It has been shown recently [J. L. Lado et al., Phys. Rev. Lett. 113, 027203 (2014)] that edge magnetic moments in graphene-like nanoribbons are strongly influenced by the intrinsic spin-orbit interaction. Due to this interaction an anisotropy comes a
bout which makes the in-plane arrangement of magnetic moments energetically more favorable than that corresponding to the out-of-plane configuration. In this paper we raise both the edge magnetism problem as well as differential conductance and shot noise Fano factor issues, in the context of finite-size flakes within the Coulomb blockade (CB) transport regime. Our findings elucidate the following problems: (i) modification of the CB diamonds by the appearance of the in-plane magnetic moments, (ii) modification of the CB diamonds by intrinsic spin-orbit interaction.
We analyze the process of thermalization, dynamics and the eigenstate thermalization hypothesis (ETH) for the single impurity Anderson model, focusing on the Kondo regime. For this we construct the complete eigenbasis of the Hamiltonian using the num
erical renormalization group (NRG) method in the language of the matrix product states. It is a peculiarity of the NRG that while the Wilson chain is supposed to describe a macroscopic bath, very few single particle excitations already suffice to essentially thermalize the impurity system at finite temperature, which amounts to having added a macroscopic amount of energy. Thus given an initial state of the system such as the ground state together with microscopic excitations, we calculate the spectral function of the impurity using the microcanonical and diagonal and grand canonical ensembles. By adding or removing particles at a certain Wilson energy shell on top of the ground state, we find qualitative agreement between the spectral functions calculated for different ensembles. This indicates that the system thermalizes in the long-time limit, and can be described by an appropriate statistical-mechanical ensemble. Moreover, by calculating the impurity spectral density at the Fermi level and the dot occupancy for energy eigenstates relevant for microcanonical ensemble, we find good support for ETH. The ultimate mechanism responsible for this effective thermalization within the NRG can be identified as Anderson orthogonality: the more charge that needs to flow to or from infinity after applying a local excitation within the Wilson chain, the more the system looks thermal afterwards at an increased temperature. For the same reason, however, thermalization fails if charge rearrangement after the excitation remains mostly local.
We study the spin-resolved transport properties of T-shaped double quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we calculate the linear conductance and the spin polarization of the current for various
model parameters and at different temperatures. We show that an effective exchange field due to the presence of ferromagnets results in different conditions for Fano destructive interference in each spin channel. This spin dependence of the Fano effect leads to perfect spin polarization, the sign of which can be changed by tuning the dots levels. Large spin polarization occurs due to Coulomb correlations in the dot, which is not directly coupled to the leads, while finite correlations in the directly-coupled dot can further enhance this effect. Moreover, we complement accurate numerical results with a simple qualitative explanation based on analytical expressions for the zero-temperature conductance. The proposed device provides a prospective example of an electrically-controlled, fully spin-polarized current source, which operates without an external magnetic field.
We study the electric and thermoelectric transport properties of correlated quantum dots coupled to two ferromagnetic leads and one superconducting electrode. Transport through such hybrid devices depends on the interplay of ferromagnetic-contact ind
uced exchange field, superconducting proximity effect and correlations leading to the Kondo effect. We consider the limit of large superconducting gap. The system can be then modeled by an effective Hamiltonian with a particle-non-conserving term describing the creation and annihilation of Cooper pairs. By means of the full density-matrix numerical renormalization group method, we analyze the behavior of electrical and thermal conductances, as well as the Seebeck coefficient as a function of temperature, dot level position and the strength of the coupling to the superconductor. We show that the exchange field may be considerably affected by the superconducting proximity effect and is generally a function of Andreev bound state energies. Increasing the coupling to the superconductor may raise the Kondo temperature and partially restore the exchange-field-split Kondo resonance. The competition between ferromagnetic and superconducting proximity effects is reflected in the corresponding temperature and dot level dependence of both the linear conductance and the (spin) thermopower.
The Andreev transport through a quantum dot coupled to two external ferromagnetic leads and one superconducting lead is studied theoretically by means of the real-time diagrammatic technique in the sequential and cotunneling regimes. We show that the
tunnel magnetoresistance (TMR) of the Andreev current displays a nontrivial dependence on the bias voltage and the level detuning, and can be described by analytical formulas in the zero temperature limit. The cotunneling processes lead to a strong modification of the TMR, which is most visible in the Coulomb blockade regime. We find a zero-bias anomaly of the Andreev differential conductance in the parallel configuration, which is associated with a nonequilibrium spin accumulation in the dot triggered by Andreev processes.
We study the spin-resolved transport through single-level quantum dots strongly coupled to ferromagnetic leads in the Kondo regime, with a focus on contact and material asymmetry-related effects. By using the numerical renormalization group method, w
e analyze the dependence of relevant spectral functions, linear conductance and tunnel magnetoresistance on the system asymmetry parameters. In the parallel magnetic configuration of the device the Kondo effect is generally suppressed due to the presence of exchange field, irrespective of systems asymmetry. In the antiparallel configuration, on the other hand, the Kondo effect can develop if the system is symmetric. We show that even relatively weak asymmetry may lead to the suppression of the Kondo resonance in the antiparallel configuration and thus give rise to nontrivial behavior of the tunnel magnetoresistance. In addition, by using the second-order perturbation theory we derive general formulas for the exchange field in both magnetic configurations of the system.
We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for gr
aphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR) and the shot noise. It is shown that for certain shapes of the graphene dots a negative differential conductance and nontrivial behavior of the TMR effect can occur.
We analyze the equilibrium and non-equilibrium frequency-dependent spin current noise and spin conductance through a quantum dot in the local moment regime. Spin current correlations are shown to behave markedly differently from charge correlations:
Equilibrium spin cross-correlations are suppressed at frequencies below the Kondo scale, and are characterized by a universal function that we determine numerically for zero temperature. For asymmetrical quantum dots dynamical spin accumulation resonance is found for frequencies of the order of the Kondo energy. At higher temperatures surprising low-frequency anomalies related to overall spin conservation appear.
An important consequence of the discovery of giant magnetoresistance in metallic magnetic multilayers is a broad interest in spin dependent effects in electronic transport through magnetic nanostructures. An example of such systems are tunnel junctio
ns -- single-barrier planar junctions or more complex ones. In this review we present and discuss recent theoretical results on electron and spin transport through ferromagnetic mesoscopic junctions including two or more barriers. Such systems are also called ferromagnetic single-electron transistors. We start from the situation when the central part of a device has the form of a magnetic (or nonmagnetic) metallic nanoparticle. Transport characteristics reveal then single-electron charging effects, including the Coulomb staircase, Coulomb blockade, and Coulomb oscillations. Single-electron ferromagnetic transistors based on semiconductor quantum dots and large molecules (especially carbon nanotubes) are also considered. The main emphasis is placed on the spin effects due to spin-dependent tunnelling through the barriers, which gives rise to spin accumulation and tunnel magnetoresistance. Spin effects also occur in the current-voltage characteristics, (differential) conductance, shot noise, and others. Transport characteristics in the two limiting situations of weak and strong coupling are of particular interest. In the former case we distinguish between the sequential tunnelling and cotunneling regimes. In the strong coupling regime we concentrate on the Kondo phenomenon, which in the case of transport through quantum dots or molecules leads to an enhanced conductance and to a pronounced zero-bias Kondo peak in the differential conductance.
The spin-polarized transport through a coherent strongly coupled double quantum dot (DQD) system is analyzed theoretically in the sequential and cotunneling regimes. Using the real-time diagrammatic technique, we analyze the current, differential con
ductance, shot noise and tunnel magnetoresistance (TMR) as a function of both the bias and gate voltages for double quantum dots coupled in series, in parallel as well as for T-shaped systems. For DQDs coupled in series, we find a strong dependence of the TMR on the number of electrons occupying the double dot, and super-Poissonian shot noise in the Coulomb blockade regime. In addition, for asymmetric DQDs, we analyze transport in the Pauli spin blockade regime and explain the existence of the leakage current in terms of cotunneling and spin-flip cotunneling-assisted sequential tunneling. For DQDs coupled in parallel, we show that the transport characteristics in the weak coupling regime are qualitatively similar to those of DQDs coupled in series. On the other hand, in the case of T-shaped quantum dots we predict a large super-Poissonian shot noise and TMR enhanced above the Julliere value due to increased occupation of the decoupled quantum dot. We also discuss the possibility of determining the geometry of the double dot from transport characteristics. Furthermore, where possible, we compare our results with existing experimental data on nonmagnetic systems and find qualitative agreement.
