Quantum transport in interacting nanodevices: from quantum dots to single-molecule transistors (original) (raw)
Linear response quantum transport through interacting multi-orbital nanostructures
Cornell University - arXiv, 2022
Nanoelectronics devices, such as quantum dot systems or single-molecule transistors, consist of a quantum nanostructure coupled to a macroscopic external electronic circuit. Thermoelectric transport between source and drain leads is controlled by the quantum dynamics of the lead-coupled nanostructure, through which a current must pass. Strong electron interactions due to quantum confinement on the nanostructure produce nontrivial conductance signatures such as Coulomb blockade and Kondo effects, which become especially pronounced at low temperatures. In this work we first provide a modern review of standard quantum transport techniques, focusing on the linear response regime, and highlight the strengths and limitations of each. In the second part, we develop an improved numerical scheme for calculation of the ac linear electrical conductance through generic interacting nanostructures, based on the numerical renormalization group (NRG) method, and explicitly demonstrate its utility in terms of accuracy and efficiency. In the third part we derive low-energy effective models valid in various commonly-encountered situations, and from them we obtain simple analytical expressions for the low-temperature conductance. This indirect route via effective models, although approximate, allows certain limitations of conventional methodologies to be overcome, and provides physical insights into transport mechanisms. Finally, we apply and compare the various techniques, taking the two-terminal triple quantum dot and the serial multi-level double dot devices as nontrivial benchmark systems.
Conductance Calculations for Real Systems on the Nanoscale
ChemPhysChem, 2002
Electron transport across molecular junctions is a rapidly growing topic at the borderline between physics and chemistry. We review calculations which were done in the Landauer transport formalism for monovalent systems, ranging from clusters to fullerenes. A realistic description of molecular conductance can be achieved by a density functional based approach to the calculation of the electronic transport properties.
Electron Transport in Strongly Correlated Nanostructures
Modern Physics Letters B, 2009
We present a short review on electron transport in strongly correlated nanostructures, quantum dots in particular. We describe briefly the main correlation effects, namely the Coulomb blockade and Kondo effect, and introduce three widely used numerical techniques to study these effects. We then give a brief summary of some more elaborate set-ups where two or more effects compete, making the transport properties very interesting to study. In particular, we report the cases of multilevel quantum dots, carbon nanotube based quantum dots, and quantum dots coupled by RKKY interaction.
Physical Review B, 2008
We apply the adaptive time-dependent density-matrix renormalization-group method ͑tDMRG͒ to the study of transport properties of quantum-dot systems connected to metallic leads. Finite-size effects make the usual tDMRG description of the Kondo regime a numerically demanding task. We show that such effects can be attenuated by describing the leads by "Wilson chains," in which the hopping matrix elements decay exponentially away from the impurity ͑t n ϰ⌳ −n/2 ͒. For a given system size and in the linear-response regime, results for ⌳Ͼ1 show several improvements over the undamped ⌳ = 1 case: perfect conductance is obtained deeper in the strongly interacting regime and current plateaus remain well defined for longer time scales. Similar improvements were obtained in the finite-bias regime up to bias voltages of the order of the Kondo temperature. These results show that with the proposed modification, the tDMRG characterization of Kondo correlations in the transport properties can be substantially improved, while it turns out to be sufficient to work with much smaller system sizes. We discuss the numerical cost of this approach with respect to the necessary system sizes and the entanglement growth during the time evolution.
The European Physical Journal B, 2006
A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum kF in an infinite chain embedding two scatterers separated by a segment of length Lc. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/kF which decay as 1/Lc and which are suppressed when Lc exceeds the thermal length LT. The analytical results given by the Hartree-Fock approximation are compared with exact numerical results obtained with the embedding method and the DMRG algorithm. PACS. 71.27.+a Strongly correlated electron systems; heavy fermions -72.10.-d Theory of electronic transport; scattering mechanisms -73.23.-b Electronic transport in mesoscopic systems
First-principles approach to electrical transport in atomic-scale nanostructures
Physical Review B, 2002
We present a first-principles numerical implementation of Landauer formalism for electrical transport in nanostructures characterized down to the atomic level. The novelty and interest of our method lies essentially on two facts. First of all, it makes use of the versatile Gaussian98 code, which is widely used within the quantum chemistry community. Secondly, it incorporates the semiinfinite electrodes in a very generic and efficient way by means of Bethe lattices. We name this method the Gaussian Embedded Cluster Method (GECM). In order to make contact with other proposed implementations, we illustrate our technique by calculating the conductance in some wellstudied systems such as metallic (Al and Au) nanocontacts and C-atom chains connected to metallic (Al and Au) electrodes. In the case of Al nanocontacts the conductance turns out to be quite dependent on the detailed atomic arrangement. On the contrary, the conductance in Au nanocontacts presents quite universal features. In the case of C chains, where the self-consistency guarantees the local charge transfer and the correct alignment of the molecular and electrode levels, we find that the conductance oscillates with the number of atoms in the chain regardless of the type of electrode. However, for short chains and Al electrodes the even-odd periodicity is reversed at equilibrium bond distances.
Electronic Correlations in Transport through Coupled Quantum Dots
Physical Review Letters, 1999
The conductance through two quantum dots in series is studied using general qualitative arguments and quantitative slave-boson mean-field theory. It is demonstrated that measurements of the conductance can explore the phase diagram of the two-impurity Anderson model. Competition between the Kondo effect and the interdot magnetic exchange leads to a two-plateau structure in the conductance as a function to the gate voltage and a two or three peak structure in the conductance versus interdot tunneling. [S0031-9007(99)09017-1]
Theory of Electronic Transport in Nanostructures
Semiconductor Modeling Techniques, 2012
As the first of three chapters on transport properties, we begin by explaining some of the key factors relevant to electron transport on a macroscopic scale. We then turn to address a range of novel nanoscale transport effects. These include the quantum Hall effect and quantised conductance, as well as the recent prediction and observation of quantised conduction associated with the spin quantum Hall effect in a topological insulator. We next consider graphene and the consequences of its unusual band structure before concluding with an overview of the potential use of “junctionless” transistors as one of the most promising approaches for future nanoscale electronic devices.
Annals of Physics, 2012
The conductance through a mesoscopic system of interacting electrons coupled to two adjacent leads is conventionally derived via the Keldysh nonequilibrium Green's function technique, in the limit of noninteracting leads [see Y. Meir et al., Phys. Rev. Lett. 68, 2512 (1991)]. We extend the standard formalism to cater for a quantum dot system with Coulombic interactions between the quantum dot and the leads. The general current expression is obtained by considering the equation of motion of the time-ordered Green's function of the system. The nonequilibrium effects of the interacting leads are then incorporated by determining the contour-ordered Green's function over the Keldysh loop and applying Langreth's theorem. The dot-lead interactions significantly increase the height of the Kondo peaks in density of states of the quantum dot. This translates into two Kondo peaks in the spin differential conductance when the magnitude of the spin bias equals that of the Zeeman splitting. There also exists a plateau in the charge differential conductance due to the combined effect of spin bias and the Zeeman splitting. The low-bias conductance plateau with sharp edges is also a characteristic of the Kondo effect. The conductance plateau disappears for the case of asymmetric dot-lead interaction.
Theory of charge transport in molecular junctions: from Coulomb blockade to coherent tunneling
The Journal of chemical physics, 2014
We study charge transport through molecular junctions in the presence of electron-electron interaction using the nonequilibrium Green's function techniques and the renormalized perturbation theory. In the perturbation treatment, the zeroth-order Hamiltonian of the molecular junction is composed of independent single-impurity Anderson's models, which act as the channels where charges come through or occupy, and the interactions between different channels are treated as the perturbation. Using this scheme, the effects of molecule-lead, electron-electron, and hopping interactions are included nonperturbatively, and the charge transport processes can thus be studied in the intermediate parameter range from the Coulomb blockade to the coherent tunneling regimes. The concept of quasi-particles is introduced to describe the kinetic process of charge transport, and then the electric current can be studied and calculated. As a test study, the Hubbard model is used as the molecular Ha...