Abstract
Rashba spin-orbit effects and electron correlations in the two-dimensional cylindrical lattices of square geometries are assessed using mesoscopic two-, three- and four-leg ladder structures. Here the electron transport properties are systematically calculated by including the spin-orbit coupling in tight binding and Hubbard models threaded by a magnetic flux. These results highlight important aspects of possible symmetry breaking mechanisms in square ladder geometries driven by the combined effect of a magnetic gauge field spin-orbit interaction and temperature. The observed persistent current, spin and charge polarizations in the presence of spin-orbit coupling are driven by separation of electron and hole charges and opposite spins in real-space. The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures (as arrays of clusters) engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors. Such studies also fall under the scope of current challenging problems in superconductivity and magnetism, topological insulators and spin dependent transport associated with numerous interfaces and heterostructures.
Highlights
Monolayer thick ribbons or ladders, threaded by a magnetic field, provide extremely versatile and tunable systems for studying band structure, electronic transport, spin and charge polarization as well as topological properties
The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors
Our results show that the spin-orbit coupling combined with a magnetic field can provide real-space separation of charge and spins leading to the spatial charge and spin inhomogeneities in these nano-ribbons
Summary
Monolayer thick ribbons or ladders, threaded by a magnetic field, provide extremely versatile and tunable systems for studying band structure, electronic transport, spin and charge polarization as well as topological properties. The hopping term and SOC coupling are modified by the exponential factor θ=2πΦ/LΦ0 This Hamiltonian is used first for an unbiased study of small multi-ladders and multi-ribbons to calculate essential spin-related and electronic properties. We consider first the half filled ribbon with 4 legs in a square 4-legged (infinite) ladder with (no magnetic field and) a non-zero Rashba term (VSO 0). The addition of the Rashba SOC term splits the energy bands as shown but the degeneracies at the special k-point(s) remain. Note that it is the time reversal symmetry that protects the degeneracies at special k-points
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