Topological phase transitions and quantum Hall effect in the graphene family

Abstract

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaks which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. This complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

“…5 , for instance, that and have positive and negative resonances depending on the resonant Dirac gap. Therefore, just as the linear Hall conductivity allows to probe topological properties of the GFM at finite frequencies 46 , so it does at the nonlinear regime. Indeed, the Chern number associated to the open Dirac cones at any point in phase space can be computed by summing the sign of or precisely at the resonant frequencies, accounting appropriately for degeneracy among mass gaps, and multiplying the result by or , respectively.…”

“…Note that this argument can be extended to the nonlinear spin, valley, and spin-valley Hall currents, allowing for obtaining the full set of Chern numbers characterizing the topological phases in buckled two-dimensional semiconductors. In addition, unlike the linear case where to obtain the Chern number one needs to measure the linear Hall conductivity at various points around a resonance to obtain the sign of its derivative 46 , here we need to evaluate at most at the four (in the non-degenerate case) resonant frequencies. Finally, we mention that the dependence of the transverse (longitudinal) conductivities on ( ) are not exclusive to the third order nonlinear case and similar conclusions should hold for higher order contributions as well.…”

“…Unravelling the interplay between topology and nonlinear effects in spin-orbit coupled monolayer semiconductors of the graphene family is a natural step at the materials science forefront, which could aid in developing next-generation technologies that meet the urgent demands for, among others, higher performance radio-frequency modulators, optically gated transistors, and practical spintronic-based devices. Nevertheless, studies on the optoelectronic properties of these materials have largely focused in their linear response 41 – 51 , which include investigations of signatures of the tunable band gap 41 , 42 , spatial dispersion 43 , 44 , the interplay between the quantum Hall effect 45 and photo-induced topology 46 , as well as of topological phase transitions in quantum forces 47 , 48 , spin-orbit photonic interactions 49 , and light beam shifts 50 , 51 . The crossroads between nonlinear dynamics and topology in the extended graphene family, potentially allowing access to topological phase transition signatures, material symmetries, selection rules, and relaxation mechanisms otherwise screened by spurious effects in the linear response, remains uncharted.…”

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

“…yx (3ω) have positive and negative resonances depending on the resonant Dirac gap. Therefore, just as the linear Hall conductivity allows to probe topological properties of the GFM at finite frequencies 46 , so it does at the nonlinear regime. Indeed, the Chern number associated to the open Dirac cones at any point in phase space can be computed by summing the sign of σ yx (3ω) precisely at the resonant frequencies, accounting appropriately for degeneracy among mass gaps, and multiplying the result by +1/2 or −1/2, respectively.…”

“…Unravelling the interplay between topology and nonlinear effects in spin-orbit coupled monolayer semiconductors of the graphene family is a natural step at the materials science forefront, which could aid in developing next-generation technologies that meet the urgent demands for, among others, higher performance radiofrequency modulators, optically gated transistors, and practical spintronic-based devices. Nevertheless, studies on the optoelectronic properties of these materials have largely focused in their linear response [41][42][43][44][45][46][47][48][49][50][51] , which include investigations of signatures of the tunable band gap 41,42 , spatial dispersion 43,44 , the interplay between the quantum Hall effect 45 and photoinduced topology 46 , as well as of topological phase transitions in quantum forces 47,48 , spin-orbit photonic interactions 49 , and light beam shifts 50,51 . The crossroads between nonlinear dy-namics and topology in the extended graphene family, potentially allowing access to topological phase transition signatures, material symmetries, selection rules, and relaxation mechanisms otherwise screened by spurious effects in the linear response, remains uncharted.…”