Identifying materials and devices which offer efficient thermoelectric effects at low temperature is a major obstacle for the development of thermal management strategies for low-temperature electronic systems. Superconductors cannot offer a solution
since their near perfect electron-hole symmetry leads to a negligible thermoelectric response; however, here we demonstrate theoretically a superconducting thermoelectric transistor which offers unparalleled figures of merit of up to $sim 45$ and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phase-tunable meaning its thermoelectric response for power generation can be precisely controlled with a small magnetic field. Our concept is based on a superconductor-normal metal-superconductor interferometer in which the normal metal weak-link is tunnel coupled to a ferromagnetic insulator and a Zeeman split superconductor. Upon application of an external magnetic flux, the interferometer enables phase-coherent manipulation of thermoelectric properties whilst offering efficiencies which approach the Carnot limit.
We present results on all-MgB2 tunnel junctions, where the tunnel barrier is deposited MgO or native-oxide of base electrode. For the junctions with MgO, the hysteretic I-V curve resembles a conventional underdamped Josephson junction characteristic
with critical current-resistance product nearly independent of the junction area. The dependence of the critical current with temperature up to 20 K agrees with the [Ambegaokar and Baratoff, Phys. Rev. Lett. 10, 486 (1963)] expression. For the junctions with native-oxide, conductance at low bias exhibits subgap features while at high bias reveals thick barriers. As a result no supercurrent was observed in the latter, despite the presence of superconducting-gaps to over 30 K.
The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and i
ts direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.
