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We investigate a one-dimensional electron liquid with two point scatterers of different strength. In the presence of electron interactions, the nonlinear conductance is shown to depend on the current direction. The resulting asymmetry of the transport characteristic gives rise to a ratchet effect, i.e., the rectification of a dc current for an applied ac voltage. In the case of strong repulsive interactions, the ratchet current grows in a wide voltage interval with decreasing ac voltage. In the regime of weak interaction the current-voltage curve exhibits oscillatory behavior. Our results apply to single-band quantum wires and to tunneling between quantum Hall edges.
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We consider arrays of Luttinger liquids, where each node is described by a unitary scattering matrix. In the limit of small electron-electron interaction, we study the evolution of these scattering matrices as the high-energy single particle states are gradually integrated out. Interestingly, we obtain the same renormalization group equations as those derived by Lal, Rao, and Sen, for a system composed of a single node coupled to several semi-infinite 1D wires. The main difference between the single node geometry and a regular lattice is that in the latter case, the single particle spectrum is organized into periodic energy bands, so that the renormalization procedure has to stop when the last totally occupied band has been eliminated. We therefore predict a strongly renormalized Luttinger liquid behavior for generic filling factors, which should exhibit power-law suppression of the conductivity at low temperatures E_{F}/(k_{F}a) << k_{B}T << E_{F}, where a is the lattice spacing and k_{F}a >> 1. Some fully insulating ground-states are expected only for a discrete set of integer filling factors for the electronic system. A detailed discussion of the scattering matrix flow and its implication for the low energy band structure is given on the example of a square lattice.
We study a dynamic boundary, e.g. a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N>2 there is a quantum phase transition at K>1/2, where the TLL phases lock together at the particle position, resulting in a non-zero transconductance equal to e^2/Nh. The transition line terminates for strong coupling at K=1- 1/N, consistent with results at large N. Another type of a dynamic boundary is a superconducting (or Bose-Einstein condensate) grain coupled to N>2 TLLs, here the transition signals also the onset of a relevant Josephson coupling.
Using a particle-based model, we simulate the behavior of a skyrmion under the influence of asymmetric funnel geometries and ac driving at zero temperature. We specifically investigate possibilities for controlling the skyrmion motion by harnessing a ratchet effect. Our results show that as the amplitude of a unidirectional ac drive is increased, the skyrmion can be set into motion along either the easy or hard direction of the funnel depending on the ac driving direction. When the ac drive is parallel to the funnel axis, the skyrmion flows in the easy direction and its average velocity is quantized. In contrast, when the ac drive is perpendicular to the funnel axis, a Magnus-induced ratchet effect occurs, and the skyrmion moves along the hard direction with a constant average velocity. For biharmonic ac driving of equal amplitude along both the parallel and perpendicular directions, we observe a reentrant pinning phase where the skyrmion ratchet vanishes. For asymmetric biharmonic ac drives, the skyrmion exhibits a combination of effects and can move in either the easy or hard direction depending on the configuration of the ac drives. These results indicate that it is possible to achieve controlled skyrmion motion using funnel geometries, and we discuss ways in which this could be harnessed to perform data transfer operations.
In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion. Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches. Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability. Thermalization rates for electron- and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes. The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined. We further discuss how momentum relaxation due to several competing mechanisms, viz. triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model. Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.
We study the DC spin current induced into an unbiased quantum spin Hall system through a two-point contacts setup with time dependent electron tunneling amplitudes. By means of two external gates, it is possible to drive a current with spin-preserving and spin-flipping contributions showing peculiar oscillations as a function of pumping frequency, electron-electron interaction and temperature. From its interference patterns as a function of the Fabry-Perot and Aharonov-Bohm phases, it is possible to extract information about the helical nature of the edge states and the intensity of the electron-electron interaction.
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