What is measured when measuring a thermoelectric coefficient?

A thermal gradient generates an electric field in any solid hosting mobile electrons. In presence of a finite magnetic field (or Berry curvature) this electric field has a transverse component. These are known as Seebeck and Nernst coefficients. As Callen argued, back in 1948, the Seebeck effect quantifies the entropy carried by a flow of charged particles in absence of thermal gradient. Similarly, the Nernst conductivity, $\alpha_{xy}$, quantifies the entropy carried by a flow of magnetic flux in absence of thermal gradient. The present paper summarizes a picture in which the rough amplitude of the thermoelectric response is given by fundamental units and material-dependent length scales. Therefore, knowledge of material-dependent length scales allows predicting the amplitude of the signal measured by experiments. Specifically, the Nernst conductivity scales with the square of the mean-free-path in metals. Its anomalous component in magnets scales with the square of the fictitious magnetic length. Ephemeral Cooper pairs in the normal state of a superconductor generate a signal, which scales with the square of the superconducting coherence length and smoothly evolves to the signal produced by mobile vortices below the critical temperature.Comment: 16 pages, 6 figure

Signatures of Electron Fractionalization in Ultraquantum Bismuth

Because of the long Fermi wavelength of itinerant electrons, the quantum limit of elemental bismuth (unlike most metals) can be attained with a moderate magnetic field. The quantized orbits of electrons shrink with increasing magnetic field. Beyond the quantum limit, the circumference of these orbits becomes shorter than the Fermi wavelength. We studied transport coefficients of a single crystal of bismuth up to 33 tesla, which is deep in this ultraquantum limit. The Nernst coefficient presents three unexpected maxima that are concomitant with quasi-plateaus in the Hall coefficient. The results suggest that this bulk element may host an exotic quantum fluid reminiscent of the one associated with the fractional quantum Hall effect and raise the issue of electron fractionalization in a three-dimensional metal.Comment: 9 pages, four figures and supposrting online materia

How heat propagates in `non-Fermi liquid' 3^3He

In Landau's Fermi liquid, transport is governed by scattering between quasi-particles. The normal liquid $^3$He conforms to this picture, but only when T$< 0.02$ T$_F$. Here, we observe that the deviation from the standard behavior is concomitant with the fermion-fermion scattering time falling below the Planckian time, $\frac{\hbar}{k_BT}$. The thermal diffusivity of this quantum liquid is bounded by a minimum set by fundamental physical constants and earlier observed in classical liquids. This implies that collective excitations of the liquid (a sound mode) are carrying heat. We argue that if heat is carried by 2k$_F$ hydrodynamic sound mode, both the amplitude and the hitherto unexplained $T^{1/2}$ temperature dependence of thermal conductivity find an explanation with no other adjustable parameter.Comment: 7 pages, 4 figures and a supplemen

Nernst effect and dimensionality in the quantum limit

Nernst effect, the transverse voltage generated by a longitudinal thermal gradient in presence of magnetic field has recently emerged as a very sensitive, yet poorly understood, probe of electron organization in solids. Here we report on an experiment on graphite, a macroscopic stack of graphene layers, which establishes a fundamental link between dimensionality of an electronic system and its Nernst response. In sharp contrast with single-layer graphene, the Nernst signal sharply peaks whenever a Landau level meets the Fermi level. This points to the degrees of freedom provided by finite interlayer coupling as a source of enhanced thermoelectric response in the vicinity of the quantum limit. Since Landau quantization slices a three-dimensional Fermi surface, each intersection of a Landau level with the Fermi level modifies the Fermi surface topology. According to our results, the most prominent signature of such a topological phase transition emerges in the transverse thermoelectric response.Comment: 13 pages, 4 figures and supplementary information; To appear in Nature Physic

Angle dependence of the orbital magnetoresistance in bismuth

We present an extensive study of angle-dependent transverse magnetoresistance in bismuth, with a magnetic field perpendicular to the applied electric current and rotating in three distinct crystallographic planes. The observed angular oscillations are confronted with the expectations of semi-classic transport theory for a multi-valley system with anisotropic mobility and the agreement allows us to quantify the components of the mobility tensor for both electrons and holes. A quadratic temperature dependence is resolved. As Hartman argued long ago, this indicates that inelastic resistivity in bismuth is dominated by carrier-carrier scattering. At low temperature and high magnetic field, the threefold symmetry of the lattice is suddenly lost. Specifically, a $2\pi/3$ rotation of magnetic field around the trigonal axis modifies the amplitude of the magneto-resistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we mapped the boundary in the (field, temperature) plane separating two electronic states. In the less-symmetric state, confined to low temperature and high magnetic field, the three Dirac valleys cease to be rotationally invariant. We discuss the possible origins of this spontaneous valley polarization, including a valley-nematic scenario.Comment: 15 pages, 14 figure