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Register a new userOn the Nernst effect in fluctuating superconductors: Serbyn, Skvortsov, and Varlamov reply
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This is an extended Reply to Comment by A. Sergeev, M.Y. Reizer, and V. Mitin [arXiv:0906.2389] on our Letter [Phys. Rev. Lett. 102, 067001 (2009)]. We explicitly demonstrate that all claims by Sergeev et al. are completely unfounded, because their underlying theoretical work contains multiple errors and inconsistencies. For this reason, there is no need to revise the existing theories of thermoelectric response in superconductors.
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We present a new method to study the Nernst effect and diamagetism of an extreme type-II superconductor dominated by phase fluctuations. We work directly with vortex variables and our method allows us to tune vortex parameters (e.g., core energy and number of vortex species). We find that diamagnetic response and transverse thermoelectric conductivity ($alpha_{xy}$) persist well above the Kosterlitz-Thouless transition temperature, and become more pronounced as the vortex core energy is increased. However, they textit{weaken} as the number of internal vortex states are increased. We find that $alpha_{xy}$ closely tracks the magnetization $(-M/T)$ over a wide range of parameters.
A theory of the fluctuation-induced Nernst effect is developed for arbitrary magnetic fields and temperatures beyond the upper critical field line in a two-dimensional superconductor. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation (which includes quantum fluctuations) of the Nernst coefficient and give its asymptotic dependencies in various regions on the phase diagram. It is argued that the magnitude and the behavior of the Nernst signal observed experimentally in disordered superconducting films can be well-understood on the basis of the superconducting fluctuation theory.
We present a study of the Nernst effect in amorphous 2D superconductor InO$_x$, whose low carrier density implies low phase rigidity and strong superconducting phase fluctuations. Instead of presenting the abrupt jump expected at a BCS transition, the Nernst signal evolves continuously through the superconducting transition as previously observed in underdoped cuprates. This contrasts with the case of Nb$_{0.15}$Si$_{0.85}$, where the Nernst signal due to vortices below T$_{c}$ and by Gaussian fluctuations above are clearly distinct. The behavior of the ghost critical field in InO$_x$ points to a correlation length which does not diverge at $T_c$, a temperature below which the amplitude fluctuations freeze, but phase fluctuations survive.
We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $ u(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_ u$ at which $ u/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^star$- in agreement with gap opening detected in ARPES data. We track $T^star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^star(p)$ to $p=0$ yields $T^star(pto 0)simeq T_N(0)$, the Neel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^star(p)$ extrapolates linearly to zero at $psimeq p_{rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{rm c}$, and not $T^star$. This confirms that the pseudogap phase is not a form of precursor superconductivity.
We respond to P. Aos comment in arXiv:1907.09263, which suggests that vortex many-body effects are the origin of Hall sign reversal in few-unit-cell thick Bi-2212 cuprate crystals (Phys. Rev. Lett. 122, 247001 (2019)). Our experimental results are incompatible with the theoretical predictions detailed in Aos comment.
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