The interplay between the Kondo effect and the inter-dot magnetic interaction in a coupled-dot system is studied. An exact result for the transport properties at zero temperature is obtained by diagonalizing a cluster, composed by the double-dot and its vicinity, which is connected to leads. It is shown that the system goes continuously from the Kondo regime to an anti-ferromagnetic state as the inter-dot interaction is increased. The conductance, the charge at the dots and the spin-spin correlation are obtained as a function of the gate potential.

A theoretical study of single electron capacitance spectroscopy in quantum dots is presented. Exact diagonalizations and the unrestricted Hartree-Fock approximation have been used to shed light over some of the unresolved aspects. The addition spectra of up to 15 electrons is obtained and compared with the experiment. We show evidence for understanding the decrease of the single electron tunneling rates in terms of the behavior of the ω → 0 spectral weight function.Single electron capacitance spectroscopy (SECS) [1,2] has been a breakthrough in the experimental knowledge of the electronic structure of a quantum dot (QD). Ashoori and co-workers [1,2] have been able to determine the energies required to introduce electrons one by one, from 0 to 50, into a QD. The electrons tunnel into the QD by means of a vertical gate bias, and change the capacitance of the device. The measurement of that capacitance as a function of the Fermi energy E F in one electrode shows a discrete set of almost equally spaced peaks of different intensities. A peak appears whenever E F = µ(N) = E 0 (N) − E 0 (N − 1), with E 0 (N) being the ground state (GS) energy of N electrons in the QD. In this way,

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The persistent current through a quantum dot inserted in a mesoscopic ring of length L is studied. A cluster representing the dot and its vicinity is exactly diagonalized and embedded into the rest of the ring. It is shown that the persistent current at the Kondo regime is enhanced relative to the current flowing either when the dot is at resonance or along a perfect ring of the same length. In the Kondo regime, the current scales as L 21͞2 , unlike the L 21 scaling of a perfect ring. We discuss the possibility of detection of the Kondo effect by means of a persistent current measurement.[S0031-9007(99)09451-X] PACS numbers: 73.23. Ra, 72.15.Qm, 73.20.Dx Electron transport through a quantum dot (QD) has been a subject of many experimental and theoretical studies in the past few years. These small devices contain several millions of real atoms, but behave as if they were single artificial atoms. Similar to real atoms, they have a discrete spectrum of energy, which has been measured [1] and theoretically understood on the basis of a confinement potential and a full many-body electron-electron interaction treatment [2]. Unlike real atoms, electronic transport can be realized through a single QD. Experimental results [3] show periodic oscillations of the conductance as a function of the electron density in the QD. These oscillations can be explained on the basis of a transport mechanism governed by Coulomb blockade and single-electron tunneling [4].Another manifestation of electron-electron interaction which was theoretically predicted [5] some years ago is the Kondo effect in a QD coupled to external leads. In this case, however, the effect is due to correlations between the electrons inside the QD and the conduction electrons in the leads. When the system operates in the so-called Kondo regime, a resonance in the vicinity of the Fermi level, localized at the QD, provides a new channel for the mesoscopic current to tunnel through, creating new phenomena which can be detected in a transport experiment. We have recently proposed [6] a current measurement on a ring connected to two leads having a QD inserted in one of its arms where the signature of the Kondo effect would be clearly reflected. Measurements of the current in a similar device have already demonstrated [7] the coherent character of the transport through the QD. However, this experiment was not appropriate to observe the Kondo effect. Its observation is a delicate task since it depends on several different energy scales and their relative sizes, such as the coupling constant between the QD and leads t 0 , the Kondo temperature T K , and the energy spacing between the dot levels De. For example, if t 02 ͞W . De, where W is the ring bandwidth, the charge and energy quantization in the QD is lost and the Kondo effect disappears. On the other hand, diminishing t 0 leads to an exponential reduction of T K [8]. So, in order to get simultane-ously accessible temperatures and charge-energy quantization De must be large enough, which implies small size QD. Very ...

We investigate the size scaling of the conductance of surface disordered graphene sheets of width W and length L. Metallic leads are attached to the sample ends across its width. At E ~ 0, the conductance scales with the system size as follows: i) For constant W/L, it remains constant as size is increased, at a value which depends almost lineally on that ratio; this scaling allows the definition of a conductivity value that results similar to the experimental one. ii) For fixed width, the conductance decreases exponentially with length L, both for ordered and disordered samples. Disorder reduces the exponential decay, leading to a higher conductance. iii) For constant length, conductance increases linearly with width W, a result that is exclusively due to the tails of the states of the metallic wide contact. iv) The average conductance does not show an appreciable dependence on magnetic field. Away from E = 0, the conductance shows the behavior expected in two-dimensional systems with surface disorder, i.e., ballistic transport.Comment: 4 pages, 5 figures, RevTe

A recent experimental study showed that, distorting a CoPc molecule adsorbed on a Au(111) surface, a Kondo effect is induced with a temperature higher than 200 K. We examine a model in which an atom with strong Coulomb repulsion (Co) is surrounded by four atoms on a square (molecule lobes), and two atoms above and below it representing the apex of the STM tip and an atom on the gold surface (all with a single, half-filled, atomic orbital). The Hamiltonian is solved exactly for the isolated cluster, and, after connecting the leads (STM tip and gold), the conductance is calculated by standard techniques. Quantum interference prevents the existence of the Kondo effect when the orbitals on the square do not interact (undistorted molecule); the Kondo resonance shows up after switching on that interaction. The weight of the Kondo resonance is controlled by the interplay of couplings to the STM tip and the gold surface, and between the molecule lobes. Coupling of localized spins to conduction electrons may lead to a transport anomaly known as the Kondo effect [1,2]. This effect, that usually shows up at low temperatures, consists of a sharp peak at the Fermi level, whose half-width is known as the Kondo temperature (T K ), and a conductance close to one conductance quantum G 0 = 2e 2 /h. The Kondo temperature in the case of magnetic impurities in non-magnetic metals is around 50 K [1], whereas in artificial atoms (quantum dots) is just a few hundred mK [3,4]. In a recent experiment [5,6] it has been shown that it is possible to control the characteristics, and even the existence, of the Kondo resonance by modifying the chemical surroundings of a magnetic atom. The experiments were carried out on a cobalt phthalocyanine molecule (CoPc) adsorbed on a Au(111) surface. Dehydrogenation of this molecule (d-CoPc) by means of voltage pulses from a Scanning Tunneling Microscope (STM) triggered a Kondo effect with a rather high Kondo temperature (T K ≈ 200 K). This temperature is even higher than that observed for bare Co adsorbed on a similar surface [6,7]. Besides such a high T K , one of the most remarkable results of [5] is the fact that the undistorted molecule does not show a Kondo effect, while it is readily promoted by distorting the molecule upon dehydrogenation. Topographic images taken by means of the STM [5] indicated that the CoPc molecule has four almost non-overlapping lobes symmetrically placed around the Co atom. Dehydrogenation distorts the molecule and forces those lobes to overlap. In addition it strongly decreases the distance from the molecule lobes to the gold surface and increases the Co/gold surface distance in approximately 30% [5].We hereby propose a simple model that accounts for some of the salient features of the experiment described above. We take a model Hamiltonian on a small atomic arrangement which is solved exactly, and subsequently connected to semi-infinite chains used to describe the STM tip and the gold surface. Fig. 1 depicts this atomic arrangement. A central site with a single atomic or...

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on "odd-even" effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero. PACS. 73.63.-b Electronic transport in nanoscale materials and structures -73.63Kv Quantum dots -71.27.+a Strongly correlated electron systems a Present address:and linearly coupled two dots, as well as small molecules [1,8,9].Stimulated by the rich physics harbored by interacting nanostructures, the field has seen a rapid development of powerful numerical techniques to obtain the conductance. These include the well-established numericalrenormalization group approach (NRG) [10][11][12][13], various density-matrix renormalization group (DMRG) based methods [14][15][16], including in particular, the recently developed time-dependent DMRG (tDMRG) [17][18][19][20][21][22], Quantum Monte Carlo simulations (see, e.g., Ref.[23]), flowequation approaches [24], as well as exact diagonalization combined with an embedding procedure, the embeddedcluster approximation (ECA) [25][26][27][28]. We wish to distinguish the latter method from other cluster-embedding ap-

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.