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We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value.
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The effect of deconfinement due to finite band offsets on transport through quantum wires with two constrictions is investigated. It is shown that the increase in resonance linewidth becomes increasingly important as the size is reduced and ultimately places an upper limit on the energy (temperature) scale for which resonances may be observed.
When a quantum wire is weakly confined, a conductance plateau appears at e^2/h with decreasing carrier density in zero magnetic field accompanied by a gradual suppression of the 2e^2/h plateau. Applying an in-plane magnetic field B|| does not alter the value of this quantization; however, the e^2/h plateau weakens with increasing B|| up to 9 T, and then strengthens on further increasing B||, which also restores the 2e^2/h plateau. Our results are consistent with spin-incoherent transport in a one-dimensional wire.
Quantum conductance fluctuations are investigated in disordered 3D topological insulator quantum wires. Both experiments and theory reveal a new transport regime in a mesoscopic conductor, pseudo-ballistic transport, for which ballistic properties persist beyond the transport mean free path, characteristic of diffusive transport. It results in non-universal conductance fluctuations due to quasi-1D surface modes, as observed in long and narrow Bi$_2$Se$_3$ nanoribbons. Spin helical Dirac fermions in quantum wires retain pseudo-ballistic properties over an unusually broad energy range, due to strong quantum confinement and weak momentum scattering.
Thermoelectric transport coefficients are determined for semiconductor quantum wires with weak thickness fluctuations. Such systems exhibit anomalies in conductance near 1/4 and 3/4 of 2e^2/h on the rising edge to the first conductance plateau, explained by singlet and triplet resonances of conducting electrons with a single weakly bound electron in the wire [T. Rejec, A. Ramsak, and J.H. Jefferson, Phys. Rev. B 62, 12985 (2000)]. We extend this work to study the Seebeck thermopower coefficient and linear thermal conductance within the framework of the Landauer-Buettiker formalism, which also exhibit anomalous structures. These features are generic and robust, surviving to temperatures of a few degrees. It is shown quantitatively how at elevated temperatures thermal conductance progressively deviates from the Wiedemann-Franz law.
We propose a new method for dynamic nuclear polarisation in a quasi one-dimensional quantum wire utilising the spin-orbit interaction, the hyperfine interaction, and a finite source-drain potential difference. In contrast with current methods, our scheme does not rely on external magnetic or optical sources which makes independent control of closely placed devices much more feasible. Using this method, a significant polarisation of a few per cent is possible in currently available InAs wires which may be detected by conductance measurements. This may prove useful for nuclear-magnetic-resonance studies in nanoscale systems as well as in spin-based devices where external magnetic and optical sources will not be suitable.
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