Active and Passive Transport of Cargo in a Corrugated Channel: A Lattice Model Study

Inside cells, cargos such as vesicles and organelles are transported by molecular motors to their correct locations via active motion on cytoskeletal tracks and passive, Brownian diffusion. During the transportation of cargos, motor-cargo complexes (MCC) navigate the confining and crowded environment of the cytoskeletal network and other macromolecules. Motivated by this, we study a minimal two-state model of motor-driven cargo transport in confinement and predict transport properties that can be tested in experiments. We assume that the motion of the MCC is directly affected by the entropic barrier due to confinement if it is in the passive, unbound state, but not in the active, bound state where it moves with a constant bound velocity. We construct a lattice model based on a Fokker Planck description of the two-state system, study it using a kinetic Monte Carlo method and compare our numerical results with analytical expressions for a mean field limit. We find that the effect of confinement strongly depends on the bound velocity and the binding kinetics of the MCC. Confinement effectively reduces the effective diffusivity and average velocity, except when it results in an enhanced average binding rate and thereby leads to a larger average velocity than when unconfined.Comment: 12 pages, 7 figure

Integer quantum Hall effect in a square lattice revisited

We investigate the phenomenon of integer quantum Hall effect in a square lattice, subjected to a perpendicular magnetic field, through Landauer-B\"uttiker formalism within the tight-binding framework. The oscillating nature of longitudinal resistance and near complete suppression of momentum relaxation processes are examined by studying the flow of charge current using Landauer-Keldysh prescription. Our analysis for the lattice model corroborates the finding obtained in the continuum model and provides a simple physical understanding.Comment: 5 pages, 5 figure

Effect of Dephasing on Electron Transport in a Molecular Wire: Green's Function Approach

The effect of dephasing on electron transport through a benzene molecule is carefully examined using a phenomenological model introduced by B\"{u}ttiker. Within a tight-binding framework all the calculations are performed based on the Green's function formalism. We investigate the influence of dephasing on transmission probability and current-voltage characteristics for three different configurations ({\em ortho}, {\em meta} and {\em para}) of the molecular system depending on the locations of two contacting leads. The presence of dephasing provides a significant change in the spectral properties of the molecule and exhibits several interesting patterns that have so far remain unexplored.Comment: 8 pages, 10 figure

Spin-orbit interaction induced spin selective transmission through a multi-terminal mesoscopic ring

Spin dependent transport in a multi-terminal mesoscopic ring is investigated in presence of Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we use a general spin density matrix formalism to evaluate all three components ($P_x$, $P_y$ and $P_z$) of the polarization vector associated with the charge current through the outgoing leads. It explores the dynamics of the spin polarization vector of current propagating through the system subjected to the Rashba and/or the Dresselhaus spin-orbit couplings. The sensitivity of the polarization components on the electrode-ring interface geometry is discussed in detail. Our present analysis provides an understanding of the coupled spin and electron transport in mesoscopic bridge systems.Comment: 11 pages, 14 figure

Spin Hall effect in a Kagome lattice driven by Rashba spin-orbit interaction

Using four-terminal Landauer-B\"{u}ttiker formalism and Green's function technique, in this present paper, we calculate numerically spin Hall conductance (SHC) and longitudinal conductance of a finite size kagome lattice with Rashba spin-orbit (SO) interaction both in presence and absence of external magnetic flux in clean limit. In the absence of magnetic flux, we observe that depending on the Fermi surface topology of the system SHC changes its sign at different values of Fermi energy, along with the band center. Unlike the infinite system (where SHC is a universal constant $\pm \frac{e}{8 \pi}$), here SHC depends on the external parameters like SO coupling strength, Fermi energy, etc. We show that in the presence of any arbitrary magnetic flux, periodicity of the system is lost and the features of SHC tends to get reduced because of elastic scattering. But again at some typical values of flux ($\phi=1/2, 1/4, 3/4..., etc.) the system retains its periodicity depending on its size and the features of spin Hall effect (SHE) reappears. Our predicted results may be useful in providing a deeper insight into the experimental realization of SHE in such geometries.Comment: 10 pages, 10 figure

Magneto-transport in a mesoscopic ring with Rashba and Dresselhaus spin-orbit interactions

Electronic transport in a one-dimensional mesoscopic ring threaded by a magnetic flux is studied in presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in presence of the spin-orbit interactions and leads to a method of determining the strength of the Dresselhaus interaction. In addition to this, the persistent currents for ordered and disordered rings have been investigated numerically. It is observed that, the presence of the spin-orbit interaction, in general, leads to an enhanced amplitude of the persistent current. Numerical results corroborate the respective analytical findings.Comment: 7 pages, 7 figure

Selective spin transport through a quantum heterostructure: Transfer matrix method

In the present work we propose that a one-dimensional quantum heterostructure composed of magnetic and non-magnetic atomic sites can be utilized as a spin filter for a wide range of applied bias voltage. A simple tight-binding framework is given to describe the conducting junction where the heterostructure is coupled to two semi-infinite one-dimensional non-magnetic electrodes. Based on transfer matrix method all the calculations are performed numerically which describe two-terminal spin dependent transmission probability along with junction current through the wire. Our detailed analysis may provide fundamental aspects of selective spin transport phenomena in one-dimensional heterostructures at nano-scale level.Comment: 12 pages, 15 figures (Accepted for Publication in: International Journal of Modern Physics B