Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. II. Transport properties

Guigou, M.; Martin, Thierry; Crépieux, Adeline

doi:10.1103/physrevb.80.045421

Cited by 9 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, a single TLL can have inhomogeneities: e.g., a contact between an interacting TLL and a Fermi-liquid lead, a key ingredient of most transport measurements, is often studied as an inhomogeneous TLL wire smoothly interpolating between interacting (TLL) and noninteracting (Fermi-liquid) regions or as a two-wire junction with the Luttinger parameter abruptly changing at the junction. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] A junction of three quantum wires with different Luttinger parameters has been studied in the weak coupling regime. 21,[57][58][59] The experimental importance of junctions of TLL wires with generally unequal Luttinger parameters motivates an in-depth study of their properties, which is the main objective of the present paper.…”

mentioning

confidence: 99%

Junctions of multiple quantum wires with different Luttinger parameters

et al. 2012

View full text Add to dashboard Cite

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 numerical results show very good agreement with the analytical predictions. For three spinless wires, i.e., a Y junction, we analytically determine the full phase diagram, and compute all fixed-point conductances as a function of the three Luttinger parameters.

show abstract

mentioning

confidence: 99%

Junctions of multiple quantum wires with different Luttinger parameters

et al. 2012

View full text Add to dashboard Cite

show abstract

“…It allows us to calculate explicitly the Green's function of the wire. The effect of the screening on the spectral properties was then presented, whereas the effect on the transport properties will be presented in a separate paper 33 .…”

Section: Discussionmentioning

confidence: 99%

“…Technical details are given in appendices. The calculation of transport properties such as current and finite-frequency noise will be presented in a separate paper 33 .…”

Section: Introductionmentioning

confidence: 99%

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

2009

Self Cite

View full text Add to dashboard Cite

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when Kc > 1/2 and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunnel density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.PACS numbers:

show abstract

“…Off diagonal elements G φθ and G θφ are for instance unavoidable in transport problems involving the injection of electrons in the bulk of LLs. [23,24,25,26,27] In the present "extended" impurity problem, all Green's functions are needed because the impurity action contains both fields θ and φ [see Eq. ( 12) below].…”

Section: Euclidean Action and Green's Functionsmentioning

confidence: 99%

Renormalization flow of a weak extended backscattering Hamiltonian in a non-chiral Tomonaga–Luttinger liquid

Popoff¹,

Lebedev²,

Raymond³

et al. 2021

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We consider a non-chiral Luttinger liquid in the presence of a backscattering Hamiltonian which has an extended range. Right/left moving fermions at a given location can thus be converted as left/right moving fermions at a different location, within a specific range. We perform a momentum shell renormalization group treatment which gives the evolution of the relative degrees of freedom of this Hamiltonian contribution under the renormalization flow, and we study a few realistic examples of this extended backscattering Hamiltonian. We find that, for repulsive Coulomb interaction in the Luttinger liquid, any such Hamiltonian contribution evolves into a delta-like scalar potential upon renormalization to a zero temperature cutoff. On the opposite, for attractive couplings, the amplitude of this kinetic Hamiltonian is suppressed, rendering the junction fully transparent. As the renormalization procedure may have to be stopped because of experimental constraints such as finite temperature, we predict the actual spatial shape of the kinetic Hamiltonian at different stages of the renormalization procedure, as a function of the position and the Luttinger interaction parameter, and show that it undergoes structural changes. This renormalized kinetic Hamiltonian has thus to be used as an input for the perturbative calculation of the current, for which we provide analytic expressions in imaginary time. We discuss the experimental relevance of this work by looking at one-dimensional systems consisting of carbon nanotubes or semiconductor nanowires.

show abstract

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. II. Transport properties

Cited by 9 publications

References 24 publications

Junctions of multiple quantum wires with different Luttinger parameters

Junctions of multiple quantum wires with different Luttinger parameters

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

Renormalization flow of a weak extended backscattering Hamiltonian in a non-chiral Tomonaga–Luttinger liquid

Contact Info

Product

Resources

About