Coulomb-blockade oscillations in disordered quantum wires

The conductance of narrow wires, defined by a split-gate technique in the two-dimensional electron gas in a modulation-doped GaAs-${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructure, is studied experimentally as a function of gate voltage, temperature, and magnetic field. Both intentionally (Be doped) and unintentionally disordered wires are investigated. Periodic conductance oscillations as a function of gate voltage are found in both systems, in the regime where only a few hundred electrons are present in the wire. The dominant oscillations are very regularly spaced, with a period that is quite insensitive to a strong magnetic field, and persist up to a few kelvin. A strong magnetic field is found to enhance the amplitude of the oscillations up to values approaching ${\mathit{e}}^2$/h. The experimental data are analyzed in terms of a theory for Coulomb-blockade oscillations in the conductance of a quantum dot in the regime of comparable level spacing ΔE and charging energy ${\mathit{e}}^2$/C, based on the assumed presence of a conductance-limiting segment in the wire. Good agreement with the experiment is obtained for the temperature dependence of the oscillations, using physically reasonable parameter values. At low temperatures, a crossover from the classical regime ${\mathit{k}}_{\mathit{B}}$T≳ΔE to the quantum regime ${\mathit{k}}_{\mathit{B}}$T≲ΔE is found. The appearance of additional periodicities and the onset of irregular oscillations at very low temperatures in some of the wires are attributed to the presence of multiple segments. No magnetoconductance oscillations are observed, in support of the recently predicted Coulomb blockade of the Aharonov-Bohm effect.