Luttinger liquids

Tomonaga-Luttinger liquid state [14-16], unconventional superconductivity [17], etc. These molecular conductors once used to be called organic metals, but nowadays this terminology has become obsolete in order to avoid possible confusion with organometallies. ... 

The authors use optical spectroscopy of gate-induced charge carriers to show that, at low temperature and small lateral electric field, charges become localized onto individual molecules in shallow trap states, but that at moderate temperatures an electric field is able to detrap them, resulting in transport that is not temperature-activated. This work demonstrates that transport in such systems can be interpreted in terms of classical semiconductor physics and there is no need to invoke onedimensional Luttinger liquid physics [168]. 

Summary. We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different. 

The only source of drag in the Luttinger liquid is interwire backscattering, associated with a large momentum transfer between the wires. The model predicts a distinctive temperature dependence of the corresponding contribution... 

The parameter A here is related to the conventional interaction parameter g of the Luttinger liquid g = 1/A. This relation follows from the definition g = vp/u in terms of the velocity of the collective mode (plasmon) u, and its value u = (7m/m)A in the Calogero-Sutherland model [14, 13]. For the rational values of A and at T = 0 the density-density correlation function is known exactly [14, 13]. Due to the integrability of the model, Ai k,w) 0 only in a finite interval of u> around u> = Uik [15]. We found this interval for k < 27rnj ... 

It is thus desirable to examine the resonant tunneling in a Luttinger liquid in a broad range of temperature down to T = 0 and for various parameters of the barriers. Our purpose in this paper is to analyze transport through a double barrier of arbitrary strength, strong or weak, symmetric or asymmetric, within a general analytical method applicable to all these situations. 

Transport in one-channel quantum wires, where electrons form a Luttinger liquid, differs significantly from the Fermi liquid case. In particular, impurity effects are stronger in Luttinger liquids, and even a weak impurity potential... 

The above Hartree-Fock argument provides a qualitatively correct picture at small g but underestimates fluctuations in Luttinger liquids. As shown below, the ratchet current growth at small voltages differs from our estimate ... 

More generally, one dimensional correlated electron systems appear over the years as a growing and important field in condensed matter theory. One main reason of that comes from the fact that these systems serve as a theoretical laboratory to explore new methods of solution, analytically or numerically. A second main reason - we would say more physical - comes from the fact that over the years, more and more experimental realisations of these systems appear. New concepts emerge from such studies as the ones included in the phenomenology of Luttinger-liquids [18],... 

Otherwise, the umklapp interaction flows to zero and the fixed points g, g are as before. One also has z 1( ) -0, where 0 = ( , g, g )/4, that is, 0 = I in both the repulsive and attractive sectors. This again confirms the existence of the Luttinger liquid ground state. Figure 5 shows how the phase diagram of Fig. 4 is modified in the presence of umklapp. 

Spin and charge excitations are thus decoupled by coulombic interactions in the one-dimensional electron gas. However, the one-dimensional Fermion system is not a Fermi liquid, as indicated by the behavior of the momentum distribution function, which does not exhibit a Fermi step at kF and presents a single-particle density of states vanishing according to a power law singularity at EF. This is a Luttinger liquid [29] with... 

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