Quantum interference effects in two double quantum dots-molecules embedded in an Aharonov–Bohm ring M.L. Ladro ´ n de Guevara a,Ã , G.A. Lara b , P.A. Orellana a a Universidad Cato ´lica del Norte, Casilla 1280, Antofagasta, Chile b Universidad de Antofagasta, Casilla 170, Antofagasta, Chile article info Article history: Received 17 December 2009 Accepted 11 January 2010 Available online 15 January 2010 Keywords: Electronic transport Quantum dots Quantum interference abstract We study equilibrium and non-equilibrium transport of non-interacting electrons through two quantum dot molecules embedded in an Aharonov–Bohm interferometer, and focus in several quantum interference effects occurring in both regimes. We obtain analytical expressions for the transmission and the density of states, and we calculate numerically the current at zero temperature. We show that the system exhibits Fano resonances, total suppression of transmission, and bound states in the continuum. In equilibrium we find a magnetic flux-dependent effective level attraction and lines of perfect transmission when the intramolecular coupling is weak. This feature has strong consequences in the non-equilibrium regime, where the I–V characteristics displays a region of negative differential conductance induced by the magnetic flux. The current suffers an abrupt rise for small bias voltages as consequence of an effective level attraction of the hybridized levels produced by the flux. The decrease of current is result of the destruction of this effect when the bias is increased. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Electron transport in systems of multiple quantum dots, and in particular in coupled double quantum dots (DQD), has been a subject of intensive research in recent years. The coupled DQD was initially studied in its similitude with a real molecule [1], but the interest on this system has turned to several other directions, as its possible use in spintronics [3] and quantum computing [2]. One of the key features of transport in quantum dots is the high degree of phase coherence of electrons, one of the basic quantum phenomena. Quantum coherence manifests in the presence of different electronic pathways, and this has motivated the study of quantum dot structures embedded in interferom- eters. Systems as a coupled DQD embedded in a ring [4–7], or ‘quantum dot molecule’, have received much attention recently for the variety of quantum interference effects they show. Experiments have allowed to observe in this structure Aharo- nov–Bohm (AB) oscillations of the conductance and Fano resonances [4,8,9], and theoretical works have predicted other quantum coherence consequences as Dicke effect [7] and bound states in the continuum [5]. The interplay of electronic interac- tions and quantum interference in the DQD embedded in a ring is explored in Refs. [10–14], showing no conventional behaviors in Kondo and Coulomb blockade regimes. Spin dependent transport in the same system with ferromagnetic leads is considered in Refs. [15,16] and in the presence of Rashba spin–orbit interaction in Ref. [17]. From the application point of view, an interesting feature exhibited quantum dots is the negative differential conductance (NDC) [18]. NDC has been studied in single as well as in double quantum dot systems, and it has applications in amplifiers and oscillators in the microwave, mm-wave and Terahertz frequency ranges [19]. In multilevels quantum dots NDC can occur when states have different couplings to the leads [20–23]. In a serial double quantum dot, negative differential conductance can be produced when the bias breaks the transmission channel extended along the system [24]. Other theoretical works on generation of NDC in double quantum dot molecules connected in series are Refs. [25–29]. In a DQD embedded in an Aharonov-ring, magnetic-flux-induced NDC was found in the strong interdot repulsion regime [12]. A similar result was found by Mourokh and Smirnov in a double molecule with three terminals [30]. Recently, it was reported NDC induced by the electronic correlation in a side-coupled DQD [31]. Our work aims to study a system of two double quantum dot molecules in an Aharonov–Bohm interferometer. This system exhibits a phenomenology different from the DQD molecule in an AB ring, and it presents novel results in the situation out of equilibrium. This configuration resembles in some aspects to two uncoupled quantum dots in an AB interferometer [32] and it captures some of its physics, but a richer phenomenology arises from the fact that we are dealing with double quantum dots ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physe Physica E 1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.01.014 Ã Corresponding author. E-mail address: mlladron@ucn.cl (M.L. Ladro ´ n de Guevara). Physica E 42 (2010) 1637–1642