Band structure effects on the nonlinear optical response of bilayer graphene

Recently, Rabi-like oscillations that occur far from resonance were predicted in monolayer graphene. In bilayer graphene, when the trigonal warping effect is taken into account, this new Rabi frequency shows a zero non-trivial minimum as a function of the strength of the applied electric field in addition to the trivial minimum at zero field. The zero non-trivial minimum occurs where the ‘leg pocket’ of the Fermi surface develops, described in the pioneering work of McCann et al. [Eur. Phys. J. Special Topics 148, 91 (2007)]. Thereafter, the anomalous Rabi frequency varies linearly with the square of the intensity of the applied field consistent with a bilayer system without trigonal warping. It is seen that this anomalous Rabi frequency is affected much more by trigonal warping than the conventional Rabi frequency. The induced current is also significantly affected by the trigonal warping. A fully numerical solution of the optical Bloch equations completely corroborates the analytical findings and provides a basis for the approximation schemes employed.     

A theoretical study of pump–probe experiment in single-layer,bilayer and multilayer graphene

The pump–probe experiment is typically used to study relaxation phenomena in nonlinear optical systems. Here we use it as a tool to study the phenomenon of anomalous Rabi oscillations in graphene that was predicted recently in single-layer graphene. Unlike conventional Rabi oscillations, anomalous Rabi oscillations are unique to graphene (and possibly to surface states of topological insulators (TIs)), attributable to the pseudospin (conventional spin for TI) degree of freedom and Dirac-fermion character of the graphene system. A pump pulse of a finite duration long enough to contain a large number of cycles induces a current density that oscillates with the frequency of the pump pulse. The amplitude associated with these fast oscillations is seen to exhibit much slower oscillations with a frequency given by \({ 2 \omega ^2_{\mathrm {R}} }/{ \omega } \) – the anomalous Rabi frequency, where ω _R is the conventional Rabi frequency and ω is the frequency of the external pump field. This effect is easily probed by a probe pulse subsequent to the pump, where it manifests itself as periodic oscillations of the probe susceptibility as a function of pump duration at each probe frequency. Alternatively, it is also seen as an oscillatory function of the pump–probe delay with other variables remaining fixed. This period corresponds to the anomalous Rabi frequency. An analysis of the previously reported experimental data confirms the presence of anomalous Rabi oscillations in graphene.     

Probing interlayer coupling in twisted single‐crystal bilayer graphene by Raman spectroscopy

Twisted bilayer graphene, in which interlayer interaction plays a critical role in this coupled system, is characterized for its angle‐dependent electronic and optical properties. Here, we present a systematic Raman study of single‐crystal twisted bilayer graphene grains, with the spectra of each bilayer graphene precisely correlated to its twist angle using combined transmission electron microscopic technique. Van Hove singularities develop as a result of band rehybridization at the crossing Dirac cones of the two layers, giving rise to a critical twist angle that determines the energy separation between the saddle points in the band structure and the resonance Raman spectra accordingly. The 2D mode becomes sensitive to the twist angle, showing the angle‐dependent position, peak width, and intensity. Our results interpreted in the framework of angle‐dependent double resonance scattering provide an important experimental perspective in understanding the coupled bilayer graphene system. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_rf is close to the Rabi frequency ω₁ in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ? are accompanied by higher-frequency oscillations at frequencies nω_rf and nω_rf ± ?, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ? on the sign of the detuning ω₁ ? ω_rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_rf + ? increases, while the amplitude at the difference frequency ω_rf ? ? decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′₁ centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.     

扭转双层石墨烯物理性质、制备方法及其应用的研究进展

石墨烯是一种准二维蜂窝网状结构新型纳米材料,石墨烯的层数和构型对其性能产生重要影响.固体中准粒子的量子状态由其本身的对称性质所决定,扭转双层石墨烯打破了对称性,引起了强烈的层间耦合作用,改变了扭转双层石墨烯的电子能带、声子色散、形成能垒等物性,产生了独特的性能,如可以连续调控带隙0-250 meV,光电效应的响应度相比于单层石墨烯提高了80倍,因此对扭转双层石墨烯功能化研究有重大意义.本文同时还论述了扭转双层石墨烯向类金刚石转变的理论与实验研究进展,发现扭转双层石墨烯呈现出具有类金刚石结构与性能特征.进一步阐述调控扭转双层石墨烯的扭转角度对其内在性能的影响,揭示这种新型纳米结构在原子层次的行为特征.最后介绍了如何调控制备扭转双层石墨,分析其调控机理,讨论了各种制备工艺的不足与发展趋势.因此本文从扭转双层石墨烯的输运性质、晶体结构转变、制备三个方面展开阐述,并对其在先进电子器件领域的潜在应用进行了展望.     

Towards T 1-limited magnetic resonance imaging using Rabi beats

Two proof-of-principle experiments toward T ₁-limited magnetic resonance imaging with NV centers in diamond are demonstrated. First, a large number of Rabi oscillations is measured and it is demonstrated that the hyperfine interaction due to the NV??s ¹⁴N can be extracted from the beating oscillations. Second, the Rabi beats under V-type microwave excitation of the three hyperfine manifolds is studied experimentally and described theoretically.     

旋转双层石墨烯的电子结构

本文将第一性原理和紧束缚方法结合起来, 研究了层间不同旋转角度对双层石墨烯的电子能带结构和态密度的影响. 分析发现, 旋转双层石墨烯具有线性的电子能量色散关系, 但其费米速度随着旋转角度的减小而降低. 进一步研究其电子能带结构发现, 不同旋转角度的双层石墨烯在M点可能会出现大小不同的的带隙, 而这些能隙会增强双层石墨烯的拉曼模强度, 并由拉曼光谱实验所证实. 通过对比双层石墨烯的晶体结构和电子态密度, 发现M点处带隙来自于晶体结构中的“类AB堆垛区”. 关键词： 旋转双层石墨烯 第一性原理 紧束缚 电子结构     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

Phase Separation in a Spin Density Wave State of Twisted Bilayer Graphene

JETP Letters - Twisted bilayer graphene at the so-called magic twist angle θ ∼ 1° is theoretically studied. In the absence of interaction between electrons, the system under study...     

Graphite,Graphene, and the Flat Band Superconductivity

Superconductivity has been observed in bilayer graphene [1, 2]. The main factor that determines the mechanism of the formation of this superconductivity is the “magic angle” of twist of two graphene layers, at which the electronic band structure becomes nearly flat. The specific role played by twist and by the band flattening has been earlier suggested for explanations of the signatures of room-temperature superconductivity observed in the highly oriented pyrolytic graphite (HOPG), when the quasi two-dimensional interfaces between the twisted domains are present. The interface contains the periodic array of misfit dislocations (analogs of the boundaries of the unit cell of the Moiré superlattice in bilayer graphene), which provide the possible source of the flat band. This demonstrates that it is high time for combination of the theoretical and experimental efforts in order to reach the reproducible room-temperature superconductivity in graphite or in similar real or artificial materials.     

Signatures of bulk topology in the non-linear optical spectra of Dirac-Weyl materials

Graphene, topological insulators (TI) and the Weyl semimetal are shown to be well-characterized using the phenomenon of anomalous Rabi oscillation (ARO). These oscillations occur far from conventional resonance and Floquet theory shows them to be unique to these systems. Of particular interest is the bulk topological insulator (TI) where the wave-vector dependent frequency of the ARO is seen to be gapped in topologically trivial situations and gapless when there is a non-vanishing Chern number. It is shown that the Chern number may be directly inferred by performing a pump-probe experiment in the bulk without referring to surface states. A simpler alternative to the Lindblad method is invoked in order to incorporate dephasing effects that despite leading to a non-unitary time evolution of the wave-function, is nevertheless, probability conserving. The differential transmission coefficient versus the pump pulse duration (when all else is held fixed) has the form of a sinusoidal function with an amplitude that decays as a power law in the pump duration (alternatively, the “area” of the pump pulse). The exponent of this power law decay is indicative of the Chern number of the bulk in case of TI and more generally indicative of the particular member of the family of materials that may be collectively referred to as – Dirac-Weyl materials.     

Decay of rabi oscillations induced by magnetic dipole interactions in dilute paramagnetic solids

Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E′₁ centers in glassy silica and [AlO₄]⁰ centers in quartz.     

垂直电场下扭转双层石墨烯光学吸收性质的理论研究

层间扭转角度是对石墨烯物理性质宽波段可调谐的一个新参量.本文采用2°<θ<15°扭转角度下的连续近似模型,获得了不同扭转角度双层石墨烯分别在有、无电场下的能带结构,通过电子-光子相互作用跃迁速率,计算模拟了范霍夫奇点附近电子带内跃迁和带间跃迁所引起的光学吸收谱.结果表明,在无外加电场时,带间跃迁吸收峰的位置随着扭转角度的增大而发生从红外到可见光波段的蓝移,且吸收系数增大,带内跃迁的光学吸收系数相对于带间跃迁高出2个数量级;而存在外加电场时,两个范霍夫奇点在波矢空间的位置发生偏移,带间跃迁吸收峰发生分裂,且两个分裂的吸收峰位置随着电场强度的不断增大而反向行进.上述研究结果对石墨烯材料在光电器件方面的应用有一定指导作用.     

Rabi oscillations in two-level semiconductor systems

Rabi oscillations in coherent optical excitations in bulk GaAs and quantum dot two-level systems may be converted into deterministic photocurrents, with the impurities or dots providing the tag for each qubit. Here we perform a theoretical analysis of the damping of Rabi oscillations in two-level semiconductor systems. Present calculations, through optical Bloch equations on excitonic two-level In_xGa_1−xAs quantum-dot systems, are found in good agreement with the corresponding experimental data. Calculated results indicate that the nature underlying the dephasing mechanism associated to the damping of the measured Rabi oscillations, which has previously remained as an open question, may be associated with a field-dependent recombination rate related to the inhomogeneous broadening of the excitonic lines in the In_xGa_1−xAs two-level QD system.     

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on the magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with theoretical expectations. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that, for energies in a gap of the lattice band structure, the molecules cannot dissociate.     

Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.     

Rabi Oscillations of Paramagnetic Ions in Solids: Role of Electrostatic Interactions

We study the decay of Rabi oscillations of magnetically coupled impurity ions diluted in the solid. Electrostatic interactions between the ions treated as charged defects shift their g-factors and result in valuable correlations of their Larmor frequencies if the ions are close enough. We find an increase in the decay time of Rabi oscillations in comparison with the case of uncharged defects. The magnitude of the effect depends on the ratio between the impurity and the total defect concentrations, as well as on the type of the electron paramagnetic resonance line broadening mechanism (by random electric fields, electric field gradients, etc.). We present results in the arbitrary order of multipole expansion with respect to valence electron coordinates of the paramagnetic ion. Corresponding corrections to the decay times of Rabi oscillations of Nd³⁺ ions in CaWO₄ crystal are obtained.     

Excitonic Rabi oscillations in a quantum dot: local field impact

The influence of local fields on the excitonic Rabi oscillations in an isolated, arbitrary shaped quantum dot (QD) has been theoretically investigated. QD interaction with both a classical electromagnetic field and quantum light has been considered. In the classical light, time harmonic and ultrashort pulse excitations are analyzed. The general formalism has been formulated for quantum light and applied to the case of a Fock qubit. Noticeable modification of the Rabi oscillation dynamics induced by the local fields is predicted to be observable in QDs exposed to both classical and quantum light. In particular, the bifurcation and anharmonism in the Rabi oscillations have been revealed under time harmonic excitation and a dependence of the Rabi oscillation period on the QD depolarization has been obtained.     

Calculation of electron spectra and some problems in the thermodynamics of graphene layers

The expressions for the energy spectra of monolayer, bilayer, and multilayer graphene, as well as epitaxial graphene, are derived using the quantum Green’s functions method. Analytic expressions are obtained for the densities of states of these systems. It is shown that a bandgap can appear the spectrum of an epitaxial graphene bilayer. A number of problems in the thermodynamics of electrons in free and epitaxial graphene layers are considered as applications. Analytic expressions are obtained for the chemical potential and heat capacity in the limiting cases of low and high temperatures. Quantum oscillations of heat capacity in graphene are analyzed taking into account the Coulomb interaction. The Berry phase of epitaxial graphene is investigated.     

Rabi flopping in a two-level system with a time-dependent energy renormalization: intersubband transitions in quantum wells

We obtain pulse-driven Rabi oscillations guided by a generalization of the rotating-wave approximation to include, in the optical-Bloch equations, two-level systems with a time-varying transition energy. We achieve this by using chirped pulses with the central frequency given by the time-varying transition energy. Using this approach, we predict Rabi oscillations in intersubband transitions in a two-subband n-type modulation-doped quantum well by taking into account the time-dependent intersubband energy-gap renormalization due to depolarization-shift effects. We obtain Rabi oscillations for jpi (j=0,1,2, ) pulses in the presence of dephasing.