Topologically guaranteed enhancement of nonlinear optical conductivity of graphene in the presence of spin-orbit coupling

Abstract

We demonstrate that a topological invariant term in graphene (e.g., spin-orbit coupling or interlayer coupling induced trigonal warping) can lead to a strong nonlinear optical response. We present a full quantummechanical analysis of the third-order nonlinear optical conductivity of the monolayer graphene with a finite Rashba spin-orbit coupling. For energy of the incident photon below the maximum height of the trigonal warping and the Rashba coupling strength exceeding a critical value the nonlinear conductance is enhanced dramatically in comparison with that in the absence of the topological term. Due to the trigonal warping effect and the topologically inequivalent change of the geometry of the energy band, the strong nonlinear effect persists, as long as the incident photon energy is limited below the energy maximum defined by the spin-orbit coupling. Disciplines Engineering | Science and Technology Studies Publication Details Liu, Z., Sanderson, M., Cao, J. & Zhang, C. (2014). Topologically guaranteed enhancement of nonlinear optical conductivity of graphene in the presence of spin-orbit coupling. Physical Review B Condensed Matter and Materials Physics, 90 (23), 235430-1-235430-6. This journal article is available at Research Online: http://ro.uow.edu.au/eispapers/3830 PHYSICAL REVIEW B 90, 235430 (2014) Topologically guaranteed enhancement of nonlinear optical conductivity of graphene in the presence of spin-orbit coupling Zheng Liu,1 Matthew Sanderson,2 J. C. Cao,1,* and C. Zhang2,† 1Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, China 2School of Physics, University of Wollongong, New South Wales 2522, Australia (Received 1 September 2014; revised manuscript received 27 November 2014; published 22 December 2014) We demonstrate that a topological invariant term in graphene (e.g., spin-orbit coupling or interlayer coupling induced trigonal warping) can lead to a strong nonlinear optical response. We present a full quantum-mechanical analysis of the third-order nonlinear optical conductivity of the monolayer graphene with a finite Rashba spin-orbit coupling. For energy of the incident photon below the maximum height of the trigonal warping and the Rashba coupling strength exceeding a critical value the nonlinear conductance is enhanced dramatically in comparison with that in the absence of the topological term. Due to the trigonal warping effect and the topologically inequivalent change of the geometry of the energy band, the strong nonlinear effect persists, as long as the incident photon energy is limited below the energy maximum defined by the spin-orbit coupling. DOI: 10.1103/PhysRevB.90.235430 PACS number(s): 73.63.Bd, 78.66.Tr, 78.67.−n