Quantum fluctuation theorem in an interacting setup: point contacts in fractional quantum Hall edge state devices

We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.     

Reprint of : Measuring the Luttinger liquid parameter with shot noise

We explore the low-frequency noise of interacting electrons in a one-dimensional structure (quantum wire or interaction-coupled edge states) with counterpropagating modes, assuming a single channel in each direction. The system is driven out of equilibrium by a quantum point contact (QPC) with an applied voltage, which induces a double-step energy distribution of incoming electrons on one side of the device. A second QPC serves to explore the statistics of outgoing electrons. We show that measurement of a low-frequency noise in such a setup allows one to extract the Luttinger liquid constant K which is the key parameter characterizing an interacting 1D system. We evaluate the dependence of the zero-frequency noise on K and on parameters of both QPCs (transparencies and voltages).     

Measuring the Luttinger liquid parameter with shot noise

We explore the low-frequency noise of interacting electrons in a one-dimensional structure (quantum wire or interaction-coupled edge states) with counterpropagating modes, assuming a single channel in each direction. The system is driven out of equilibrium by a quantum point contact (QPC) with an applied voltage, which induces a double-step energy distribution of incoming electrons on one side of the device. A second QPC serves to explore the statistics of outgoing electrons. We show that measurement of a low-frequency noise in such a setup allows one to extract the Luttinger liquid constant K which is the key parameter characterizing an interacting 1D system. We evaluate the dependence of the zero-frequency noise on K and on parameters of both QPCs (transparencies and voltages).     

Enhancement of the shot noise of a quantum dot–Luttinger lead system

We investigate the joint effects of the intralead electron interaction and Coulombic dot–lead interaction on the shot noise of a quantum dot coupled to Luttinger liquid leads. A formula of the shot noise is derived by applying the nonequilibrium Green function technique. The shot noise is enhanced by the dot–lead interaction. For a weak or moderately strong interaction the differential shot noise demonstrates resonant-like behavior as a function of bias and gate voltages. In the limit of strong interaction resonant behavior disappears and the differential shot noise and Fano factor scale as a power law in bias voltage. Under some parameters, the differential shot noise may become negative around resonant peaks, and the physical reason is analyzed.     

4He Luttinger liquid in nanopores

We study the low-temperature properties of a 4He fluid confined in nanopores, using large-scale quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.     

Current fluctuations in an interacting quantum dot

We calculate the counting statistics of electron transfer through an open quantum dot with charging interaction. A dot that is connected to leads by two single-channel quantum point contacts in an in-plane magnetic field is described by a Luttinger liquid with impurity at the Toulouse point. We find that the fluctuations of the current through this conductor exhibit distinctive interaction effects. Fluctuations saturate at high voltages, while the mean current increases linearly with the bias voltage. All cumulants higher than the second one reach at large bias a temperature independent limit.     

Resonant tunneling between Luttinger liquids: a solvable case

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonization and refermionization methods, we find a mapping to a Kondo-type problem which possesses a nontrivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the nonlinear current-voltage characteristics and analyze the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.     

Interedge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime

Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.     

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.     

Reprint of : Regular and singular Fermi liquid in triple quantum dots: Coherent transport studies

A system of three coupled quantum dots in a triangular geometry (TQD) with electron–electron interaction and symmetrically coupled to two leads is analyzed with respect to the electron transport by means of the numerical renormalization group. Varying gate potentials this system exhibits extremely rich range of regimes with different many-electron states with various local spin orderings. It is demonstrated how the Luttinger phase changes in a controlled manner which then via the Friedel sum rule formula exactly reproduces the conductance through the TQD system. The analysis of the uncoupled TQD molecule from the leads gives a reliable qualitative understanding of various relevant regimes and an insight into the phase diagram with the regular Fermi liquid and singular-Fermi liquid phases.     

Photoconductance of a one-dimensional quantum dot

The ac-transport properties of a one-dimensional quantum dot with non-Fermi liquid correlations are investigated. It is found that the linear photoconductance is drastically influenced by the interaction. While for weak interaction it shows peak-like resonances, in the strong interaction regime it assumes a step-like behavior. In both cases the photo-transport provides precise informations about the quantized plasmon modes in the dot. Temperature and voltage dependences of the sideband peaks are treated in detail. Characteristic Luttinger liquid power laws are found. Received 23 October 2001     

Equilibration of a one-dimensional quantum liquid

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures, the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids, these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.     

The shot noise of the quantum dot weakly coupled to Luttinger liquid

We study the nonequilibrium transport through a single-level quantum dot weakly coupled to Luttinger liquid leads. A general shot noise expression is derived by using nonequilibrium Green function technique. We find that the differential shot noise and differential conductance demonstrate resonant-like behavior as a function of the bias voltage and the quantum dot's energy level for a weak or moderately strong interaction. In the limit of strong electron-electron interaction, the resonant behavior disappears and shows bias-voltage-dependent power law scalings. And the Fano factor also scales as a power law in high bias voltage region. In addition, the Fano factor is enhanced with the electron-electron interaction increased. It implies that the Fano factor can be controlled by tuning the electron-electron interaction in the leads.     

Luttinger liquid at the edge of undoped graphene in a strong magnetic field

We demonstrate that an undoped two-dimensional carbon plane (graphene) whose bulk is in the integer quantum Hall regime supports a nonchiral Luttinger liquid at an armchair edge. This behavior arises due to the unusual dispersion of the noninteracting edge 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 nonintegral exponent. In proximity to a bulk lead, the edge may undergo a quantum phase transition between the Luttinger liquid phase and a metallic state.     

Proposal for direct measuring of the Majorana number in a topological superconductor using a quantum dot

We propose to directly measure the Majorana number for one-dimensional topological superconductors using a quantum dot. The setup consists of two topological superconducting wires with four Majorana zero modes, which are coupled to an external quantum dot. The measurement is achieved by utilizing the definition of the Majorana number, which is the charge-parity flipping when changing the boundary condition for the topological superconductor. We consider a control of the boundary condition with voltage gates. When the voltage on the gate are modulated sequentially, the boundary conditions changes and the parity of the superconducting state flips. We demonstrate that this parity flipping will change the electron occupation probability of the quantum dot, which reflects the value of the Majorana number.     

Bosonization theory for tunneling spectra in smooth edges of quantum Hall systems

We calculate the spectral function of a smooth edge of a quantum Hall system in the lowest Landau level by means of a bosonization technique. We obtain a general relationship between the one electron spectral function and the dynamical structure factor. The resulting – characteristics exhibit, at low voltage and temperature, power law scaling, generally different from the one predicted by the chiral Luttinger liquid theory, and in good agreement with recent experimental results.     

Spin-polarized conductance induced by tunneling through a magnetic impurity

Using the zero mode method, we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent alpha(>or=1). We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, that the conductance as a function of temperature is G approximately equal (e(2)/h)(T/T(F))(2(alpha-2)), whereas for off-resonance conditions the conductance is G approximately equal (e(2)/h)(T/T(F))(2(alpha-1)). By applying either a gate voltage or a magnetic field or both, one of the spin components can be in resonance while the other is off resonance causing a strong asymmetry between the spin-up and spin-down conductances.     

Fractional Josephson current through a Luttinger liquid with topological excitations

Recently, the Majorana fermion has received great attentions due to its promising application in the fault-tolerant quantum computation. This application requires more accessible methods to detect the motion and braiding of the Majorana fermions. We use a Luttinger liquid ring to achieve this goal, where the ring geometry is nontrivial in the sense that it leads to fermion-parity-dependent topological excitations. First, we briefly review the essential physics of the Luttinger liquid and the Majorana fermion, in order to give an introduction of the general framework used in the following main work. Then, we theoretically investigated the DC Josephson effect between two topological superconductors via a Luttinger liquid ring. A low-energy effective Hamiltonian is derived to show the existence of the fractional Josephson current. Also, we find that the amplitude of the Josephson current, which is determined by the correlation function of Luttinger liquid, exhibits different behaviors in terms of the parity of Luttinger liquid due to the topological excitations. Our results suggest a possible method to detect the Majorana fermions and their tunneling process.     

Hidden duality and associated instabilities of Tomonaga–Luttinger liquid on lattice

Hidden duality and its associated instabilities of the spinless Luttinger liquid on lattice are reported. The local quantum fluctuations due to the general multi-particle umklapp and other processes and the long-distance chiral modes compete and as a result produce a hierarchy of exotic charge density instabilities. Explicit bosonic quantum operators for the local density fluctuations are constructed and are used to make identification of the Luttinger liquid with the classical 2D Coulomb gas with -term and with the rich hidden duality.     

Observation of quantum capacitance in the Cooper-pair transistor

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, it behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage and has two parts, the geometric capacitance, C(geom), and the quantum capacitance C(Q). The latter is due to the level anticrossing caused by the Josephson coupling and is dual to the Josephson inductance. It depends parametrically on the gate voltage and its magnitude may be substantially larger than C(geom). We have detected C(Q) in our CPT, by measuring the in phase and quadrature rf signal reflected from a resonant circuit in which the CPT is embedded. C(Q) can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.