We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker [Europhys. Lett. 35, 523 (1996)] to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify in particular rectification effects that increase device performance.PACS numbers: 85.50.Fi

Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of timereversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to specific additional relations that follow from the combination of symmetries, beyond microreversibility. We discuss these relations in several illustrative situations. We show the reciprocity between spin-Hall and inverse spin-Hall effects, and the reciprocity between spin-injection and magnetoelectric spin currents. We discuss the symmetry and reciprocity relations of Seebeck, Peltier, spin-Seebeck and spin-Peltier effects in systems with and without coupling to superconductors. PACS numbers: 73.23.-b,85.75.-d,72.15.Jf,74.25.fg arXiv:1207

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.

We investigate the time-dependent fluctuations of the electric current injected from a reservoir with a nonequilibrium spin accumulation into a mesoscopic conductor. We show how the current noise power directly reflects the magnitude of the spin accumulation in two easily noticeable ways. First, as the temperature is lowered, the small-bias noise saturates at a value determined by the spin accumulation. Second, in the presence of spin-orbit interactions in the conductor, the current noise exhibits a sample-dependent mesoscopic asymmetry under reversal of the electric current direction. These features provide for a purely electric protocol for measuring spin accumulations.Noise measurements on nonequilibrium electric currents are very efficient probes of the dynamics and nature of the charge carriers. 1 At low temperature, the classical JohnsonNyquist noise is suppressed and quantum effects govern the behavior of the surviving shot noise. In the mesoscopic regime, the noise power S is reduced below its uncorrelated Poisson value S 0 = 2|q| I , where I is the average electric current, by the Fano factor F = S/S 0 . The value of F depends on the electronic dynamics. For instance, one finds F = 1/3 in diffusive systems and F = 1/4 in ballistic chaotic systems. 1,2 Alternatively, shot noise measurements have determined the charge |q| of current-carrying quasiparticles in normal-metal/superconductor junctions and in the fractional quantum Hall effect. 1-3 In this manuscript, we further illustrate the usefulness of current noise measurements by showing how they can reveal the magnitude of nonequilibrium spin accumulations. Our results provide for a purely electric protocol to measure spin accumulations, which has the potential to quantitatively determine their magnitude. It therefore goes one step further than the optical methods used so far to detect magnetoelectrically generated spin accumulations. 4,5 Alternatively, the noise measurement we propose, coupled with an electric measurement of the spin Hall and inverse spin Hall effects, 6-8 can provide key experimental information on the conversion between spin accumulations and spin currents.A number of works have investigated charge current noise from polarized reservoirs. Reference 9 suggested using current and noise measurements in the single-channel limit to measure the spin injection efficiency from a ferromagnet for weak spin-flip scattering. Other related works have pointed out that noise measurements in hybrid paramagnetic/ferromagnetic structures can reveal information on the relative orientation of the ferromagnets 10 and on the spin relaxation processes in the paramagnet. 11-14 These results have been at least partially confirmed by numerical simulations. 15 In noninteracting systems, current cross-correlations have a sign determined by the statistics of the charge carriers. Investigations of a single-level interacting fermionic quantum dot coupled to ferromagnetic leads have demonstrated the emergence of positive (bosonlike) current cross-correlations for ce...

We investigate nonlinear transport through quantum coherent metallic conductors contacted to superconducting components. We find that in certain geometries, the presence of superconductivity generates a large, finite-average rectification effect. Specializing to Andreev interferometers, we show that the direction and magnitude of rectification can be controlled by a magnetic flux tuning the superconducting phase difference at two contacts. In particular, this results in the breakdown of an Onsager reciprocity relation at finite bias. The rectification current is macroscopic in that it scales with the linear conductance, and we find that it exceeds 5% of the linear current at sub-gap biases of a few tens of microelectronvolts.