Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1803.07359 · Physical review. B./Physical review. B

Conductance of fractional Luttinger liquids at finite temperatures

P. P. Aseev, Daniel Loss, Jelena Klinovaja

Published Jul 16, 2018• 12 citations
arXivHTMLPDF

Abstract

We study the electrical conductance in single-mode quantum wires with Rashba spin-orbit interaction subjected to externally applied magnetic fields in the regime in which the ratio of spin-orbit momentum to the Fermi momentum is close to an odd integer, so that a combined effect of multi-electron interaction and applied magnetic field leads to a partial gap in the spectrum. We study how this partial gap manifests itself in the temperature dependence of the fractional conductance of the quantum wire. We use two complementing techniques based on bosonization: refermionization of the model at a particular value of the interaction parameter and a semiclassical approach within a dilute soliton gas approximation of the functional integral. We show how the low-temperature fractional conductance can be affected by the finite length of the wire, by the properties of the contacts, and by a shift of the chemical potential, which takes the system away from the resonance condition. We also predict an internal resistivity caused by a dissipative coupling between gapped and gapless modes.

DOI
10.1103/physrevb.98.045416

Related papers

Conductance through contact barriers of a finite-length quantum wire

Siddhartha Lal, Sumathi Rao, Diptiman Sen

We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature, and a magnetic field, on the conductivity. We explain the deviations of the conductivity from ${2Ne}^{2}/h$ in wires that are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin-split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin valve that only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.

arXiv:cond-mat/0104402•Physical review. B, Condensed matter•Apr 22, 2002•13 citations

Conductance of a Quantum Wire in the Wigner-Crystal Regime

К. А. Матвеев

We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T<<J this effect is small, and the conductance of the wire remains close to 2e2/h. At T>>J the spin effect reduces the conductance to e2/h.

arXiv:cond-mat/0310261•Physical Review Letters•Mar 9, 2004•184 citations

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

Georg W. Winkler, Martin Ganahl, Dirk Schuricht +2 more

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s -wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with SO interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton–antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

arXiv:1701.03793•New Journal of Physics•Apr 28, 2017•11 citations

Transmission through a potential barrier in Luttinger liquids with a topological spin gap

Nikolaos Kainaris, Sam T. Carr, A. D. Mirlin

We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy theory is gapped by interaction (Luther-Emery liquid). There are two distinct phases of this nature, of which one is of particular interest as it exhibits nontrivial interaction-induced topological properties. Focusing on this phase and using bosonization and an expansion in the tunneling strength we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state-mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping this fractional spin, single electrons can tunnel across the impurity even though the bulk spectrum for spin excitations is gapped. This results in a finite LDOS below the bulk gap and in a nonmonotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase, which combines features of a topological spin insulator and a topological charge metal, in which the topology can be probed by measuring transport properties.

arXiv:1709.08965•Physical review. B./Physical review. B•Mar 2, 2018•13 citations

Conductance of one-dimensional quantum wires

Ken‐Ichiro Imura, K.-V. Pham, Pascal Lederer +1 more

We discuss the conductance of quantum wires in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization-group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of bulk contact the leading-order corrections to the conductance for two different boundary conditions, which reproduce in the absence of bulk contact, respectively, the standard 2T source-drain (SD) conductance ${G}_{\mathrm{SD}}^{(2)}{=e}^{2}/h$ and ${G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,$ where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance ${G}_{\mathrm{SD}}^{(3)}$ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.

arXiv:cond-mat/0111358•Physical review. B, Condensed matter•Jul 11, 2002•37 citations

Resonant heat transport through a Luttinger liquid

Ilya V. Krive

Thermal transport through one-dimensional systems of strongly interacting electrons is studied in two cases: (i) a finite Luttinger liquid (LL) wire containing a strong impurity, and (ii) a LL ring connected by quantum wires to noninteracting electron reservoirs. It is shown that, for (i), a temperature-induced resonant transport takes place under certain conditions. In case (ii) the heat conductance under resonance conditions does not depend on the electron-electron interaction and the system thermal conductance coincides with the maximal Fermi-liquid thermal value.

Physical review. B, Condensed matter•May 15, 1999•9 citations
We study the electrical conductance in single-mode quantum wires with Rashba spin-orbit interaction subjected to externally applied magnetic fields in the regime in which the ratio of spin-orbit momentum to the Fermi momentum is close to an odd integer, so that a combined effect of multi-electron interaction and applied magnetic field leads to a partial gap in the spectrum. We study how this partial gap manifests itself in the temperature dependence of the fractional conductance of the quantum wire. We use two complementing techniques based on bosonization: refermionization of the model at a particular value of the interaction parameter and a semiclassical approach within a dilute soliton gas approximation of the functional integral. We show how the low-temperature fractional conductance can be affected by the finite length of the wire, by the properties of the contacts, and by a shift of the chemical potential, which takes the system away from the resonance condition. We also predict an internal resistivity caused by a dissipative coupling between gapped and gapless modes.
We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature, and a magnetic field, on the conductivity. We explain the deviations of the conductivity from 2Ne2/h{2Ne}^{2}/h2Ne2/h in wires that are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin-split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin valve that only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.
We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T<<J this effect is small, and the conductance of the wire remains close to 2e2/h. At T>>J the spin effect reduces the conductance to e2/h.
We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s -wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with SO interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton–antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.
We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy theory is gapped by interaction (Luther-Emery liquid). There are two distinct phases of this nature, of which one is of particular interest as it exhibits nontrivial interaction-induced topological properties. Focusing on this phase and using bosonization and an expansion in the tunneling strength we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state-mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping this fractional spin, single electrons can tunnel across the impurity even though the bulk spectrum for spin excitations is gapped. This results in a finite LDOS below the bulk gap and in a nonmonotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase, which combines features of a topological spin insulator and a topological charge metal, in which the topology can be probed by measuring transport properties.
We discuss the conductance of quantum wires in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization-group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of bulk contact the leading-order corrections to the conductance for two different boundary conditions, which reproduce in the absence of bulk contact, respectively, the standard 2T source-drain (SD) conductance GSD(2)=e2/h{G}_{\mathrm{SD}}^{(2)}{=e}^{2}/hGSD(2)​=e2/h and GSD(2)=ge2/h,{G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,GSD(2)​=ge2/h, where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance GSD(3){G}_{\mathrm{SD}}^{(3)}GSD(3)​ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.
Thermal transport through one-dimensional systems of strongly interacting electrons is studied in two cases: (i) a finite Luttinger liquid (LL) wire containing a strong impurity, and (ii) a LL ring connected by quantum wires to noninteracting electron reservoirs. It is shown that, for (i), a temperature-induced resonant transport takes place under certain conditions. In case (ii) the heat conductance under resonance conditions does not depend on the electron-electron interaction and the system thermal conductance coincides with the maximal Fermi-liquid thermal value.