The SU (4)−SU (2) crossover, driven by an external magnetic field h, is analyzed in a capacitivelycoupled double-quantum-dot device connected to independent leads. As one continuously charges the dots from empty to quarter-filled, by varying the gate potential Vg, the crossover starts when the magnitude of the spin polarization of the double quantum dot, as measured by n ↑ − n ↓ , becomes finite. Although the external magnetic field breaks the SU (4) symmetry of the Hamiltonian, the ground state preserves it in a region of Vg, where n ↑ − n ↓ = 0. Once the spin polarization becomes finite, it initially increases slowly until a sudden change occurs, in which n ↓ (polarization direction opposite to the magnetic field) reaches a maximum and then decreases to negligible values abruptly, at which point an orbital SU (2) ground state is fully established. This crossover from one Kondo state, with emergent SU (4) symmetry, where spin and orbital degrees of freedom all play a role, to another, with SU (2) symmetry, where only orbital degrees of freedom participate, is triggered by a competition between gµBh, the energy gain by the Zeeman-split polarized state and the Kondo temperature T SU (4) K , the gain provided by the SU (4) unpolarized Kondo-singlet state. At fixed magnetic field, the knob that controls the crossover is the gate potential, which changes the quantum dots occupancies. If one characterizes the occurrence of the crossover by V max g , the value of Vg where n ↓ reaches a maximum, one finds that the function f relating the Zeeman splitting, Bmax, that corresponds to V max g , i.e., Bmax = f V max g , has a similar universal behavior to that of the function relating the Kondo temperature to Vg. In addition, our numerical results show that near the SU (4) Kondo temperature and for relatively small magnetic fields the device has a ground state that restricts the electronic population at the dots to be spin polarized along the magnetic field. These two facts introduce very efficient spin-filter properties to the device, also discussed in detail in the paper. This phenomenology is studied adopting two different formalisms: the Mean Field Slave Bosons Approximation, which allows an approximate analysis of the dynamical properties of the system, and a Projection Operator Approach, which has been shown to describe very accurately the physics associated to the ground state of Kondo systems.

The analysis of the impact of spin-orbit coupling (SOC) on the Kondo state has generated considerable controversy, mainly regarding the dependence of the Kondo temperature T K on SOC strength. Here, we study the one-dimensional (1D) single impurity Anderson model (SIAM) subjected to Rashba (α) and Dresselhaus (β) SOC. It is shown that, due to time-reversal symmetry, the hybridization function between impurity and quantum wire is diagonal and spin independent (as it is the case for the zero-SOC SIAM), thus the finite-SOC SIAM has a Kondo ground state similar to that for the zero-SOC SIAM. This similarity allows the use of the Haldane expression for T K , with parameters renormalized by SOC, which are calculated through a physically motivated change of basis. Analytic results for the parameters of the SOCrenormalized Haldane expression are obtained, facilitating the analysis of the SOC effect over T K . It is found that SOC acting in the quantum wire exponentially decreases T K while SOC at the impurity exponentially increases it. These analytical results are fully supported by calculations using the Numerical Renormalization Group (NRG), applied to the wide-band regime, and the Projector Operator Approach, applied to the infinite-U regime. Literature results, using Quantum Monte Carlo, for a system with Fermi energy near the bottom of the band, are qualitatively reproduced, using NRG. In addition, it is shown that the 1D SOC SIAM for arbitrary α and β displays a persistent spin helix SU(2) symmetry similar to the one for a 2D Fermi sea with the restriction α = β.

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The paper studies the electronic current in a one-dimensional lead under the effect of spin–orbit coupling and its injection into a metallic conductor through two contacts, forming a closed loop. When an external potential is applied, the time reversal symmetry is broken and the wave vector k of the circulating electrons that contribute to the current is spin-dependent. As the wave function phase depends upon the vector k, the closed path in the circuit produces spin-dependent current interference. This creates a physical scenario in which a spin-polarized current emerges, even in the absence of external magnetic fields or magnetic materials. It is possible to find points in the system’s parameter space and, depending upon its geometry, the value of the Fermi energy and the spin–orbit intensities, for which the electronic states participating in the current have only one spin, creating a high and totally spin-polarized conductance. For a potential of a few tens of meV, it is possible to obtain a spin-polarized current of the order of μA. The properties of the obtained electronic current qualify the proposed device as a potentially important tool for spintronics applications.