We examine the low-energy physics of graphene in the presence of a circularly polarized electric field in the terahertz regime. Specifically, we derive a general expression for the dynamical polarizability of graphene irradiated by an ac electric field. Several approximations are developed that allow one to develop a semianalytical theory for the weak field regime. The ac field changes qualitatively the single and many electron excitations of graphene: undoped samples may exhibit collective excitations (in contrast to the equilibrium situation), and the properties of the excitations in doped graphene are strongly influenced by the ac field. We also show that the intensity of the external field is the critical control parameter for the stability of these excitations.
Using Floquet theory, we illustrate that Floquet Weyl fermions can be created in circularly-polarised-light-irradiated three-dimensional stacked graphene systems. One or two semi-Dirac points can be formed due to overlapping of Floquet sub-bands. Each pair of Weyl points have a two-component semi-Dirac point parent, instead of a four-component Dirac point parent. Decreasing the light frequency will make the Weyl points move in the momentum space, and the Weyl points can approach to the Dirac points when the frequency becomes very small. The frequency-amplitude phase diagram is worked out. It i…
Topological states of matter in equilibrium, as well as out of equilibrium, have been thoroughly investigated during the last years in condensed-matter and cold-atom systems. However, the geometric topology of the studied samples is usually trivial, such as a ribbon or a cylinder. In this paper, we consider a graphene Möbius band irradiated with circularly polarised light. Interestingly, due to the non-orientability of the Möbius band, a homogeneous quantum Hall effect cannot exist in this system, but the quantum spin Hall effect can. To avoid this restriction, the irradiation is applied in a …
Gapless bilayer graphene is susceptible to a variety of spontaneously gapped states. As predicted by theory and observed by experiment, the ground state is however topologically trivial, because a valley-independent gap is energetically favorable. Here, we show that under the application of interlayer electric field and circularly polarized light, one valley can be selected to exhibit the original interaction instability while the other is frozen out. Tuning this Floquet system stabilizes multiple competing topological ordered states, distinguishable by edge transport and circular dichroism. N…
We propose a tunable optical setup to engineer topologically nontrivial flat bands in twisted bilayer graphene under circularly polarized light. Using both analytical and numerical calculations, we demonstrate that nearly flat bands can be engineered at small twist angles near the magic angles of the static system. The flatness and the gaps between these bands can be tuned optically by varying laser frequency and amplitude. We study the effects of interlayer hopping variations on Floquet flat bands and find that lattice relaxation favors their formation. Furthermore, we find that, once formed,…
The coherent charge transport through an illuminated graphene ribbon is studied as function of electronic doping, frequency and strength of the electromagnetic driving, for monochromatic circularly polarized light. We focus on the DC current carried by 2D bulk carriers which is dominant (over edge transport) for short and wide enough samples. Broad dips in conductance are predicted for one-photon and multi-photon resonances between the valence and conductance bands. The residual conductance can be associated with evanescent states and related to dynamical gaps in the Floquet quasi-energy spect…
We theoretically investigate the impurity levels and exchange interaction between magnetic impurities in graphene driven by an off-resonant circularly polarized light field. Our analysis captures the non-perturbative effects resulting from scattering with magnetic impurities with a strong onsite potential. Under irradiation, a dynamical band gap opens up at the Dirac point, allowing impurity levels to exist inside the gap. These impurity levels are shown to give rise to a resonance feature in the exchange energy for impurities located either at the same or different sublattices. The exchange i…
A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from M…
We demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in graphene can be strongly modified by a time-periodic driving field even in the weak drive regime. This effect is due to the opening of a dynamical band gap at the Dirac points when graphene is exposed to circularly polarized light. Using Keldysh-Floquet Green's functions, we develop a theoretical framework to calculate the time-averaged RKKY coupling under weak periodic drives and show that its magnitude in undoped graphene can be decreased controllably by increasing the driving strength, while mostly maintaining its f…
Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge stat…
In the presence of a circularly polarized mid-infrared radiation graphene develops dynamical band gaps in its quasi-energy band structure and becomes a Floquet insulator. Here we analyze how topologically protected edge states arise inside these gaps in the presence of an edge. Our results show that the gap appearing at $\hbarΩ/2$, where $\hbar Ω$ is the photon energy, is bridged by two chiral edge states whose propagation direction is set by the direction of the polarization of the radiation field. Therefore, both the propagation direction and the energy window where the states appear can be …
Magneto conductivities in Weyl semimetals (WSM) in presence of small fields are studied using quasi-classical Boltzmann transport equations (BTE). Following such formalism here we consider irradiation via circularly polarized light on a two-node time reversal breaking WSM already under a dc/static electric field and study the magneto-transport properties due to the presence of chiral anomaly. Chiral anomaly affects both longitudinal magnetoconductivity as well as planar Hall conductivity. {As our field set-up causes continuous time variation in the relative orientation between the fields, one …
In two-dimensional (2D) electron systems, an off-resonant high-frequency circularly polarized electromagnetic field can induce the quasi-stationary bound electron states of repulsive scatterers. As a consequence, the resonant scattering of conduction electrons through the quasi-stationary states and the capture of conduction electrons by the states appear. The present theory describes the transport properties of 2D electron gas irradiated by a circularly polarized light, which are modified by these processes. Particularly, it is demonstrated that irradiation of 2D electron systems by the off-r…
We have formulated a theory for investigating the conditions which are required to achieve entangled states of electrons on graphene and three-dimensional (3D) topological insulators (TIs). We consider the quantum entanglement of spins by calculating the exchange energy. A gap is opened up at the Fermi level between the valence and conduction bands in the absence of doping when graphene as well as 3D TIs are irradiated with circularly-polarized light. This energy band gap is dependent on the intensity and frequency of the applied electromagnetic field. The electron-photon coupling also gives r…
We demonstrate theoretically that an off-resonant circularly polarized electromagnetic field can induce a persistent current in carbon nanotubes, which corresponds to electron rotation about the nanotube axis. As a consequence, the nanotubes acquire magnetic moment along the axis, which depends on their crystal structure and can be detected in state-of-the-art measurements. This effect and related phenomena are analyzed within the developed Floquet theory describing the electronic properties of the nanotubes irradiated by the field.
Employing the Landauer-Buttiker formula we investigate the spin and valley dependence of Seebeck effect in low-buckled Dirac materials (LBDMs), whose band structure are modulated by local application of a gate voltage and off-resonant circularly polarized light. We calculate the charge, spin and valley Seebeck coefficients of an irradiated LBDM as functions of electronic doping, light intensity and the amount of the electric field in the linear regime. Our calculation reveal that all Seebeck coefficients always shows an odd features with respect to the chemical potential. Moreover, we show tha…
We investigate topological characteristics of the photon-dressed band structure of $α$-$\mathcal{T}_3$ lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at $ {\bf K}$ and ${\bf K}^{\prime}$ (except at $α=0$ and 1), which reveals the absence of inversion symmetry in the system. At $α=1/\sqrt{2}$, the gap between …
We apply a circularly and linearly polarized terahertz field on a monolayer of graphene taking into account spin-orbit interactions of the intrinsic and Rashba type. It turns out that the field can not only be used to induce a gap in the energy spectrum, but also to close an existing gap due to the different reaction of the spin components on circularly polarized light. Signatures of spin-orbit coupling on the density of states of the driven system can be observed even for energies where the static density of states is independent of spin-orbit interactions. Furthermore it is shown that the ti…
Graphene irradiated by a circularly polarized laser has been predicted to be a Floquet topological insulator showing a laser-induced quantum Hall effect. A circularly polarized laser also drives the system out of equilibrium resulting in non-thermal electron distribution functions that strongly affect transport properties. Results are presented for the Hall conductance for two different cases. One is for a closed system such as a cold-atomic gas where transverse drift due to non-zero Berry curvature can be measured in time of flight measurements. For this case the effect of a circularly polari…
We demonstrated theoretically that the renormalization of the electron energy spectrum near the Dirac point of graphene by a strong high-frequency electromagnetic field (dressing field) drastically depends on polarization of the field. Namely, linear polarization results in an anisotropic gapless energy spectrum, whereas circular polarization leads to an isotropic gapped one. As a consequence, the stationary (dc) electronic transport in graphene strongly depends on parameters of the dressing field: A circularly polarized field monotonically decreases the isotropic conductivity of graphene, whe…
We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a non-equilibrium steady state that is well-described by topologically non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dress…
