Thermoelectric Response Near a Quantum Critical Point: The Case of ${\mathrm{CeCoIn}}_5$

We present a study of thermoelectric coefficients in ${\mathrm{CeCoIn}}_5$ down to 0.1 K and up to 16 T in order to probe the thermoelectric signatures of quantum criticality. In the vicinity of the field-induced quantum critical point, the Nernst coefficient $\nu$ exhibits a dramatic enhancement without saturation down to the lowest measured temperature. The dimensionless ratio of the Seebeck coefficient to the electronic specific heat shows a minimum at a temperature close to threshold of the quasiparticle formation. Close to $T_c(H)$, in the vortex-liquid state, the Nernst coefficient behaves anomalously in puzzling contrast with other superconductors and standard vortex dynamics.

Figure 1

(a) The Seebeck coefficient divided by temperature as a function of temperature for different magnetic fields in a semilog plot. Note the upturn near the QCP. (b) Temperature dependence of the Nernst coefficient divided by temperature $\nu /T$. Close to the QCP, this quantity never saturates. The inset defines the convention used for the sign of the Nernst coefficient (see text).

Figure 2

(a) The temperature dependence of $q$, the dimensionless ratio of thermopower to electronic specific heat at three magnetic fields. The temperature marked by the arrow designs the threshold of the quasiparticle formation according to the temperature dependence of the Lorenz number as reported by Paglione et al. [7]. (b) A comparison of the field dependence of $\nu /T$, $\gamma$ (as reported in Ref. 3) and $A^{1/2}$ (taken from Ref. 2).

Figure 3

Contour plot of $\nu /T$ in the ($B$, $T$) plane. The color scale is logarithmic. Note the presence of two hot regions close to $H_{c2}$ and $T_c$. The inset is a zoom on the region near $H_{c2}$. The variation of three temperature scales, the onset of $T^2$ resistivity (solid squares), the minimum in $L/L_0$ (open squares), the and minimum in $q$ (open circles) with magnetic field is also shown.

Figure 4

(a)(b) Normalized magnitudes $r$ of $r=N/N_n$ (open circles), $S/S_n$ (solid circles), and $\rho /{\rho }_n$ (solid line) in the vicinity of superconducting transition for 1 and 5 T. For all fields, the onset of superconductivity leads to a faster collapse of the Nernst signal. Note also the small shoulder at 1 T. (c)(d) The additional contribution to transverse thermoelectricity in the vortex liquid regime obtained by subtracting the normalized Seebeck coefficient off the normalized Nernst signal.