Transport and elementary excitations of a Luttinger liquid

Content Provider	Semantic Scholar
Author	Cuniberti, Gianaurelio Sassetti, Maura Kramer, Bernhard K.
Copyright Year	1995
Abstract	The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to chargewave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and aquantum inductance . Recently, frequencyand time-dependent electrical transport processes in nanostructures have become a subject at which increasing experimental effort has been directed [1, 2]. Since they provide insight into the elementary excitations of these systems of geometrically confined interacting electrons, such investigations are of great fundamental interest. In addition, potential applications of nanostructures in future electronic devices, which will have to be operated at very high frequencies, require detailed knowledge of their ACtransport behaviour. The theory of AC quantum transport has been mostly restricted to non-interacting electrons [3, 4], and to driven systems [5, 6]. Coulomb repulsion was partly taken into account by including a classical charging term [7]. On the other hand, in the DC transport through quantum dots, correlation effects were shown to be of great importance [8]. In view of the quantum nature of the systems, which has to be properly taken into account in transport theory, the study of the AC-transport properties of a Luttinger modelshould be of considerable interest [9], since the latter is a paradigmatic example of a correlated electron system. We explore in this paper the linear AC transport in the Luttinger system with a long-range interaction . We show that the conductance, 0(ω), is a product of two functions. One of them is the inverse of the derivative of the dispersion relation of the collective excitations. The other is given by the Fourier transform of the applied electric probe field. Our result implies that a short-range interaction does not lead to qualitative changes in the the behaviour of 0(ω) as compared with the non-interacting limit. Only its magnitude, and the Fermi velocity, vF , are scaled byg andg−1, respectively, whereg−2 is the interaction strength. For strong and long-range interaction, the presence of a plasmon-like charge-wave mode in the dispersion 0953-8984/96/020021+06$19.50c © 1996 IOP Publishing Ltd L21 L22 Letter to the Editor relation [10] leads to a resonance in 0(ω) at ωp ∝ vF /λg, whereλ is the ‘effective range’ of the interaction. We will see below that the resonance is independent of the shape of the electrical probe field if the range of the latter̀ < λ. The resonance should be observable in an experiment. In fact, Raman scattering measurements on quantum wires [11] were interpreted within such a picture. Here, we want to point out that one can detect the resonance at temperatures lower thanωp by anAC-conductance experiment . This would provide evidence for the Luttingerliquid nature of electrons in quantum wires [12] or of the edge states in the fractional quantum Hall [6] effect without relying on determinations of temperature dependences. In addition, we show that for sufficiently strong and long-range interaction the results can be understood in terms of a quantum capacitanceand aquantum inductance , C ≡ C0 g 2 λ , L ≡ L0 λ, in analogy with a classical wire ( C0, L0 constants). For the microscopic understanding of the Coulomb blockade effect [13] in submicrometre tunnel contacts such quantities are of crucial importance. In previous theories, they were introduced phenomenologically. The important message of this letter is that for a system to show capacitive behaviour, the interaction should be long range. The Luttinger liquid is a model for the low-energy excitationsof one-dimensional (1D) interacting electrons [14]. Its major importance is that the excitation spectrum can be calculated analytically, as can many other properties, like the linear conductivity, even in the presence of perturbing potentials [9]. The main assumptions are: (1) linearization of the free-electron dispersion relation near the Fermi level; and (2) extension of the energy spectrum to include negative energies. For spinless particles, the subject of this letter, with interactionV (x) = V0 δ(x) and neglecting backward scattering, the Hamiltonian is H = h̄vF 2g ∫ R 0 dx ( g5(x) + 1 g ( ∂
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Language	English
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Subject Keyword	Adjudication Arabic numeral 0 Conductance (graph) Electric Capacitance Electron Electrons Emoticon Energy, Physics Excitation Experiment Femtometer Interaction Intermediate-Conductance Calcium-Activated Potassium Channels Light transport theory Nanostructured Materials Observable Plasmon Quantity Quantum Hall effect Quantum capacitance Quantum dot Quantum number Quantum wire Quasiparticle Raman scattering Resonance Velocity (software development)
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