2005. The red solid line is a fit of the $x = 0.16$ data to Eq. \ref{['eq:decoup']}, which gives a decoupling temperature of $T_{\mathrm{dec}}$ = 290 mK. The blue dotted line is a linear fit to the $x = 0.17$ data that gives a residual linear term of ${\kappa^0_{\mathrm{xx}}}/{T} = 4.0 \pm 0.1$ mW/K$^2$cm for the $x = 0.17$ sample. (b) Thermal Hall conductivity of NCCO for $x=0.16$ (sample 1) and $x = 0.17$ at $H = 15$ T plotted as $\kappa_{\mathrm{xy}} / T$ vs $T$. We extract a residual linear term of $\kappa^0_{\mathrm{xy}}/T = 175 \pm 20$ mW/K$^2$m for $x = 0.16$ and $\kappa^0_{\mathrm{xy}}/T = 17.5 \pm 10$ mW/K$^2$m for $x = 0.17$ (dashed lines).
• Figure 4: (a) Thermal conductivity of NCCO at $x = 0.16$ (sample 1, red) plotted as $\kappa_{\mathrm{xx}}/T$ vs $T$ at $H = 15$ T. The dashed green line is the electronic contribution obtained from the WF law (see text). (b) Electronic part of the thermal Hall conductivity plotted as $\kappa^{e}_{\mathrm{xy}}/ T$ vs $T$ for NCCO $x = 0.16$ (red) at $H = 15$ T. For $T>4$ K, $\kappa^{e}_{\mathrm{xy}}$ (open red circles) is obtained by subtracting the $\kappa_{\mathrm{xy}}$ of the $x=0.17$ sample from the $x=0.16$ data (Fig. \ref{['fig2']}(b)), assuming the phononic $\kappa_{\mathrm{xy}}$ is the same in $x=0.16$ and $x=0.17$, and that the electronic contribution to the $x=0.17$ data is negligible. The dashed green line represents an upper bound on the electronic contribution, set by $L_{0}\sigma_{\mathrm{xy}}$ from the WF law. $L_{0}\sigma_{\mathrm{xy}}$ is calculated by using a temperature-independent Hall coefficient $R_\mathrm{H}$ and temperature-dependent $\rho_{\mathrm{xx}} (T)$ data of PCCO at $x = 0.17$Tafti2014, but adjusted for $\rho_0 = 2.7\,\mu\Omega$ cm. In order to match the value of $\kappa^{e}_{\mathrm{xy}}/T = 175 \pm 20$ mW/K$^2$m at $T\rightarrow$ 0, we get a Hall coefficient of $R_\mathrm{H}$ = 0.36 mm$^{3}$/C, which is roughly half of the expected value (see text).
• Figure 5: Quantum oscillation pattern observed by TDO measurement. (a) The oscillatory part of the TDO signal after removing a smooth background at $T = 1.8$ K. (b) Plot of TDO signal derivative $df/dB$ vs. $1/B$ with locations of extrema marked; traces vertically offset for visibility. Inset: $1/B$ vs. index $n$ of extrema; slope of linear fit yields $F_1 = 300 \pm 20$ T. (c) FFT of data showing the high-frequency peak at $F_2 = 11 300 \pm 100$ T.