Localization in one-dimensional disordered or quasiperiodic noninteracting systems in the presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed to exponential localization in short-ranged systems. Exponential localization is synonymous with insulating behavior in the thermodynamic limit. Here we show that the same is not true for algebraic localization. We show, on general grounds, that depending on the strength of the algebraic decay, the algebraically localized states can be actually either conducting or insulating in thermodynamic limit. We exemplify this statement with explicit calculations on the Aubry-André-Harper model in the presence of power-law hopping, with the power-law exponent $\alpha >1$, so that the thermodynamic limit is well defined. We find a phase of this system where there is a mobility edge separating completely delocalized and algebraically localized states, with the algebraically localized states showing signatures of superdiffusive transport. Thus, in this phase, the mobility edge separates two kinds of conducting states, ballistic and superdiffusive. We trace the occurrence of this behavior to near-resonance conditions of the on-site energies that occur due to the quasiperiodic nature of the potential.

We propose two new approaches for regulating spin polarization and spin inversion in a conducting junction within a tight-binding framework based on wave-guide theory. The system comprises a magnetic quantum ring with finite modulation in site potential is coupled to two non-magnetic electrodes. Due to close proximity an additional tunneling is established between the electrodes which regulates electronic transmission significantly. At the same time the phase associated with site potential, which can be tuned externally yields controlled transmission probabilities. Our results are valid for a wide range of parameter values which demonstrates the robustness of our proposition. We strongly believe that the proposed model can be realized in the laboratory.

We report transport properties and particle current rectification operation in a double-stranded tight-binding ladder network within non-equilibrium Green’s function formalism that can easily be generalized in multi-stranded systems. First, we explore the rectification operation considering the model of an artificial double-stranded DNA molecular system with Fibonacci type substitutional sequence. Substitutional sequences form quasi-periodic potentials. This analysis may shed new light in designing efficient nanoscale rectifier. It can also be directly implemented to different biomolecular systems like nucleic acids and most proteins as they follow quasi-periodic orders. Motivated with this fact, we consider different configurations depending on the choices of on-site energies and/or inter or intra strand nearest-neighbor hopping integrals in the form of Aubry–André–Harper (AAH) model (that also obeys quasi-periodic order), and in all the cases we find almost current rectification even at very low bias region. Along with this, we observe that the phase (positive or negative) of rectification can suitably be engineered by tuning the Fermi energy and AAH phase. The effects of electron–electron (e–e) interaction and temperature are also studied, which show that a reasonably large rectification can be observed even for moderate temperature range and e–e interaction strength.

Magnetic helix (MH) structure can be a role model for future spintronic devices. Utilizing the advantage of constructing possible magnetic configurations, in this work we investigate spintronic behavior in a helical geometry with finite magnetic ordering. The interplay between short- and long-range hopping of electrons yields many nontrivial features which are thoroughly studied. Quite interestingly, we see that the MH exhibits the strong chiral-induced spin-selectivity effect, like what is observed in chiral molecules. Finally, to make the model more realistic, we also examine the effect of helical dynamics. All the results are valid for a wide range of physical parameters, which prove the robustness of our analysis.

A new proposal is given to control local magnetic field in a molecular junction. In presence of finite bias a net circular current is established in the molecular ring which induces a magnetic field at its centre. Allowing a direct coupling between two electrodes, due to their close proximity, and changing its strength we can regulate circular current as well as magnetic field for a wide range, without disturbing any other physical parameters. We strongly believe that our proposal is quite robust compared to existing approaches of controlling local magnetic field and can be verified experimentally.