Luttinger-liquid-like transport in long InSb nanowires

Abstract

Long nanowires of degenerate semiconductor InSb in asbestos matrix (wire diameter is around 50 A, length 0.1 -1 mm) were prepared. Electrical conduction of these nanowires is studied over a temperature range 1.5 -350 K. It is found that a zero-field electrical conduction is a power function of the temperature G ∝ T α with the typical exponent α ≈ 4. Current-voltage characteristics of such nanowires are found to be nonlinear and at sufficiently low temperatures follows the power law I ∝ V β . It is shown that the electrical conduction of these nanowires cannot be accounted for in terms of ordinary single-electron theories and exhibits features expected for impure Luttinger liquid. For a simple approximation of impure LL as a pure one broken into drops by weak links, the estimated weak-link density is around 10 3 − 10 4 per cm. Electron-electron correlation effects being negligible in three-dimensional case play the dominant role in one dimension. As a result, the physical properties of a onedimensional (1D) metal are expected to be dramatically different from properties of usual metals with a Fermi liquid of electrons. One of the main consequences of the electron-electron Coulomb repulsive interaction is the decrease of the energy density of states around the Fermi energy. The resulting electron state depends on details of electron-electron interaction. In the absence of the long-range interaction an 1D electron liquid (so-called "Luttinger liquid" [5] (LL)) is formed, whereas longrange Coulomb interaction leads to 1D Wigner crystal [6]. Transport properties of 1D electron systems are the subject of very high interest. It was shown that in Coulomb blockade systems the tunnelling transparency of a barrier vanishes due to electron-electron interaction resulting to the power-law zero-bias anomaly for the conduction [7] (see also [8]). For the particular case of LL similar result was also obtained by more strong methods [2][3][4]9,10]. A role of impurity scattering in the presence of shortrange [4,11] and long-range [10,12] interactions was also intensively studied.Luttinger-liquid-like behaviour for tunnelling into fractional Hall edge states predicted in [9] was recently observed in a GaAs-Al 0.1 Ga 0.9 As heterostructure in quantum Hall regime with the filling factor 1/3 [13]. However each of these edge states have properties of so-called "chiral Luttinger liquid" but not those of LL. They are similar but not identical. Luttinger-liquid behaviour was predicted also for carbon nanotubes [15,16]. Small (below one order of magnitude) voltage and temperature variations of the conductance of single-walled nanotubes consistent with the expectations for LL were observed experimentally [14].In the present paper we report an electric conduction of InSb nanowires in an asbestos matrix. It has been found that it follows the power law over 5 orders of conduction variation and can be described as conduction of a pure LL broken into drops by weak links, the estimated weak-link density being around 10 3 − 10 4 per cm. Natural as...

Polymer Nanofibers and Nanotubes: Charge Transport and Device Applications

“…However, as can be seen from Table 1, for all the polymer fibers under consideration β ≠ α + 1, and, moreover, β is always less than α, which can not be explained by the LL or ECB theory. [53] The same disagreement with a pure LL model has been found for inorganic 1D nanowires [54,55] and can be associated with the fact that a LL in the presence of disorder may not exhibit features typical for a clean case. [61] The interchain interactions may cause a renormalization of the exponents at high temperatures, whereas interchain hopping destroys the LL state at low temperatures.…”

“…[48] A The LL state survives for a few 1D chains coupled by Coulomb interactions, and can be stabilized in the presence of impurities for more than two coupled 1D chains. [49,50] According to the LL theory, I-V curves taken at different temperatures should be fitted by the general equation: [52,53] and doped semiconductor nanowires of InSb (α ~ 2-7, β ~ 2 -6) [54] and NbSe 3 (α ~ 1 -3, β ~ 1.7 -2.7), [55] and for fractional quantum Hall edge states in GaAs (α, β ~ 1.4 -2.7). [56] The LL, WC or Environmental Coulomb blockade (ECB) [53] models are currently debated in order to explain the above-mentioned power-law behavior in 1D systems.…”

“…[52][53][54][55][56] It is evident that polymer nanofibers and nanotubes differ from 1D carbon nanotubes and semiconductor nanowires.…”

One-Dimensional Conduction in Charge-Density-Wave Nanowires

“…This power-law behavior has been observed in various 1D systems, such as ballistic single-wall [4] and diffusive multi-wall carbon nanotubes [5], degenerately doped semiconductor nanowires [6], and fractional quantum Hall edge states [7]. Each of these systems revealed new behavior, but also raised questions.…”

Quantum interference and spin-charge separation in a disordered Luttinger liquid

“…21,22 The LL nature of these strongly correlated quantum wires has been supported by a wealth of experimental findings. 8,9,10,11,12,13,14,15,16,19,20,21,22 Another class of strongly-correlated quantum wires that has recently attracted a lot of interest is ultracold atomic gases confined to 1D geometry, for review see Ref. 23.…”