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arXiv:cond-mat/0004146 · Physical Review Letters

Where is the Luttinger Liquid in One-Dimensional Semiconductor Quantum Wire Structures?

D. W. Wang, Andrew J. Millis, S. Das Sarma

Published Nov 20, 2000• 30 citations
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Abstract

We present the theoretical basis for analyzing resonant Raman scattering experiments in one-dimensional systems described by the Luttinger-liquid fixed point. We make experimentally testable predictions for distinguishing Luttinger liquids from the Fermi liquid and argue that presently available quantum wire systems are not in the regime where Luttinger-liquid effects are important.

DOI
10.1103/physrevlett.85.4570

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We present the theoretical basis for analyzing resonant Raman scattering experiments in one-dimensional systems described by the Luttinger-liquid fixed point. We make experimentally testable predictions for distinguishing Luttinger liquids from the Fermi liquid and argue that presently available quantum wire systems are not in the regime where Luttinger-liquid effects are important.
A theory of resonant Raman scattering spectroscopy of one-dimensional electronic systems is developed on the assumptions that (i) the excitations of the one-dimensional electronic system are described by the Luttinger-liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one-dimensional electronic system, and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a ``double-peak'' structure with the lower peak involving multispinon excitations with total spin S=0S=0S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power-law dependence, involving the Luttinger-liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the ``Luttinger-liquid'' and ``Fermi-liquid'' calculations of resonant Raman spectroscopy (RRS) spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger-liquid features which may be observed in future RRS experiments.
Recent advances in single atom manipulation have made it possible to create "wires" in the form of atomic scale linear structures on a semiconductor surface. If such structures are to be used in future electronic devices, it will be necessary to know to what extent they behave as one-dimensional conductors, in which the presence of electron-electron interactions in the wire lead to properties quite different from those found in higher-dimensional systems. In particular, it would be useful to know if these structures retain any of the Luttinger liquid properties that are predicted for a pure one-dimensional metal. However, experimental studies of such structures have so far yielded unclear and contradictory results. We investigate this problem theoretically by creating a highly simplified model of a wire on a surface--a chain of atoms that includes electron-electron interactions to represent the wire, coupled to a similar chain that excludes electron-electron interactions to represent, albeit crudely, the surface. We present results for the eigenstates and spectral functions for such systems that suggest that many Luttinger liquid indicators are present. However the system as a whole retains some residual Fermi liquid characteristics, and therefore merges properties of both one and higher dimensions.
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In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.