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

Multiple nodeless superconducting gaps in optimally-doped SrTi1−x_{1-x}Nbx_{x}O3_{3}

We present the first study of thermal conductivity in superconducting SrTi$_{1-x}$Nb$_{x}$O$_{3}$, sufficiently doped to be near its maximum critical temperature. The bulk critical temperature, determined by the jump in specific heat, occurs at a significantly lower temperature than the resistive T$_{c}$. Thermal conductivity, dominated by the electron contribution, deviates from its normal-state magnitude at bulk T$_{c}$, following a Bardeen-Rickayzen-Tewordt (BRT) behavior, expected for thermal transport by Bogoliubov excitations. Absence of a T-linear term at very low temperatures rules out the presence of nodal quasi-particles. On the other hand, the field dependence of thermal conductivity points to the existence of at least two distinct superconducting gaps. We conclude that optimally-doped strontium titanate is a multigap nodeless superconductor.Comment: 6 pages including a supplemen

Critical doping for the onset of a two-band superconducting ground state in SrTiO3−δ_{3-\delta}

In doped SrTiO$_{3}$ superconductivity persists down to an exceptionally low concentration of mobile electrons. This restricts the relevant energy window and possible pairing scenarios. We present a study of quantum oscillations and superconducting transition temperature, $T_{c}$ as the carrier density is tuned from $10^{17}$ to $10^{20}$ $cm^{-3}$ and identify two critical doping levels corresponding to the filling thresholds of the upper bands. At the first critical doping, which separates the single-band and the two-band superconducting regimes in oxygen-deficient samples, the steady increase of T$_{c}$ with carrier concentration suddenly stops. Near this doping level, the energy dispersion in the lowest band displays a downward deviation from parabolic behavior. The results impose new constraints for microscopic pairing scenarios.Comment: 5 pages of main article and 4 pages of supplemen

Unveiling the double-peak structure of quantum oscillations in the specific heat

Quantum oscillation phenomenon is an essential tool to understand the electronic structure of quantum matter. Here we report the first systematic study of quantum oscillations in the electronic specific heat $C_{el}$ in natural graphite. We show that the crossing of a single spin Landau level and the Fermi energy give rise to a double-peak structure, in striking contrast to the single peak expected from Lifshitz-Kosevich theory. Intriguingly, the double-peak structure is predicted by the kernel term for $C_{el}/T$ in the free electron theory. The $C_{el}/T$ represents a spectroscopic tuning fork of width 4.8 $k_B T$ which can be tuned at will to resonance. Using a coincidence method, the double-peak structure can be used to accurately determine the Lande $g$-factor of quantum materials. More generally, the tuning fork can be used to reveal any peak in fermionic density of states tuned by magnetic field, such as Lifshitz transition in heavy-fermion compounds.Comment: 22 pages, 5 figure

Metallicity and Superconductivity in Doped Strontium Titanate

Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean free path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries of Migdal-Eliashberg approximation. An intimate connection between dilute superconductivity and aborted ferroelectricity is widely suspected. In this review, we give a brief account of ongoing research on bulk strontium titanate as an insulator, a metal, and a superconductor