Linear response quantum transport through interacting multi-orbital nanostructures (original) (raw)

Quantum transport in interacting nanodevices: From quantum dots to single-molecule transistors

2022

The enormous interest in industrial application of semiconductor components has led to the development of unprecedented control over the manufacture of electronic devices on the nanometer scale. This allows to perform highly controllable and fine-tuned experiments in the quantum regime where exotic effects can nowadays be measured. Among those, breakthrough measurements of electrical conductance experimentally confirmed the Kondo effect - a many-body quantum effect involving macroscopic entanglement. In quantum dot devices, enhanced conductance below a characteristic energy scale is the signature of Kondo singlet formation. Precise predictions of quantum transport properties in similar nanoelectronics devices is therefore desired to design optimal functionality and control. Standard mesoscopic transport methods suffer from limitations in nanostructure specifics, set-up design, energy, temperature and voltage regime of applicability. To overcome these issues, such that we obtain modelling flexibility and accurate conductance predictions, in this thesis we analytically derive alternative and improved quantum transport formulations having as their starting point scattering theory in the Landauer-Buettiker formula, linear response theory in the Kubo formula, nonequilibrium Keldysh theory in the Meir-Wingreen formula and Fermi liquid theory in the Oguri formula. We perform a systematic benchmark of our exact expressions, comparing with the standard approaches using a state-of-the-art numerical renormalization group techniques (NRG). The new formulations not only reproduce literature results, but also show higher accuracy and computational efficiency, as well as a wider applicability under regimes and conditions out of reach by existing methods. We also derive generalized effective models for multi-orbital two-lead interacting nanostructures in both Coulomb blockade and mixed-valence regime, which yield reusable conductance predictions directly in terms of the effective model parameters. We conclude by applying our novel formulations to complex nanoelectronics systems, including a single-molecule benzene transistor, a charge-Kondo quantum dot made from graphene and a semiconductor triple quantum dot.

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.

Quantum transport in a single molecular transistor at finite temperature

Scientific Reports, 2021

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron–electron and electron–phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron–phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

Low-temperature transport through a quantum dot: Finite-U results and scaling behavior

Physical Review B, 2002

The infinite-U Anderson model is applied to non-equilibrium transport through a quantum dot containing two spin levels weakly coupled to two leads. At low temperatures, the Kondo peak in the equilibrium density of states is split upon the application of a voltage bias. The split peaks, one at the chemical potential of each lead, are suppressed by non-equilibrium dissipation. In a magnetic field, the Kondo peaks shift away from the chemical potentials by the Zeeman energy, leading to an observable peak in the differential conductance when the non-equilibrium bias equals the Zeeman energy. PACS numbers: 72.15.Qm 73.40.Gk 73.20.Dx 73.50.Fq 1

Correlation effects in the transport through quantum dots

We study the charge and heat transport through the correlated quantum dot with a finite value of the charging energy U = ∞ . The Kondo resonance appearing at temperatures below TK is responsible for several qualitative changes of the electric and thermal transport. We show that under such conditions the semiclassical Mott relation between the thermopower and electric conductivity is violated. We also analyze the other transport properties where a finite charging energy U has a significant influence. They are considered here both, in the limit of small and for arbitrarily large values of the external voltage eV = µL −µR and/or temperature difference TL −TR. In particular, we check validity of the Wiedemann-Franz law and the semiclassical Mott relation.

Signatures of electron correlations in the transport properties of quantum dots

Physical review. B, Condensed matter, 1996

The transition matrix elements between the correlated N and N +1 electron states of a quantum dot are calculated by numerical diagonalization. They are the central ingredient for the linear and non-linear transport properties which we compute using a rate equation. The experimentally observed variations in the heights of the linear conductance peaks can be explained. The knowledge of the matrix elements as well as the stationary populations of the states allows to assign the features observed in the non-linear transport spectroscopy to certain transition and contains valuable information about the correlated electron states. PACS numbers: 73.20.Dx, 73.20.Mf, 73.40.Gk By using modern nanostructure fabrication technology a few electrons can be confined to very small regions in space . In these so-called quantum dots or artificial atoms the Coulomb interaction between the electrons is very important for understanding their quantum mechanical properties. Weak coupling to external reservoirs via tunnel barriers allows to observe single electron transport effects like the Coulomb blockade oscillations in the linear conductance at millikelvin temperatures . In non-linear transport, features are observed which are closely related to the excitation spectrum of the interacting electrons .

Low-temperature transport in ac-driven quantum dots in the Kondo regime

Physical Review B, 2001

We present a fully nonequilibrium calculation of the low temperature transport properties of a quantum dot in the Kondo regime when an AC potential is applied to the gate voltage. We solve a time dependent Anderson model with finite on-site Coulomb interaction. The interaction self-energy is calculated up to second order in perturbation theory in the on-site interaction, in the context of the Keldysh non-equilibrium technique, and the effect of the AC voltage is taken into account exactly for all ranges of AC frequencies and AC intensities. The obtained linear conductance and time-averaged density of states of the quantum dot evolve in a non trivial way as a function of the AC frequency and AC intensity of the harmonic modulation..

Nonlinear low-temperature transport of electrons through a multilevel quantum dot

Superlattices and Microstructures

Nonlinear electron transport through a semiconductor quantum dot in the low-temperature Kondo regime is studied theoretically. Particular emphasis is put on examining the effects of the inherent multilevel electronic structure of the semiconductor dot. Combining the nonequilibrium Green function method with the noncrossing approximation, we derived differential conductance as a function of the source-drain voltage and found that characteristic side peaks appear in addition to the Kondo peak. These side peaks, which survive dissipation broadening, should provide a hallmark of Kondo correlation in this system.

Low-temperature transport through a quantum dot

2005

Contents: (1) Model of a lateral quantum dot system (2) Thermally-activated conduction: onset of the Coulomb blockade oscillations and Coulomb blockade peaks at low temperature (3) Activationless transport through a blockaded quantum dot: inelastic and elastic co-tunneling (4) Kondo regime in transport through a quantum dot: effective low-energy Hamiltonian; linear response; weak coupling regime; strong coupling regime; beyond linear response;