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Register a new userTunable non-equilibrium Luttinger liquid based on counter-propagating edge channels
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We investigate energy transfer between counter-propagating quantum Hall edge channels (ECs) in a two-dimensional electron system at filling factor u=1. The ECs are separated by a thin impenetrable potential barrier and Coulomb coupled, thereby constituting a quasi one-dimensional analogue of a spinless Luttinger liquid (LL). We drive one, say hot, EC far from thermal equilibrium and measure the energy transfer rate P into the second, cold, EC using a quantum point contact as a bolometer. The dependence of P on the drive bias indicates breakdown of the momentum conservation, whereas P is almost independent on the length of the region where the ECs interact. Interpreting our results in terms of plasmons (collective density excitations), we find that the energy transfer between the ECs occurs via plasmon backscattering at the boundaries of the LL. The backscattering probability is determined by the LL interaction parameter and can be tuned by changing the width of the electrostatic potential barrier between the ECs.
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The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the electron-doped side of the Dirac cone and the other surface to the hole-doped side, the quantum Hall edge channels are counter-propagating. The opposite edge mode direction, combined with the opposite helicities of top and bottom surfaces, allows for scattering between these counter-propagating edge modes. The total Hall conductance is integer valued only when the scattering is strong. For weaker interaction, a non-integer quantum Hall effect is expected and measured.
We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix S, which describes the splitting of the electric current among the leads. The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials. The associated non-equilibrium steady state depends on S and is explicitly constructed. In this context we develop a non-equilibrium bosonization procedure and compute some basic correlation functions. Luttinger liquids with general anyon statistics are considered. The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures. Both the charge and heat transport are studied. The exact current-current correlation function is derived and the zero-frequency noise power is determined.
We demonstrate that an undoped two-dimensional carbon plane (graphene) whose bulk is in the integer quantum Hall regime supports a non-chiral Luttinger liquid at an armchair edge. This behavior arises due to the unusual dispersion of the non-interacting edges states, causing a crossing of bands with different valley and spin indices at the edge. We demonstrate that this stabilizes a domain wall structure with a spontaneously ordered phase degree of freedom. This coherent domain wall supports gapless charged excitations, and has a power law tunneling $I-V$ with a non-integral exponent. In proximity to a bulk lead, the edge may undergo a quantum phase transition between the Luttinger liquid phase and a metallic state when the edge confinement is sufficiently strong relative to the interaction energy scale.
We report selective injection of both spin-up and spin-down single electrons into a quantum dot (QD) from spin-polarized non-equilibrium quantum Hall edge channels (ECs) generated by selective transmission of spin-resolved ECs using a surface gate placed at a distance from the QD. We change the spin polarization of non-equilibrium ECs by changing the bias voltages applied to different source Ohmic contacts. The efficiency of spin-up electron injection reaches 0.5, which is approximately 0.2 higher than that induced by spin-dependent tunnel coupling between QD and ECs. On the other hand, the efficiency of spin-down electron injection reaches 0.4. In addition, we rectify the underestimation of the efficiency of spin filtering for equilibrium ECs by numerically subtracting the contribution of the excited states in the QD. The obtained spin-filtering efficiency is higher than that evaluated from the raw experimental data and increases with magnetic field as expected with the increase in the spatial separation between ECs.
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $eta$ the weak link is always a relevant perturbation which suppresses transport strongly. At zero temperature the current voltage relation of the link is $Isim exp(-E_0/eV)$ where $E_0simeta/kappa$ and $kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $exp(-sqrt{{cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_{eta}sim 1/eta $ from the impurity.
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