Nernst Effect and Diamagnetism in Phase Fluctuating Superconductors

We study superconducting systems in the regime where superconductivity is destroyed by phase fluctuations. We find that the Nernst effect has a much sharper temperature decay than predicted by Gaussian fluctuations, with an onset temperature that tracks $T_c$ rather than the pairing temperature. We find a close quantitative connection with diamagnetism—the ratio of magnetization to transverse thermoelectric conductivity reaches a fixed value at high temperatures. We interpret measurements on underdoped cuprates in terms of a dilute vortex liquid over a wide temperature range above $T_c$.

Figure 1

Transverse thermoelectric conductivity for a single plane. Inset: diamagnetic response.

Figure 2

Contour plot of $\log [{\alpha }_{xy}^{2d}h/2e{k}_B]$. When comparing to the Nernst signal $e_N\approx {\alpha }_{xy}/{\sigma }_{xx}$ in Ref. 1, note that for small $T$ and $H$, the interlayer coupling $J_{\perp }$, absent in the simulations, stabilizes $3d$ superconductivity. In addition, $3d$ fluctuations suppress ${\alpha }_{xy}$ at low $T$ and large $H$ [7].

Figure 3

The dimensionless ratio $|M_z|/T{\alpha }_{xy}$. At high $T$, the ratio is expected to saturate to a value of 2 for all magnetic fields. Inset: $|M_z|/T{\alpha }_{xy}$ vs $T/T_{\mathrm{KT}}$ for $H=0.31H_0$

Figure 4

Nernst coefficient times conductivity (●) of underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ ($x=0.12$, $T_c=28\mathrm{K}$). The experimental data [1] are shifted by a constant quasiparticle background ${\nu }_B{\sigma }_{xx}=-0.011\mathrm{V}/\mathrm{K}\Omega \mathrm{T}\mathrm{m}$. The data at $T=30\mathrm{K}$ (▪) are divided by 4 to fit in the figure. This point is very close to $T_c$, and hence $\nu {\sigma }_{xx}$ is likely dominated by $3d$ fluctuations, not considered in our simulations (× with error bars). Inset: log-log plot of $(\nu -{\nu }_B){\sigma }_{xx}$ vs $T$. Data (●) and high $T$ expansion, Eq. (5), for $J_h$ (solid line) and $J_l$ (dotted line).