Crossover from ‘mesoscopic’ to ‘universal’ phase for electron transmission in quantum dots

Abstract

The measurement of phase in coherent electron systems--that is, 'mesoscopic' systems such as quantum dots--can yield information about fundamental transport properties that is not readily apparent from conductance measurements. Phase measurements on relatively large quantum dots recently revealed that the phase evolution for electrons traversing the dots exhibits a 'universal' behaviour, independent of dot size, shape, and electron occupancy. Specifically, for quantum dots in the Coulomb blockade regime, the transmission phase increases monotonically by pi throughout each conductance peak; in the conductance valleys, the phase returns sharply to its starting value. The expected mesoscopic features in the phase evolution--related to the dot's shape, spin degeneracy or to exchange effects--have not been observed, and there is at present no satisfactory explanation for the observed universality in phase behaviour. Here we report the results of phase measurements on a series of small quantum dots, having occupancies of between only 1-20 electrons, where the phase behaviour for electron transmission should in principle be easier to interpret. In contrast to the universal behaviour observed thus far only in the larger dots, we see clear mesoscopic features in the phase measurements when the dot occupancy is less than approximately 10 electrons. As the occupancy increases, the manner of phase evolution changes and universal behaviour is recovered for some 14 electrons or more. The identification of a transition from the expected mesoscopic behaviour to universal phase evolution should help to direct and constrain theoretical models for the latter.

Influence of interference on the Kondo effect in a quantum dot

“…This is due to the Kondo effect, involving the screening of the spin 1/2 of the quantum dot by conduction electrons in the leads. If there is an additional tunneling path connecting the two leads that does not pass through the quantum dot, then some interesting interference phenomena take place [4][5][6][7][8] .…”

Mesoscopic behavior of the transmission phase through confined correlated electronic systems

“…Our goal was to determine how correlation effects influence the transmission phase, and whether they are able to explain the existing experimental observations of Ref. [4,6,9,10]. In order to compute the complex transmission amplitude of the scattering matrix corresponding to strongly correlated systems we have extended the embedding method previously used for conductance computations.…”

“…The experiments were performed at very low temperatures (T ≈ 80 mK) where the temperature was estimated to be the smallest energy scale in the system. In a more recent experiment at even lower temperatures (T ≈ 30 mK), Avinum-Kalish et al 9 investigated small QD's with zero to few tens of electrons. Their estimations of the energy scales involved in the experiments are the following: the temperature K b T ≈ 0.003 meV, the level spacing δ ≈ 0.5 meV, the level width Γ ≈ 0.03 − 0.3 meV, and the charging energy U = 1 − 3 meV.…”

“…32 In another line of work, a very simple solution to the puzzle posed by Refs. [4,6,9] was recently proposed. 33 The approach is based on the Constant Interaction Model (CIM), which treats QD in the CB regime as noninteracting, up to a constant charging energy term.…”

Transient probing of the symmetry and the asymmetry of electron interference

“…31 With a QD sitting on one arm, making the other arm of the ring as a reference, studies on the resonant tunneling through the QD have been experimentally carried out. [32][33][34][35][36][37][38][39] Ring-shaped natural molecules and artificial molecules are useful nanostructures that can host the AB effect and at the same time provide manipulable geometric symmetry. For ring-shaped natural molecules, effective use of magnetic fluxes either requires unrealistically high magnetic fields 40 or other special conditions.…”