This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable parameter α to create a distorted empty lattice. In this model, two neighboring sites are considered to be connected to each other in order to belong to the same cluster, if both of them are occupied as per the criterion of usual percolation and the distance between them is less than or equal to a certain value, called connection threshold d. While spanning becomes difficult in distorted lattices as is manifested by the increment of the percolation threshold pc with α, an increased connection threshold d makes it easier for the system to percolate. The scaling behavior of the order parameter through relevant critical exponents and the fractal dimension d f of the percolating cluster at pc indicate that this new type of percolation may belong to the same universality class as ordinary percolation. This model can be very useful in various realistic applications since it is almost impossible to find a natural system that is perfectly ordered.

We determine wave number q and frequency ω dependent spin Hall conductivity σ s yx (q, ω) for a disordered two dimensional electron system with Rashba spin orbit interaction when q is transverse to the electric field. Both the conventional definition of spin current and its new definition which takes care of the conservation of spins, have been considered. The spin Hall conductivitivities for both of these definitions are qualitatively similar. σ s yx (q, ω) is zero at q = 0, ω = 0 and is maximum at q = 0 and at small but finite ω whose value depends on different parameters of the system. Interestingly for ω → 0, σ s yx (q) resonates when Λ ≃ Lso which are the wavelength (Λ = 2π/q) of the electric field's spatial variation and the length for one cycle of spin precession respectively. The sign of the out-of-plane component of the electrons' spin flips when the sign of electric field changes due to its spatial variation along transverse direction. It changes the mode of spin precession from clockwise to anti-clockwise or vice versa and consequently a finite spin Hall current flows in the bulk of the system.

We calculate spin-Hall conductivities in the two dimensional electron systems with Rashba spinorbit interaction. The salient feature is that, apart from the usual spin-Hall conductivity σ z xy which corresponds to the induction of out-of-plane spin-current due to the application of transverse charge current, there is a novel spin-Hall conductivity σ ⊥ xy which arises due to the induction of transverse spin-polarized current in the transverse direction by the application of in-plane spinpolarized current. This phenomenon which we call as 'spin-spin' Hall effect is a spin analog of conventional Hall effect, but with no magnetic field. This contribution may be understood through the spin-diffusive equation.

No abstract

No abstract