Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peak-value of AHC is as high as the bare-buble contribution. We find that the wave number, q, at which the peaks occur is the inverse of the geometric mean of the mean free path of an electron and the spin-exchange length scale. Although the Rashba energy is responsible for the peak-value of AHC, the peak position is independent of it.Comment: 5 pages, 4 figure

Site percolation in distorted square and simple cubic lattices with flexible number of neighbors

This paper exhibits a Monte Carlo study on site percolation using the Newmann-Ziff algorithm in distorted square and simple cubic lattices where each site is allowed to be directly linked with any other site if the euclidean separation between the pair is at most a certain distance d, called the connection threshold. Distorted lattices are formed from regular lattices by a random but controlled dislocation of the sites with the help of a parameter {\alpha}, called the distortion parameter. The distinctive feature of this study is the relaxation of the restriction of forming bonds with only the nearest neighbors. Owing to this flexibility and the intricate interplay between the two parameters {\alpha} and d, the site percolation threshold may either increase or decrease with distortion. The dependence of the percolation threshold on the average degree of a site has been explored to show that the obtained results are consistent with those on percolation in regular lattices with extended neighborhood and continuum percolation.Comment: 9 pages, 6 figures, Accepted in Phys. Rev.

Frequency- and transverse wave-vector-dependent spin Hall conductivity in two-dimensional electron gas with disorder

We determine wave number $q$ and frequency $\omega$ dependent spin Hall conductivity $\sigma_{yx}^s(q, \omega)$ for a disordered two dimensional electron system with Rashba spin orbit interaction when \q is {\it 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. $\sigma_{yx}^s(q, \omega)$ is zero at $q=0, \omega =0$ and is maximum at $q=0$ and at small but finite $\omega$ whose value depends on different parameters of the system. Interestingly for $\omega \to 0$, $\sigma_{yx}^s(q)$ resonates when $\Lambda \simeq L_{so}$ which are the wavelength $(\Lambda = 2\pi/q)$ 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 {\it vice versa} and consequently a finite spin Hall current flows in the bulk of the system.Comment: 6 pages; 6 figures; major changes including the titl

Transport properties of spin-orbit coupled electronic system

This thesis is a theoretical study of the e ect of spin-charge coupled dynamics on the transport properties of two dimensional electron systems (2DES) with spin-orbit interaction. It includes a prediction of a new phenomenon which is named as spin-spin Hall effect and studies on anomalous Hall and spin Hall e ect when the applied electric field is inhomogeneous. The calculations are mainly based on the Kubo formalism of the linear response theory. The plan of the thesis is as follows – Chapter 1: This chapter is an introduction to the thesis. The two main directions of spintronics research is briefly pointed out. The spin orbit coupling is discussed in the context of controlling the electronic spin in semiconductor structures. The term that plays the key role behind all the phenomena addressed in this thesis is the Rashba spin orbit coupling term. This term originates from the lack of structural inversion symmetry in semiconductor heterostructures. The origin of such an asymmetry and the occurrence of the Rashba term is presented including an outline of its derivation. Chapter 2: It demonstrates how the presence of the Rashba coupling can be explored to explain as well as to predict some novel e ects in 2DES. Some essential general properties of the Rashba Hamiltonian that cause the spin-charge coupled transport in these systems are discussed. The proposal of SFET is presented followed by an overview of the three spin-dependent Hall e ects, namely, anomalous Hall e ect, spin Hall e ect and spin-spin Hall e ect. The corresponding conductivities are related to the current-current correlation functions. The problem of conservation of spin current and its possible way-out to perform linear response theory is reviewed. Chapter 3: This chapter is devoted to Anomalous Hall E ect (AHE), which is an intensively studied problem, yet awaits a clear physical understanding of its origin. AHE is studied in a disordered two dimensional electron system with Rashba spin-orbit coupling and ferromagnetic exchange interaction. It is known that when the Fermi level goes well above the band gap created by the exchange interaction, the anomalous Hall conductivity(AHC) vanishes in the metallic weak scattering regime due to disorder correction. It is shown that AHC may re-occur if the applied electric field is inhomogeneous, specifically, if it varies periodically in its own direction. The system parameters are related to the wavelength of this variation which may be properly tuned to maximize the magnitude of AHC. Chapter 4: It contains a study on spin-Hall e ect; a phenomenon originally predicted long back in 1971 and gained renewed interest in the spintronics perspective. In a two dimensional pure Rashba system, the spin Hall conductivity (SHC) takes a universal value which is exactly canceled by -function disorders irrespective of their concentration. In this chapter, SHC as a function of frequency and finite wave-vector (perpendicular to the electric field) is derived including disorder vertex correction. In the zero-frequency limit, dc- SHC resonates when the periodicity of the electric field matches with the spin-precession length scale. The physical mechanism responsible for this extraordinary e ect is also described. Further, it is numerically shown that this result also holds (in fact with enhanced magnitude of SHC) when the modified definition for conserved spin-current is considered. Chapter 5: This chapter predicts the existence of a novel phenomenon which may be called as spin-spin Hall effect. When the full charge-spin Hall conductivity matrix is calculated for a Rashba 2DES, it is found that there is another non-zero term apart from SHC. VIII This term originates from the correlation of in-plane currents. A current of x-spin-polarized electrons in x-direction induces a current of y-spin-polarized electrons in y-direction. The effect of Dresselhaus spin orbit interaction on this phenomenon is also discussed.The research was carried out under the supervision of Prof. S S Mondal of the Theoretical Physics division under the SPS [School of Physical Sciences