We present theoretical studies on models for experimental determination of spin correlations and detection of quantum entanglement of spatially separated electrons of Cooper pairs. These models are based on both electric current cross-correlations and simpler dc current measurements. By proper optimization of the entanglement witness method, we demonstrate that entanglement detection is possible with any magnetic detectors regardless of their efficiency. This allows us to break the relatively high previously established limit of detector efficiency / (spin polarization), p > 1/ root 3 approximate to 58%.

We present a detailed theoretical description of the electron transport through a canted quantum dot (QD) spin valve consisting of QD weakly coupled to ferromagnetic leads with noncollinear magnetization directions. In such a system, we can observe the nonequilibrium accumulated spin on the QD and virtual particle exchange processes between the QD and the ferromagnetic electrodes resulting in an effective exchange field that can be controlled by the gate or bias voltages. The exchange field affects the spin dynamics in the QD and can be used for spin manipulation. We analyze a general Bloch equation, which describes the complex spin dynamics on the QD, and we find its solutions for various useful and important limits. We obtain analytical relations between the spin accumulated on the QD and the DC current flowing in the analyzed system for the linear and nonlinear transport regimes. Surprisingly, the DC current is related to three distinct projections of the QD spin that also can be controlled by the bias and gate voltages and are independent of the electrode coupling asymmetry. Thus the ferromagnetic electrodes can act effectively as spin detectors that translate spin information into a charge signal, while the readout direction can be controlled electrically. We also predict a new type of zero-bias anomaly that is related to both the switching of the spin detection direction at the zero bias and to the spin dynamics due to the exchange field. These findings allow us to explain the tunnel magnetoresistance (TMR) characteristics from the recent experiment, where the nonequilibrium spin transport in the canted quantum dot spin valve was studied and signatures of out of equilibrium spin precession, that are electrically tunable, were observed. Additionally, we demonstrate various experimental schemes for determination of the effect of the local exchange field from the TMR characteristics also at relatively higher temperatures as compared to other technologies.

We report applying the autoclaved hydrothermal method for obtaining conductive reduced graphene oxide (rGO) fibers for potential flexible electronic applications, such as supercapacitors, transistors, or sensing applications. The reduction of GO was performed in the temperature range 120 to 180 °C under increased pressure of ca. 8 bar in a sealed Teflon lined up, stainless steel autoclave. The fiber’s diameter and length were defined by the glass tube used as the mold for reducing GO water suspension (diameter of 600 µm and length of 8 cm). After drying, in an ambient atmosphere, the hydrogel fiber shrinks to ca. 50 µm in diameter and 6 cm in length (collapsed pore structure). The drying process, in addition to enhancing electrical conductivity, also increases the mechanical strength of the fibers due to the stronger overlapping of the graphene flakes. The best performance was observed in the fiber reduced at the highest temperature studied, 180 °C, and a minimum temperature of 120 °C is necessary to obtain a fiber. Electrical conductivity was measured using the 4-probe method. The results were analyzed within the framework of variable range hopping and Arrhenius models to pinpoint the best model describing electrical conductivity in dry rGO fibers.

Following recent achievements in quantum-coherent manipulation and detection of individual atomic spins with the use of spin-polarized scanning tunneling microscope, we propose how to observe and utilize the Hanle effect in electronic transport in such setups. We show that the Hanle experiment can be used to observe the single spin precession driven by the intrinsic exchange field. This field is a result of virtual particle exchange processes, and its magnitude and sign can be controlled electrically. We also show that from detailed analysis of the Hanle resonance curve one can determine the spin relaxation time from dc current measurements.

This article focuses on EPR relaxation measurements in various carbon samples, e.g., natural carbons-anthracite, coal, higher anthraxolites, graphite; synthetically obtained carbons-glassy carbons, fullerenes, graphene, graphene oxide, reduced graphene oxide, graphite monocrystals, HOPG, nanoribbons, diamonds. The short introduction presents the basics of resonant electron spin relaxation techniques, briefly describing the obtained parameters. This review presents gathered results showing the processes leading to electron spin relaxation and typical ranges of electron spin relaxation rates for many different carbon types.

We develop the theory of the electron transport through quantum dot weakly coupled to ferromagnetic leads with noncollinear magnetization directions, that has been studied in recent experiments. One can observe much richer transport behavior of the canted quantum dot spin valves, as compared to single magnetic tunnel junctions, that relies on the possibility to generate a nonequilibrium accumulated spin on the quantum dot and the presence of the exchange interaction between dot and electrodes, depending on system parameters such as gate and bias voltages, the charging energy, an asymmetry of the tunnel couplings, and the external magnetic field. We demonstrate that one can extract information about spin dynamics on quantum dot from the dc current–voltage characteristic even at the linear response, and detect the exchange field similarly to the FMR (ferromagnetic resonance) experiment. This exchange field can be widely used in nano-spinelectronics, as a local field controlled by the gate or bias voltages also at high temperatures.

We present a theoretical description of the spin accumulation effect in metallic Fermi leads on the Kondo effect in the quantum dot attached to those. It has been shown that the spin accumulation by breaking the spin symmetry leads to the suppression of the Kondo effect in some cases. In order to better understand the observed effects, we analyze the spin currents in the system, depending on the spin accumulation of the electrodes, for both symmetrical and anti-symmetrical configuration of spin accumulation. We demonstrate that in the absence of the Kondo resonance splitting the suppression of the Kondo effect is related to the presence of the non-equilibrium spin current in the system.

We present a detailed theoretical description of the influence of the spin accumulation in metallic Fermi leads on the Kondo effect in systems such as quantum dots and Kondo alloys. We discuss an interplay of the spin accumulation, magnetic field, and ferromagnetic leads spin polarization on the Kondo spin-dependent densities of states, conductance, and resistance. It has been shown that the presence of the above-mentioned factors by breaking the spin symmetry leads to the suppression of the Kondo effect. However, for appropriately selected parameter values, these effects can compensate each other, which may lead to the restoration of the Kondo effect in the analyzed systems. We also address some recent experiments related to the spin current in the Kondo alloys.

We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreeev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively.

We analyze a Josephson junction between two superconductors interconnected through a normal-state nanostructure made of two parallel nanowires with embedded quantum dots. We study the influence of interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases for local and nonlocal (split) Cooper pairs. In the AB effect the phase of electron is affected by magnetic flux, while in the AC effect the phase of the electron in solid state can be modified due to the Rashba spin-orbit coupling. In the low-transmission regime the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively. We demonstrate that by the addition of the quantum dots the Cooper pair splitting can be made perfectly efficient and that the AC phase is different for non-spin-flip and spin-flip transport processes.

We analyze a model of double quantum dot Cooper pair splitter coupled to two ferromagnetic detectors, and demonstrate the possibility of determination of spin correlation by current measurements. We use perturbation theory taking account of the exchange interaction with the detectors, which leads to complex spin dynamics in the dots. This affects the measured spin and restricts the use of ferromagnetic detectors to the nonlinear current-voltage characteristic regime at current plateau, where the relevant spin projection is conserved, in contrast to the linear current-voltage characteristic regime, in which the spin information is distorted. Moreover, we show that for separable states the spin correlation can only be determined in a limited parameter regime, much more restricted than in the case of entangled states. We propose an entanglement test based on the Bell inequality.

We have studied the conductance of nanoscale junctions created at a metal-semiconductor interface by the break-junction technique. The conductance traces of the nanojunctions show steps related to the formation of successive metastable configurations of a few atoms. The plateau values in the conductance traces of nanojunctions formed between a nickel tip and a doped n-type germanium surface prove dependent on the polarity of the bias voltage applied to the nanojunction. The change in the conductance is due to the formation of a Schottky barrier within the nanojunction, as confirmed by the Schottky-diode-like nonlinear current-voltage characteristics determined for metastable configurations of atoms in the nanojunctions. Thus, we demonstrate the possibility of creating an ultra-small Schottky diode at an atomic quantum point contact.

The development of quantum computing in quantum dots systems requires highly efficient and continuous solid-state source of spatially separated spin-entangled electrons. One of the approaches is a use of double quantum dot system connected to superconducting lead, where Cooper pairs provide a source of naturally entangled electrons. Apart from the source, an useful tool for detection of quantum entanglement is needed. We present entanglement detection by the ferromagnetic electrodes using entanglement witness operator method and direct measurement of spin polarized current in the system. We investigate requirements that have to be fulfilled by ferromagnetic detectors.

Entangled states are essential in basics quantum communication protocols and quantum cryptography. Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible. Method of confirming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed. Entanglement witness (EW) operator method is compared with the CHSH inequalities approach. Required spin polarization for the EW is lower than for the CHSH inequalities. System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.

We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of eta > 1/root 3 approximate to 58% required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with eta > 1/(4)root 2 approximate to 84%. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

The break-junction technique is widely used to measure electronic properties of nanoscale junctions including metal point-contacts and single-molecule junctions. In these measurements, conductance is measured as a function of electrode displacement yielding data that is analyzed by constructing conductance histograms to determine the most frequently observed conductance values in the nanoscale junctions. However much of the rich physics in these measurements is lost in this simple analysis technique. Conductance histograms cannot be used to study the statistical relation of distinct junction configurations, to distinguish structurally different configurations that have similar conductance values, or to obtain information on the relation between conductance and junction elongation. Here, we give a detailed introduction to a novel statistical analysis method based on the two-dimensional cross-correlation histogram (2DCH) analysis of conductance traces and show that this method provides new information about the relation of different junction configurations that occur during the formation and evolution of metal and single-molecule junctions. We first illustrate the different types of correlation effects by using simulated conductance traces. We then apply this analysis method to several different experimental examples. We show from break-junction measurements of different metal point-contacts that in aluminum, the first conductance histogram peak corresponds to two different junction structures. In tantalum, we identify the frequent absence of adhesive instability. We show that conductance plateaus shift in a correlated manner in iron and vanadium junctions. Finally, we highlight the applicability of the correlation analysis to single-molecule platinum-CO-platinum and gold-4,4'-bipyridine-gold junctions.