Conductance of one-dimensional quantum wires

Abstract

We discuss the conductance of quantum wires (QW) 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 (2) SD = e 2 /h and G (2) SD = 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 shows an UV-relevant deviation from the above two values, suggesting new fixed points in the ohmic limit. Non-trivial scaling exponents are predicted as a result of electron fractionalization.

Long-lived binary tunneling spectrum in the quantum Hall Tomonaga-Luttinger liquid

“…The interaction between counterpropagating channels generates small amount of dragged charges reverse-travelling in the subsidiary channels (charge fractionalization), as illustrated by coupled wave packets in Fig. 1(a) [24,32,33].…”

Junctions of multiple quantum wires with different Luttinger parameters

“…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.…”

Charge fractionalization in nonchiral Luttinger systems

“…When an electron is injected in the bulk of a quantum wire at a given Fermi point, say, −k F , this gives rise to two counterpropagating pieces which carry charge f e and (1 − f )e, respectively, where f = (1 + g)/2 [8,9,10,11,12]. We have shown that the ratio between the asymmetry A S = (I L − I R )/I S and the two-terminal conductance G 2 in the almost equilibrium regime, where the applied bias voltages are small compared to k B T /e, allows to construct a novel dimensionless ratio reflecting the charge fractionalization phenomenon,…”

“…Firstly, we introduce the chiral fields of nonchiral Luttinger liquids [1,8,9,11,15,27]. It is indeed convenient to distinguish the charge excitations propagating to the left (−) from the charge excitations propagating to the right (+).…”

“…This fractional charge is not just a statistical average, but is predicted to be a definite property of the quantum mechanical state, subject in principle to verification by repeated measurements after a single tunneling event [8,9,10,11,12].…”