Fractional conductance oscillations in quantum rings: wave packet picture of transport in a few-electron system

Abstract

We study electron transfer across a two-terminal quantum ring using a time-dependent description of the scattering process. For the considered scattering event the quantum ring is initially charged with one or two electrons, with another electron incident to the ring from the input channel. We study the electron transfer probability (T) as a function of the external magnetic field. We determine the periodicity of T for a varied number of electrons confined within the ring. For that purpose we develop a method to describe the wave packet dynamics for a few electrons participating in the scattering process, taking into full account the electron-electron correlations. We find that electron transfer across the quantum ring initially charged by a single electron acquires a distinct periodicity of half of the magnetic flux quantum (Φ0/2), corresponding to the formation of a transient two-electron state inside the ring. In the case of a three-electron scattering problem with two electrons initially occupying the ring, a period of Φ0/3 for T is formed in the limit of thin channels. The effect of disorder present in the confinement potential of the ring is also discussed.

The Split-Operator Technique for the Study of Spinorial Wavepacket Dynamics

“…Investigating the propagation of wave packets in a given system allows us to obtain information about, e.g., its energy spectrum, [1] its electric and optical conductivity, [2] its local density of states [3] and so on. In fact, wave packet dynamics methods have been successfully used in the study of the Aharonov-Bohm effect in several systems, [4][5][6][7] in the theoretical description of scanning gate microscopy experiments, [8] in understanding the break of Onsager symmetry in a semiconductor quantum wire coupled to a metal, [9] and in the interpretation of interference related effects in the experimentally obtained conductance of an asymmetric quantum ring, [10] just to mention a few examples. Lately, the interest in wave packet dynamics methods for Dirac particles has been increasing as well, [11,12] specially after the first experimental realization of graphene, [13] a single layer of carbon atoms where low energy electrons behave as massless Dirac Fermions, thus exhibiting a series of interesting transport phenomena, such as the zitterbewegung (trembling motion) [14][15][16] and Klein tunneling.…”

Role of alternance symmetry in magnetoconductance

“…Clear manifestations of the topology of cyclic systems are expected in their magnetoconductance, as the magnetic flux enclosed by the delocalized electron translates into an Aharonov-Bohm (AB) phase [14] whose consequences on the electronic transport have been discussed in the literature, be it for aromatic hydrocarbons [10,11,15], for coupled quantum dots [1,[16][17][18][19], or for ring-shaped nanostructures [20][21][22].…”

“…[9][10][11][12][13] Clear manifestations of the topology of cyclic systems are expected in their magnetoconductance, as the magnetic flux enclosed by the delocalized electron translates into an Aharonov-Bohm (AB) phase 14 whose consequences on the electronic transport have been discussed in the literature, be it for aromatic hydrocarbons 10,11,15 , for coupled quantum dots 1,[16][17][18][19] , or for ring-shaped nanostructures. [20][21][22] While the role of spatial and spin symmetries in the transport and magnetotransport of cyclic systems has been thoroughly investigated, 13,16,19,23,24 much less is known about the role of the so-called alternance symmetry. From the early times of quantum chemistry, alternance symmetry has proved very useful in predicting the properties of conjugated hydrocarbons.…”