Nonuniversal Transmission Phase Lapses through a Quantum Dot: An Exact Diagonalization of the Many-Body Transport Problem

Abstract

Systematic trends of nonuniversal behavior of electron transmission phases through a quantum dot, with no phase lapse for the transition N = 1 → N = 2 and a lapse of π for the N = 2 → N = 3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor anisotropy of the shape of the dot and strong e − e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.PACS numbers: 73.23. Hk, 73.21.La, Motivation. Measurements via Aharonov-Bohm interferometry of transmission phases (in addition to conductances) provide valuable information about fundamental transport properties through small systems [1,2]. An experimental setup conceived and employed in such studies consists of placing a two-dimensional quantum dot (QD) in one of the arms of the two-path interferometer [1,2]. In earlier experiments [1] a universal behavior of the phase was found where for each added electron the phase drops discontinuously by π (phase lapse, PL) before rising back (as expected) continuously by the same amount. This behavior was found to be independent of the number of electrons, the dot shape and spin degeneracy. The regime of mesoscopic (nonuniversal) behavior of the transport through the dot, exhibiting an irregular PL pattern and dependencies on the number of electrons and dot parameters has been observed only recently [2] for dots with a smaller number of electrons N < 15. The large majority of theoretical studies attempted to address the PL behavior in the universal regime. Nevertheless, this behavior remains puzzling and challenging [3,4].Here, we focus on the nonuniversal regime (small N ) where "the phase behavior for electron transmission should in principle be easier to interpret" [2]. To this aim, we use a transport theory, based on a computational approach entailing exact diagonalization (EXD) [5] of the QD many-body Hamiltonian. This approach includes electron correlation effects and allows systematic investigations of the transport characteristics as a function of the dot shape, number of electrons, and spin configurations. Specifically, we follow the work of Bardeen [6] where the correlated many-body states of the QD play a determining role (see below) through the socalled quasi-particle wave functions [6,7] [see Eq. (1)], replacing the single-particle orbitals used in independent-particle (and/or mean-field) approaches [8,9]. This allows evaluation of both the current and transmission phase lapse. Here our focus is on the phase-lapse phenomenon [10].The transmission probability (current) is given [6] (to lowest order) by the golden rule as a product of the square of a dot-to-lead coupling matrix element, M, and a den-

Critical analysis of a variational method used to describe molecular electron transport

“…One major issue is the large discrepancy, often of several orders of magnitude, [1][2][3] between the measured currents through molecules and values calculated theoretically. Open questions in electron transport through nanostructures, which remain unresolved after many years of research, appear also in other related areas, e. g., transport through semiconducing quantum dots 4,5 The simplest theoretical calculations of the transport in nanoscopic/molecular systems rely upon the Landauer formalism, 6,7 which ignores electron correlations. The latter are accounted for in more elaborated approaches, like those based on nonequilibrium Green functions (NEGFs), 8,9 time-dependent density matrix renormalization group (DMRG), [10][11][12] and numerical renormalization group (NRG).…”

Electron cotunneling through doubly occupied quantum dots: effect of spin configuration

“…Quantum dots are usually modeled as simple semiclassical capacitors to explain Coulomb blockade effect and spin-related transport phenomenon [6]. Although conventional approach like Green's function or master equation combined with Hubbard model has been quite successful in both the sequential tunneling and cotunneling regimes [7], there have been several theoretical attempts on dealing directly with the many-body Hamiltonian to study the few-electron transport problem recently [8,9]. However, it still presents a great challenge to obtain a fully quantum mechanical solution for cotunneling of electrons through a quantum dot that is beyond the semiclassic framework of phenomenological models.…”

Exchange and correlation effects in the transmission phase through a few-electron quantum dot

“…Many works introduced major simplifications, like spinless electrons, 5,7,8 one-dimensional QDs, 9,10 simplified models for Coulomb interaction, 5,6,11,12 or other ad hoc assumptions. 13 Even the interpretation of the simplest N = 1 → N = 2 transition is controversial, being variably attributed to the occupation of either the same 2 or a different 1 orbital from that of the first electron, to the role of excited doorway channels, 14 to electron crystallization. 12 In this paper we compute Θ by fully including exchange and correlation effects.…”