Symmetric, gated, ballistic rings as tunable electron interferometers

Linear and nonlinear transport in a small charge-tunable open quantum ring

“…In quasiballistic larger rings, the energy scale, given by a 2π AB phase change linking successive low-resistance squares (diamond-shaped top and low corners), can be determined by the Thouless energy. 6 In the nonlinear regime (Fig. 3), further deviations from the single-particle model are observed: (i) lack of phase jumps while loading electrons at zero magnetic field, (ii) linear phase (period) evolution depending on the magnetic-field direction, (iii) magnetic-field asymmetry of the AB-oscillation amplitude.…”

“…The modification of the effective radius due to the ring's finite width is a determining factor for the observation of several AB frequencies as previously reported. 6,19 In our ring, the available number of electrons can be accommodated in the first sub-band, and the measured AB oscillations only reproduce single-mode features. Thus, we will focus our discussion below using E F = 15 meV where the calculated single-mode resistance displays low-resistance lines in diamond shapes around a high-resistance core for the closed ring.…”

“…This phenomenon appears in transport measurements as a modulation with period πr 2 0 /(h/e) in B when passing a current through the ring connected to multiple leads. Also, it is possible to realize additional tuning of electron interference in the ring by gate voltage 3,6,7 and dc bias. 8 For a ring interferometer, the Casimir-Onsager relation implies that the AB-oscillation phase must remain rigid to obey symmetry rules in the magnetic field, so it can only change in π jumps.…”

“…8 For a ring interferometer, the Casimir-Onsager relation implies that the AB-oscillation phase must remain rigid to obey symmetry rules in the magnetic field, so it can only change in π jumps. 6,9,10 While this relation does not hold out of equilibrium, it has been predicted to be an asymmetric component for mesoscopic conductors in different configurations. [11][12][13] This question has been addressed for several systems, such as rings, 14,15 quantum dots, 16,17 and carbon nanotubes.…”

“…18 In a quantum ring, AB oscillations can be mapped onto the details of the confining potential and on the related energy-shell-structure properties. 6,19 The possibility to extend the single-electron modeling for many-electron semiconductor rings has been demonstrated experimentally. 20 The energy spectra for closed quantum rings were measured by magnetotransport in the rings containing about 200 electrons (two to three radial sub-bands).…”