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Using transfer matrix method, transport properties in graphene based double velocity-barrier structures under magnetic and electric fields are numerically studied. It is found that velocity barriers for the velocity ratio (the Fermi velocity inside the barrier to that outside the barrier) less than one (or for the velocity ratio greater than one) have properties similar to electrostatic wells (or barriers). The velocity barriers for the velocity ratio greater than one significantly enlarge the resonant tunneling region of electrostatic barriers. In the presence of magnetic field, the plateau width of the Fano factor with a Poissonian value shortens (or broadens) for the case of the velocity ratio less than one (or greater than one). When the Fermi energy is equal to the electrostatic barrier height, for different values of the velocity ratio, both the conductivities and the Fano factors remain fixed.

The Kondo effect and the Andreev reflection tunneling through a normal (ferromagnet)–double quantum dots–superconductor hybrid system is examined in the low temperature by using the nonequilibrium Green's function technique in combination with the slave-boson mean-field theory. The interplay of the Kondo physics and the Andreev bound state physics can be controlled by varying the interdot hopping strength. The Andreev differential conductance is mainly determined by the competition between Kondo states and Andreev states. The spin-polarization of the ferromagnetic electrode increases the zero-bias Kondo peak. The spin-flip scattering influences the Kondo effect and the Andreev reflection in a nontrivial way. For the ferromagnetic electrode with sufficiently large spin polarization, the negative Andreev differential conductance is found when the spin flip strength in the double quantum dots is sufficiently strong.

The electron transport through an Aharonov–Bohm (AB) interferometer with embedded four coupled quantum dots (QDs) is studied with the Green's function technique. The QDs are coupled to each other by the hopping integral t c . Two among them connect with the left lead and the other two with the right lead by the tunneling matrix element T which incorporates the effects of the applied magnetic field φ. The linear conductance spectra swap between the molecular levels and the atomic states by adjusting t c and T. Fano effect appears when the electrons tunnel through different channels contributed by different QDs energy levels, and the Fano resonance peaks split for large t c . The Fano factor can be manipulated by t c , T, φ, and the QD energy levels.

Using an adiabatic approximate method, spin-dependent conductance and thermopower of quasi-one-dimensional semiconductor nano-constrictions are investigated in the presence of Rashba spin–orbit interaction under an applied magnetic field. The significant quantum size, quantum coherence, and spin–orbit interaction are considered simultaneously. With the strength of the spin–orbit coupling increasing, the thermopower oscillates more rapidly, the peaks become sharper, and the intervals between adjacent peaks are narrowed. The results also indicate that the conductance and the thermopower are strongly spin-dependent due to the spin split originated from the spin–orbit interaction and the Zeeman effect.

Using the scattering matrix theory, magnetocapacitance properties are investigated in magnetic nanocontacts. In the ferromagnetic alignment, the effective potential of the exchange splitting energy acts as a quantum well for spin-up electrons and as a quantum barrier for spin-down ones, which results in spin-dependent capacitance. When the system switches from the ferromagnetic alignment to the antiferromagnetic alignment induced by an external magnetic field, the capacitance changes correspondingly. This magnetocapacitance effect can be expected to be useful in designing a magnetocapacitor.

Using scattering matrix method, the spin-dependent conductance and thermopower in ferromagnetic quantum point contacts (QPCs) are calculated at a certain temperature. The results indicate that the exchange splitting energy removes the spin degeneracy and the spin-up and spin-down electrons have different contributions to the conductance and the thermopower. The odd integer multiples of the quantized conductance, G 0 ( = e 2 / h ) , appear and the position of the peaks in thermopower shift correspondingly.

A four-terminal parallel double quantum dots (QDs) device is proposed to generate and detect the spin polarization in QDs. It is found that the spin accumulation in QDs and the spin-polarized currents in the upper and down leads can be generated when a bias voltage is applied between the left and right leads. It is more interesting that the spin polarization in the QDs can be detected using the upper and down leads. Moreover, the direction and magnitude of the spin polarization in the QDs, and in the upper and down leads can be tuned by the energy levels of QDs and the bias.