Nernst, Seebeck, and Hall effects in the mixed state of YBa2Cu3O7- delta and Bi2Sr2CaCu2O8+x thin films: A comparative study

Nernst response, viscosity and mobile entropy in vortex liquids

In a liquid of superconducting vortices, a longitudinal thermal gradient generates a transverse electric field. This Nernst signal peaks at an intermediate temperature and magnetic field, presumably where the entropy difference between the vortex core and the superfluid environment is largest. There is a puzzling similarity of the amplitude of this peak across many different superconductors. This peak can be assimilated to a minimum in the viscosity to entropy density ratio of the vortex liquid. Expressed in units ofℏkB, this minimum is one order of magnitude larger than what is seen in common liquids. Moreover, the entropy stocked in the vortex core isnotidentical to the entropy bound to a moving magnetic flux line. Due to a steady exchange of normal quasi-particles, entropy can leak from the vortex core. A slowly moving vortex will be peeled off its entropy within a distance of the order of a superconducting coherence length, provided that theΔEFratio is sufficiently large.

Universal Bound to the Amplitude of the Vortex Nernst Signal in Superconductors

A liquid of superconducting vortices generates a transverse thermoelectric response. This Nernst signal has a tail deep in the normal state due to superconducting fluctuations. Here, we present a study of the Nernst effect in two-dimensional heterostructures of Nb-doped strontium titanate (STO) and in amorphous MoGe. The Nernst signal generated by ephemeral Cooper pairs above the critical temperature has the magnitude expected by theory in STO. On the other hand, the peak amplitude of the vortex Nernst signal below T_{c} is comparable in both and in numerous other superconductors despite the large distribution of the critical temperature and the critical magnetic fields. In four superconductors belonging to different families, the maximum Nernst signal corresponds to an entropy per vortex per layer of ≈k_{B}ln2.

Quantum Criticality inside the Anomalous Metallic State of a Disordered Superconducting Thin Film

The field-induced superconductor-insulator transition (SIT) in two-dimensional (2D) systems is a famous example of a quantum phase transition. However, an emergence of an anomalous metallic state induced by field has been a long-standing problem in 2D superconductors. While theories predicted that the emergence is attributed to strong phase fluctuations of the superconducting order parameter due to quantum fluctuations, usual resistance measurements have not probed them directly. Here, using Nernst effect measurements, we uncover superconducting fluctuations in the vicinity of the field-induced metallic state in an amorphous Mo_{x}Ge_{1-x} thin film. The field range where the vortex Nernst signals are detectable remains nonzero toward zero temperature, and it locates inside the metallic state defined by the magnetoresistance, indicating that the metallic state results from quantum vortex liquid (QVL) with phase fluctuations due to quantum fluctuations. Slow decay of transport entropy of vortices in the QVL with decreasing temperature suggests that the metallic state originates from broadening of a quantum critical point in SIT.

AC measurement of the Nernst effect of thin films at low temperatures

We describe an alternating current method to measure the Nernst effect in superconducting thin films at low temperatures. The Nernst effect is an important tool in the understanding of superconducting fluctuations and, in particular, vortex motion near critical points. However, in most materials, the Nernst signal in a typical experimental setup rarely exceeds a few μV, in some cases being as low as a few nV. DC measurements of such small signals require extensive signal processing and protection against stray pickups and offsets, limiting the sensitivity of such measurements to >1 nV. Here, we describe a method utilizing a one-heater-two-thermometer setup with the heating element and thermometers fabricated on-chip with the sample, which helped to reduce the thermal load and temperature lag between the substrate and the thermometer. Using AC heating power and 2ω measurement, we are able to achieve sub-nanovolt sensitivity in 20 nm-30 nm thin superconducting films on a glass substrate, compared to a sensitivity of ∼10 nV using DC techniques on the same setup.

Nernst effect in metals and superconductors: a review of concepts and experiments

The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in the presence of a magnetic field. At the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: (i) the contribution of quasi-particles to the Nernst signal is negligible; and (ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Bridgman relation, measures the flow of transverse entropy caused by a longitudinal particle flow. Along the lines of Landauer's approach to transport phenomena, the magnitude of the transverse magneto-thermoelectric response is linked to the quantum of thermoelectric conductance and a number of material-dependent length scales: the mean free path, the Fermi wavelength, the de Broglie thermal wavelength and the superconducting coherence length. Extremely mobile quasi-particles in dilute metals generate a widely-documented Nernst signal. Fluctuating Cooper pairs in the normal state of superconductors have been found to produce a detectable Nernst signal with an amplitude conforming to the Gaussian theory, first conceived by Ussishkin, Sondhi and Huse. In addition to these microscopic sources, mobile Abrikosov vortices, mesoscopic objects simultaneously carrying entropy and magnetic flux, can produce a sizeable Nernst response. Finally, in metals subject to a magnetic field strong enough to truncate the Fermi surface to a few Landau tubes, each exiting tube generates a peak in the Nernst response. The survey of these well-established sources of the Nernst signal is a helpful guide to identify the origin of the Nernst signal in other controversial cases.

Local charge and spin currents in magnetothermal landscapes

A scannable laser beam is used to generate local thermal gradients in metallic (Co2FeAl) or insulating (Y3Fe5O12) ferromagnetic thin films. We study the resulting local charge and spin currents that arise due to the anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE), respectively. In the local ANE experiments, we detect the voltage in the Co2FeAl thin film plane as a function of the laser-spot position and external magnetic field magnitude and orientation. The local SSE effect is detected in a similar fashion by exploiting the inverse spin Hall effect in a Pt layer deposited on top of the Y3Fe5O12. Our findings establish local thermal spin and charge current generation as well as spin caloritronic domain imaging.

The Nernst effect and the boundaries of the Fermi liquid picture

Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect has been explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrary to what has been often assumed, the so-called Sondheimer cancelation does not imply a negligible Nernst response in a Fermi liquid. In fact, the amplitude of the Nernst response measured in various metals in the low-temperature limit is scattered over six orders of magnitude. According to the data, this amplitude is roughly set by the ratio of electron mobility to Fermi energy, in agreement with the implications of semi-classical transport theory.

Phase-coherence effects in vortex transport entropy

Nernst and electrical resistivity measurements in superconducting YBa2Cu3O7-delta and Bi2Sr2CaCu2O8+delta with and without columnar defects show a distinctive thermodynamics of the respective liquid vortex matter. At a field-dependent high temperature region in the H-T phase diagram, the Nernst signal is independent of structural defects in both materials. At lower temperatures, in YBa2Cu3O7-delta, defects contribute only to the vortex mobility, and the transport entropy is that of a system of vortex lines. The transition to lower temperatures in Bi2Sr2CaCu2O8+delta has a different origin; the maximum in the Nernst signal when decreasing temperature is not associated with transport properties but with the entropy behavior of pancake vortices in the presence of structural defects.

Ambipolar Nernst effect in NbSe2

The first study of the Nernst effect in NbSe2 reveals a large quasiparticle contribution with a magnitude comparable and a sign opposite to the vortex signal. Comparing the effect of the charge density wave (CDW) transition on Hall and Nernst coefficients, we argue that this large Nernst signal originates from the thermally induced counterflow of electrons and holes and indicates a drastic change in the electron scattering rate in the CDW state. The results provide new input for the debate on the origin of the anomalous Nernst signal in high-T(c) cuprates.

Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped La(2-x)Sr(x)CuO4

Two general features of a superconductor, which appear at the critical temperature, are the formation of an energy gap and the expulsion of magnetic flux (the Meissner effect). In underdoped copper oxides, there is strong evidence that an energy gap (the pseudogap) opens up at a temperature significantly higher than the critical temperature (by 100-220 K). Certain features of the pseudogap suggest that it is closely related to the gap that appears at the critical temperature (for example, the variation of the gap magnitudes around the Fermi surface and their maximum amplitudes are very similar). However, the Meissner effect is absent in the pseudogap state. The nature of the pseudogap state, and its relation (if any) to the superconducting state are central issues in understanding copper oxide superconductivity. Recent evidence suggests that, in the underdoped regime, the Meissner state is destroyed above the critical temperature by strong phase fluctuations (as opposed to a vanishing of the superfluid density). Here we report evidence for vortices (or vortex-like excitations) in La(2-x)Sr(x)CuO4 at temperatures significantly above the critical temperature. A thermal gradient is applied to the sample in a magnetic field. Vortices are detected by the large transverse electric field produced as they diffuse down the gradient (the Nernst effect). We find that the Nernst signal is anomalously enhanced at temperatures as high as 150 K.