Quantum Wires: Interacting Quantum Liquids

Abstract

In 1989, the first inelastic light scattering experiments on electronic excitations in quantum wires were reported [1, 2]. Since then, a number of experimental papers appeared about, e.g., many–particle interactions and selection rules in those systems [3, 4, 5, 6, 7, 8, 9] and investigations with applied external magnetic field [10, 11, 12]. All these experiments were performed on lithographically–defined GaAs–AlGaAs structures. Consequently, the lateral sizes of these structures were on the order of 100 nm, or at least not much below [8, 9]. Unlike for the case of quantum dots, there is no well– established method of self–organized growth of modulation–doped quantum wires. During the past few years, Carbon nanotubes have evolved as new and alternative quantum–wire structures. So far, the main focus in the investigation of those very promising quantum structures by optical experiments has been on phonon excitations [13]. Phonon Raman spectroscopy has greatly helped in unveiling the topological structure of Carbon nanotubes [13]. An interesting further method to produce very narrow wires with atomic–layer precision is the so called cleaved–etched overgrowth (CEO) [14]. However, with CEO it is difficult to grow very large arrays of wires, which would be necessary to get enough signal strength in inelastic light scattering experiments. Hence, there are so far no reports of inelastic light scattering experiments on CEO wires, though these might be promising structures for high–sensitivity experiments. As mentioned, most of the existing experimental reports are on lithographically–defined GaAs–AlGaAs quantum wires with rather mesoscopic widths. Hence, in those experimental structures, typically several Q1D subbands are occupied with electrons. In this chapter we will discuss both, experiments and calculations on such samples. The main focus will be on the microscopic origin of confined plasmons and interesting internal interaction effects in a magnetic field. These experimental results are described well within the RPA, i.e., a Fermi–liquid theory, as we will see later.