Electron transitions for Dirac Hamiltonians with flat bands under electromagnetic radiation: Application to the α−T3 graphene model

Abstract

In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency Ω. When a flat band is present two kinds of resonant transitions are found. Considering the α − T3 graphene model as a minimal model with a flat band and Dirac cones, and describing the dynamics using the interaction picture, we study the band transitions induced by an external electromagnetic field. We found that transitions depend upon the relative angle between the electron momentum and the electromagnetic field wavevector. For parallel incidence, the transitions are found using Floquet theory while for other angles perturbation theory is used. In all cases, the transition probabilities and the frequencies are found. For some special values of the parameter α or by charge doping, the system behaves as a three-level or a two-level Rabi system. All these previous results were compared with numerical simulations. A good agreement was found between both. The obtained results are useful to provide a quantum control of the system.

Dynamical Floquet spectrum of Kekulé-distorted graphene under normal incidence of electromagnetic radiation

“…The presence of this gap can be demonstrated analytically [40][41][42] and be confirmed using the standard quantum-field theory approach, where electronphoton interaction in graphene irradiated by polarized photons results in a metal-insulator transition 43 . These results extends to other Dirac materials 44,45 , like topological insulators 46 , borophene [47][48][49][50] , α−T 3 graphene [51][52][53][54] and silicene 55 . Moreover, although the electronic and optical conductivity that results from the application of an in-plane electromagnetic field has already been analytically studied 25 , until now the dynamical band structure of irradiated Kekulé graphene, where the two valley are nested in the same point, has not been explored yet.…”

Novel transport properties of the α-T3 lattice with uniform electric and magnetic fields

“…The following are examples in which a flat band is found: Lieb lattice 29 , optical lattice systems 30 , 31 , and 1 T-TaS2 material 32 , α -T 3 lattice 33 . The nondispersive flat band do not contribute to the electron transport due to the zero group velocity; however, the flat band in α -T 3 lattice leads to many peculiar characteristics in quantum transport 34 – 38 . Moreover, some attention has been devoted to the investigation of α -T 3 lattice with broken flat band.…”

Tailoring plasmon excitations in α − T3 armchair nanoribbons

“…Recently, Dirac semimetals also showed some interesting electronic properties, 52,53 although they closely resemble but not completely the same as those of α − T 3 . As a matter of fact, the unique electronic band structure of the α − T 3 model has proven to be responsible for its unusual electronic, optical, collective, magnetic and topological properties [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] which have been investigated extensively over the last several year…”