Spin-Dependent Scattering From Gated Obstacles in Graphene

Systems M.M. Asmar & S.E. Ulloa

Ohio University

Outline Motivation.

The studied system and the mathematical approach.

Results and analysis.

Conclusions.

Because of the high importance of spintronics on which the spin orbit interactions play a basic role, we study and compare the relaxation times in the presence of a gated potential to the relaxation times in the presence of SOI in graphene systems.

The importance of the relaxation times is based on their proportionality to the conductance of the system.

Motivation

The studied system and the mathematical approach

The Hamiltonian of the system:

Wave functions (at K point) are :

, and From the analytical form of the wave function we can extract some

information such as Phase shifts Differential cross sections Total cross sections Transport cross section which is inversely proportional to the relaxation time Conductance, which is proportional to the relaxation time

Total angular momentum

• C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).

m

Results and Analysis In the presence of a gated obstacle and no SOI

Ramsauer-Townsend Effect at V/2

•J. Milton Pereira, Jr., V. Mlinar, and F. M. Peeter, P RB 74, 045424 (2006)

In the presence gated obstacles and Intrinsic SOI

• C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).• Daniel Huertas-Hernando, F. Guinea,and Arne Brataas1, PRB 74,

155426 (2006).

In the presence of the gated obstacle and Rashba SOI

Comparable relaxation times

• Gierz, et al., arXiv:1004.1573.• J. Sánchez-Barriga, et al. , Diamond & Related Materials 19

(2010) 734–74

Longer spin flip relaxation times

• A.H. Castro Neto and F. Guinea, PRL 103, 026804 (2009).• N. Tombros et al., Nature (London) 448, 571 (2007).

In the presence of the gated obstacle RSOI and ISOI

ConclusionsQuasi bound states reflect themselves as

resonances in the cross section.Intrinsic SO decreases the scattering time and

shifts the resonances in the cross section.Spin flip relaxation times are much longer that

the momentum relaxation times at low energies.Momentum and spin-flip scattering times are

comparable at relatively high energies.Spin flip times and momentum relaxation times

are equal at both the K and K’ point.

Thank You