We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x = v/(2 ω), where v is the plasmon velocity and ωis the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enhancement in each wire individually.
We calculate the tunneling density of states for a Tomonaga-Luttinger liquid placed under a strong bias voltage. For the tunneling through a side-coupled point contact, one can observe the power law singularities in the tunneling density of states separately for the right- and left-movers despite the point-like tunnel contact. Deviations of the nonequilibrium tunneling exponents from the equilibrium case are discussed.
We study electron tunneling from a tip or a lead into an interacting quantum wire described by Luttinger liquid theory. Within a WKB-type approach, the Coulomb interaction between the wire and the tunneling electrons, as well as the finite traversal time are taken into account. Although the static image potential is only logarithmically suppressed against the bare Coulomb interaction, the dynamic image potential is not strong enough to alter power-law exponents entering the tunneling density of states.
We study the quantum point contact between the topological superconductor and the helical Luttinger liquid. The effects of the electron-electron interactions in the helical Luttinger liquid on the low-energy physics of this system are analyzed by the renormalization group. Among the various couplings at the point contact which arise from the tunneling via the Majorana edge channel, the induced backscattering in the helical Luttinger liquid is the most relevant for repulsive interactions. Hence, at low temperatures, the helical Luttinger liquid is effectively cut into two separated half wires. …
It is shown that a strong magnetic field applied to a bulk metal induces a Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in tunneling: the tunneling conductance scales as a power-law of voltage or temperature. The tunneling exponent increases with the magnetic field as BlnB. The zero-bias anomaly is most pronounced for tunneling with the field applied perpendicular to the plane of the tunneling junction.
We evaluate tunneling rates into/from a voltage biased quantum wire containing weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\hbar ω\leq U$. The tunneling rates are split into two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge $E_F-U$ is negative if Coulomb interaction is not too strong.
We have measured the low temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic line width decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger-liquid.
Au-induced atomic wires on the Ge(001) surface were recently claimed to be an ideal 1D metal and their tunneling spectra were analyzed as the manifestation of a Tomonaga-Luttinger liquid (TLL) state. We reinvestigate this system for atomically well-ordered areas of the surface with high resolution scanning tunneling microscopy and spectroscopy (STS). The local density-of-states maps do not provide any evidence of a metallic 1D electron channel along the wires. Moreover, the atomically resolved tunneling spectra near the Fermi energy are dominated by local density-of-states features, deviating …
Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits, or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a Numerical Renormalization Group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a non-perturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single s…
We study a hybrid system consisting of a spin-incoherent Luttinger liquid adjoined at one or both ends to a superconductor. We find the tunneling density of states diverges at low energies and exhibits a universal frequency dependence independent of the strength of the interactions in the system. We show that in spite of exponentially decaying pair correlations with distance into the spin-incoherent Luttinger liquid, the Josephson current remains robust. Compared to the zero temperature Luttinger liquid case there is a factor of 2 reduction in the critical current and a halving of the period i…
We propose a three terminal spin polarized stm setup for probing the helical nature of the Luttinger liquid edge state that appears in the quantum spin Hall system. We show that the three-terminal tunneling conductance strongly depends on the angle ($θ$) between the magnetization direction of the tip and the local orientation of the electron spin on the edge while the two terminal conductance is independent of this angle. We demonstrate that chiral injection of an electron into the helical Luttinger liquid (which occurs when $θ$ is zero or $π$) is associated with fractionalization of the spin …
The non linear charge transfer through a tunnel junction between two Luttinger systems is studied for repulsive, finite range interaction between electrons on the same, V_{11}, and on different,V_{12}, sides of the junction. Features of the Coulomb blockade effect are observed if V_{12}=0. We predict a novel interaction induced enhancement of the current if V_{12}>0. When V_{12}=V_{11}, the current is suppressed at small bias, but the ``charging energy'', obtained from the asymptotic behavior at high bias voltage, vanishes.
The paper addresses the problem whether and how it is possible to detect the Luttinger-liquid behavior from the $IV$ curves for tunneling to 1D or quasi-1D conductors. The power-law non-ohmic $IV$ curve, which is usually considered as a manifestation of the Luttinger-liquid behavior, can be also deduced from the theory of the Coulomb blockaded junction between 3D conductors affected by the environment effect. In both approaches the power-law exponents are determined by the ratio of the impedance of an effective electric circuit to the quantum resistance. Though two approaches predict different…
Coupled-wire constructions use bosonization to analytically tackle the strong interactions underlying fractional topological states of matter. We give an introduction to this technique, discuss its strengths and weaknesses, and provide an overview of the main achievements of coupled-wire constructions.
Explicit predictions for Scanning Tunneling Microscopy (STM) on interacting one-dimensional electron systems are made using the Luttinger liquid formalism. The STM current changes with distance from an impurity or boundary in a characteristic way, which reveals the spin-charge separation and the interaction strength in the system. The current exhibits Friedel-like oscillations, but also carries additional modulated behavior as a function of voltage and distance, which shows the spin-charge separation in real space. Moreover, very close to the boundary the current is strongly reduced, which is …
Within the framework of boundary conformal field theory, we evaluate the conductance of stable fixed points of junctions of two and three quantum wires with different Luttinger parameters. For two wires, the physical properties are governed by a single effective Luttinger parameters for each of the charge and spin sectors. We present numerical density-matrix-renormalization-group calculations of the conductance of a junction of two chains of interacting spinless fermions with different interaction strengths, obtained using a recently developed method [Phys. Rev. Lett. 105, 226803 (2010)]. The …
We study theoretically the photon-assisted tunneling through a quantum dot weakly coupled to Luttinger liquids (LL) leads, and find that the zero bias dc conductance is strongly affected by the interactions in the LL leads. In comparison with the system with Fermi liquid (FL) leads, the sideband peaks of the dc conductance become blurring for 1/2<g<1, and finally merge into the central peak for g<1/2, (g is the interaction parameter in the LL leads). The sidebands are suppressed for LL leads with Coulomb interactions strong enough, and the conductance always appears as a single peak for any st…
A crossover theory connecting Altshuler-Aronov electron-electron interaction corrections and Luttinger liquid behavior in quasi-1D disordered conductors has been formulated. Based on an interacting non-linear sigma model, we compute the tunneling density of states and the interaction correction to the conductivity, covering the full crossover.
We form a highly simplified model of an atomic wire on a surface by the coupling of two one-dimensional chains, one with electron-electron interactions to represent the wire and and one with no electron-electron interactions to represent the surface. We use exact diagonalization techniques to calculate the eigenstates and response functions of our model, in order to determine both the nature of the coupling and to what extent the coupling affects the Luttinger liquid properties we would expect in a purely one-dimensional system. We find that while there are indeed Luttinger liquid indicators p…
We investigate spin-charge mixing effect on resonant tunneling in spin-polarized Tomonaga-Luttinger liquid with double impurities. The mixing arises from Fermi velocity difference between two spin species due to Zeeman effect. Zero bias conductance is calculated as a function of gate voltage $V_{\rm g}$, gate magnetic field $B_{\rm g}$, temperature and magnetic field applied to the system. Mixing effect is shown to cause rotation of the lattice pattern of the conductance peaks in $(V_{\rm g},B_{\rm g})$ plane, which can be observed in experiments. At low temperatures, the contour shapes are cl…
Power law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the interacting 1-D electron system. We present a theoretical model which hosts LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from non-local and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is poss…
The renormalization of conductances in a Y junction of spinless Luttinger-liquid wires additionally coupled to acoustic longitudinal phonons is investigated in fermionic representation. This system corresponds to geometry of a tunneling experiment and exhibits the interplay between the Coulomb repulsion and the attractive retarded interaction mediated by phonons. The retardation effects related to the propagation of phonons through the junction with arbitrary transmission and reflection amplitudes are taken into account. The appearing logarithmic corrections to conductances of the junction are…
We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a single point contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of t…
Thermodynamic and transport properties of a two dimensional circular quantum dot are studied theoretically at zero magnetic field. In the limit of a large confining potential, where the dot spectrum exhibits a shell structure, it is argued that both spectral and transport properties should exhibit Luttinger liquid behavior. These predictions are verified by direct numerical diagonalization. The experimental implications of such Luttinger liquid characteristics are discussed.
We study a one-dimensional interacting electron gas with the strong Rashba spin-orbit coupling and Zeeman splitting in a quantum well. A bosonization theory is developed for this system. The tunneling current may deviate from a simple power law which is that in an ordinary Luttinger liquid. The microscopic interacting coupling and the spin-orbital parameter may be measured by varying the external magnetic field in the tunneling experiment.
We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. The rectification effect is the strongest in the absence of the time-reversal symmetry. In that case, the maximal rectification current can be comparable with the total current $\sim e^2V/h$ even for low vo…
One-dimensional wires with Rashba spin-orbit coupling, magnetic field, and strong electron-electron interactions are described by a spiral Luttinger liquid model. We develop a theory to investigate the tunneling density of states into a spiral Luttinger liquid under the proximity effect with superconductors. This approach provides a way to disentangle the delicate interplay between superconducting correlations and strong electron interactions. If the wire-superconductor boundary is dominated by Andreev reflection, we find that in the vicinity of the interface the zero-bias tunneling anomaly re…
We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor, or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it ex…
We develop a theory of tunneling spectroscopy of interacting electrons in a non-equilibrium quantum wire coupled to reservoirs. The problem is modelled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strength, and affects the distribution function of electrons in the wire as well as that of electrons emitted f…
Recent advances in single atom manipulation have made it possible to create "wires" in the form of atomic scale linear structures on a semiconductor surface. If such structures are to be used in future electronic devices, it will be necessary to know to what extent they behave as one-dimensional conductors, in which the presence of electron-electron interactions in the wire lead to properties quite different from those found in higher-dimensional systems. In particular, it would be useful to know if these structures retain any of the Luttinger liquid properties that are predicted for a pure on…
Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger liquid parameter $κ$), while the partitioning of charge is fully determined by $κ$. Moreover, unlike for charge currents, the partitioning of energy current should manifest it…
We study the tunneling current through a mesoscopic two-terminal ring with spin-orbit coupling, which is threaded by a magnetic flux. The electron-electron interaction in the ring is described in terms of a Tomonaga-Luttinger model which also allows us to account for a capacitive coupling between the ring and the gate electrode. In the regime of weak tunneling, we describe how, at temperatures lower than the mean level spacing, the peak positions of the conductance depend on magnetic flux, spin-orbit coupling strength, gate voltage, charging energy, and interaction parameters (charge and spin …
We report Coulomb drag measurements between vertically-integrated quantum wires separated by a barrier only 15 nm wide. The temperature dependence of the drag resistance is measured in the true one-dimensional (1D) regime where both wires have less than one 1D subband occupied. As a function of temperature, an upturn in the drag resistance is observed in three distinct devices at a temperature $T^* \sim 1.6$ K. This crossover in Coulomb drag behaviour is consistent with Tomonaga-Luttinger liquid models for the 1D-1D drag between quantum wires.
Tunneling spectroscopy of one-dimensional interacting wires can be profoundly sensitive to the boundary conditions of the wire. Here, we analyze the tunneling spectroscopy of a wire coupled to capacitive metallic leads. Strikingly, with increasing many-body interactions in the wire, the impact of the boundary noise becomes more prominent. This interplay allows for a smooth crossover from standard 1D tunneling signatures into a regime where the tunneling is dominated by the fluctuations at the leads. This regime is characterized by elevated zero-bias tunneling alongside a universal power-law de…
We develop a detailed theory for spin transport in a one-dimensional quantum wire described by Luttinger liquid theory. A hydrodynamic description for the quantum wire is supplemented by boundary conditions taking into account the exchange coupling between the magnetization of ferromagnetic reservoirs and the boundary magnetization in the wire. Spin-charge separation is shown to imply drastic and qualitative consequences for spin-dependent transport. In particular, the spin accumulation effect is quenched except for fine-tuned parameter regimes. We propose several feasible setups involving an …
We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the non-linear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger li…
We theoretically investigate transport in a spin incoherent one dimensional electron system, which may be realized in quantum wires at low electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi liquid leads attached to the finite length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger Liquid, provided we make the identification $g=2g_c$, where $g$ is the interaction parameter in a spinless Luttinger Liquid and…
We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and transport property as the difference between the two tunneling parameter increases. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with t…
Luttinger liquid theory describes one-dimensional electron systems in terms of non-interacting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is con…
In a recent Rapid Communication (Phys. Rev. B {\bf 63}, 121210(R) (2001)), Haüsler showed that the interaction between electrons in quantum wires may enhance the persistent spin current arising from Rashba spin-orbital coupling. In this Comments, we would like to point out that this 'enhancement' comes from a misunderstanding to the boosting persistent current in the Luttinger liquid theory. A correct calculation will not give such an enhancement of the persistent spin current. Meanwhile, we provide a Luttinger liquid theory with Rashba spin-orbital interaction by bosonization, which may show …
Luttinger liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter K. We suggest a setup to study Luttinger liquid behavior in quantum wires which allows to determine K from two independent measurements: resonant transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two measured values of K for a single probe would provide strong experimental evidence for the Luttinger liquid paradigm.
In a recent work [Phys. Rev. Lett. {\bf 108}, 136401 (2012)] we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a new paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed poin…
We present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with a GaAs/AlGaAs cleaved edge overgrown structure in a strong perpendicular magnetic field. While the 2DEG exhibits typical fractional quantum Hall features of a very high mobility sample, we observe the onset of a non-linear current-voltage characteristic in the vicinity of nu=1. For filling factor nu<1 the system is consistent with a non-Fermi liquid behavior, such as a Luttinger liquid, whereas for nu>1 we observe an Ohmic tunneling resistance between the edge and a three dimen…
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.
We study the nonequlibrium transport through a quantum dot weakly coupled to Luttinger liquids (LL). A general current expression is derived by using nonequilibrium Green function method. Then a special case of the dot with only a single energy level is discussed. As a function of the dot's energy level, we find that the current as well as differential conductance is strongly renormalized by the interaction in the LL leads. In comparison with the system with Fermi liquid (FL) leads, the current is suppressed, consistent with the suppression of the electron tunneling density of states of the LL…
We study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations non perturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the ampl…
The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency $ω$ relative to the ballistic frequency $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Luttinger liquid interaction parameter, and $L$ the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fraction…
We discuss the effects of a strong magnetic field in Quantum Wires. We show how the presence of a magnetic field modifies the role played by % which %coefficients corresponding to electron electron interaction % and the Fermi velocity producing a strong reduction of the backward scattering corresponding to the Coulomb repulsion. We discuss the consequences of this and other effects of magnetic field on the Tomonaga-Luttinger liquids and especially on their power-law behaviour in all correlation functions. The focal point is the rescaling of all the repulsive terms of the interaction between el…
We discuss the violation of spin-charge separation in generic nonlinear Luttinger liquids and investigate its effect on the relaxation and thermal transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We identify basic scattering processes compatible with the symmetry of the problem and conservation laws that lead to the decay of plasmons into the spin modes. We derive a closed set of coupled kinetic equations for the spin-charge excitations and solve the problem of thermal conductance of interacting electrons for an arbitrary relation between the quantum wire length and s…
We study tunneling of weakly-interacting spinless electrons at zero temperature through a single delta-barrier in one-dimensional wires and rings of finite lengths. Our numerical calculations are based on the self-consistent Hartree-Fock approximation, nevertheless, our results exhibit features known from correlated many-body models. In particular, the transmission in a wire of length L at the Fermi level is proportional to $L^{-2α}$ with the universal power $α$ (depending on the electron-electron interaction only, not on the strength of the delta-barrier). Similarly, the persistent current in…
We study the transport properties for a Luttinger-liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. And then the equations of motion for the bosonic phase fields are solved in the Fourier space, with which the both charge and spin conductivities for the system are calculated analytically based on the linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron…
We study a quantum phase transition which occurs in a system composed of two impurities (or quantum dots) each coupled to a different interacting (Luttinger-liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger-liquid parameter is characterized by an abrupt switc…
We present theoretical calculations and experimental measurements which reveal the Luttinger-liquid (LL) nature of elementary excitations in a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can be accounted for by spin-charge separation of the elementary e…
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a sp…
A novel method for detecting Luttinger-liquid behavior is proposed. The idea is to measure the tunneling conductance between a quantum wire and a parallel two-dimensional electron system as a function of both the potential difference between them, $V$, and an in-plane magnetic field, $B$. We show that the two-parameter dependence on $B$ and $V$ allows for a determination of the characteristic dependence on wave vector $q$ and frequency $ω$ of the {\it spectral function}, $A_{\rm LL}(q,ω)$, of the quantum wire. In particular, the separation of spin and charge in the Luttinger liquid should mani…
We study a system consisting of a junction of N quantum wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons close to the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group equations for the Kondo couplings of the spin to the electronic modes on different wires, and analyze the renormalization group flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We gen…
We report experimental temperature dependence of the amplitude of Aharonov-Bohm oscillations in the Laughlin quasiparticle interferometer. The results fit very well the thermal dephasing dependence predicted for a g = 1/3 chiral Luttinger liquid interferometer, and are clearly distinct from the activated behavior observed in single-particle resonant tunneling and Coulomb blockade devices. The small deviation from the zero-bias theory seen below 20 mK indicates yet unrecognized source of experimental decoherence, not included in theory.
