Renormalization of the one-dimensional conductance in the Luttinger-liquid model

Ponomarenko, V. V.

doi:10.1103/physrevb.52.r8666

Cited by 329 publications

(344 citation statements)

References 9 publications

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“…Interaction effects have been considered for some time, especially in the framework of the 1D Tomonaga-Luttinger model, where it is predicted that the conductance is renormalized to G = ␥͑2e 2 / h͒, with a parameter ␥ Ͼ 1 for attractive interactions, ␥ Ͻ 1 for repulsive interactions, and ␥ = 1 for a noninteracting electron gas. [4][5][6] However, it has been argued [7][8][9][10][11] that ␥ should be unity, since the measured conductance is determined by the noninteracting electrons which are injected in the wire.…”

Section: Introductionmentioning

confidence: 99%

Ground state structure and conductivity of quantum wires of infinite length and finite width

et al. 2005

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We have studied the ground state structure of quantum strips within the local spin-density approximation, for a range of electronic densities between ϳ5 ϫ 10 4 and 2 ϫ 10 6 cm −1 and several strengths of the lateral confining potential. The results have been used to address the conductance G of quantum strips. At low density, when only one subband is occupied, the system is fully polarized and G takes a value close to 0.7͑2e 2 / h͒, decreasing with increasing electron density in agreement with experiments. At higher densities the system becomes paramagnetic and G takes a value near ͑2e 2 / h͒, showing a similar decreasing behavior with increasing electron density. In both cases, the physical parameter that determines the value of the conductance is the ratio K / K 0 of the compressibility of the system to the free one.

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Section: Introductionmentioning

confidence: 99%

Ground state structure and conductivity of quantum wires of infinite length and finite width

et al. 2005

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“…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.…”

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Junctions of multiple quantum wires with different Luttinger parameters

et al. 2012

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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.

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“…Here, U is the strength of the Coulomb interaction between neighboring electrons and E F is the Fermi energy. Later works [17][18][19], however, considered a more realistic wire of ÿnite length that is connected to large, Fermi-liquid like, reservoirs at both ends. In the clean limit, the contact resistance to the reservoirs dominates the conductance and the universal value, g 0 , is restored.…”

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Multi-terminal ballistic transport in one-dimensional wires

Picciotto¹,

Störmer

Yacoby

et al. 2000

Physica E: Low-dimensional Systems and Nanostructures

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Recent experiments (Yacoby et al., Phys. Rev. Lett. 77 (1996) 4612; Solid State Commun. 101 (1997) 77; M. Rother et al., ICPS-24, Th-P137) have shown non-universal conductance quantization in one-dimensional wires that are fabricated using the cleaved edge overgrowth technique (L.N. Pfei er et al., Microelectronics J. 28 (1997) 817). In one of the papers (Yacoby et al., Phys. Rev. Lett. 77 (1996) 4612), it was speculated that the origin of the reduced conductance lies in the interface between the one-dimensional wire and the two-dimensional electron gas regions, which serve as ohmic contacts and thermal reservoirs. Here we report the results of a systematic study of such 2D-1D interfaces. By embedding a 2D-1D interaction section region of controllable length inside an otherwise isolated wire, we were able to study the properties of the coupling between these two subsystems. Our results show that 2D-1D interface is in fact the origin of the non-universal conductance. ? 2000 Elsevier Science B.V. All rights reserved. One-dimensional electronic systems, the so-called Luttinger-liquids, are expected to show unique transport properties as a consequence of the Coulomb interaction between carriers [1][2][3][4][5][6][7]. In contrast to Fermi liquid theory [8][9][10][11][12], the Luttinger model predicts that even the weakest impurity embedded in an otherwise perfectly clean 1D wire will completely suppress its conductance at zero temperature. Furthermore, the tunneling conductance into such a perfect wire will also be completely suppressed at zero temperature. * Corresponding author.One of the ÿngerprints of a clean non-interacting 1D conductor is its quantized conductance in multiples of the universal value g 0 = 2e 2 =h. This quantization results from an exact cancellation of the increasing electron velocity and the decreasing density of states as the carrier density increases [13][14][15][16]. Therefore, as subsequent 1D electronic subbands are ÿlled with electrons the conductance increases in a series of plateaus (or steps) with values equal to g 0 multiplied by the number of occupied wire modes. Surprisingly, the inclusion of interactions does not alter this prediction. Early papers [4 -7], considering inÿnitely long wires, did in fact predict quantization 1386-9477/00/$ -see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 -9 4 7 7 ( 9 9 ) 0 0 0 9 7 -1

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Renormalization of the one-dimensional conductance in the Luttinger-liquid model

Cited by 329 publications

References 9 publications

Ground state structure and conductivity of quantum wires of infinite length and finite width

Ground state structure and conductivity of quantum wires of infinite length and finite width

Junctions of multiple quantum wires with different Luttinger parameters

Multi-terminal ballistic transport in one-dimensional wires

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