Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Magneto-electronic properties of rhombohedral (ABC-stacked) trilayer graphene are investigated by the tight-binding (TB) model with all important interlayer interactions taken into account. A numerical strategy, band-like matrix, is applied to solve the huge Hamiltonian matrix and thus the eigenvalues and eigenvectors of Landau levels (LLs) are well defined. Based on the characteristics of the wave functions, the LLs are divided into three groups. These LLs are strongly affected by the stacking configuration and interlayer interactions. The LL spectra do reflect the main features of the zero-field subbands, i.e., the existence of three LL groups, specified onset energies of the three groups, and asymmetric electronic structure. In an ABC-stacked structure, the LL wave functions are each composed of six magnetic TB Bloch functions for six sublattices. Each magnetic TB Bloch function exhibits the spatial symmetry, localization feature, and oscillation modes. Three sets of effective quantum numbers are defined to index the LLs of the three groups based on the oscillation modes in specific sublattices. These effective quantum numbers are useful for defining the optical selection rules of the optical absorption spectra.     

Landau levels in uniaxially strained graphene: A geometrical approach

The effect of strain on the Landau levels (LLs) spectra in graphene is studied, using an effective Dirac-like Hamiltonian which includes the distortion in the Dirac cones, anisotropy and spatial-dependence of the Fermi velocity induced by the lattice change through a renormalized linear momentum. We propose a geometrical approach to obtain the electron’s wave-function and the LLs in graphene from the Sturm–Liouville theory, using the minimal substitution method. The coefficients of the renormalized linear momentum are fitted to the energy bands, which are obtained from a Density Functional Theory (DFT) calculation. In particular, we evaluate the case of Dirac cones with an ellipsoidal transversal section resulting from uniaxially strained graphene along the Arm-Chair (AC) and Zig-Zag (ZZ) directions. We found that uniaxial strain in graphene induces a contraction of the LLs spectra for both strain directions. Also, is evaluated the contribution of the tilting of Dirac cone axis resulting from the uniaxial deformations to the contraction of the LLs spectra.     

Low-field carrier transport properties in biased bilayer graphene

Based on a semiclassical Boltzmann transport equation in random phase approximation, we develop a theoretical model to understand low-field carrier transport in biased bilayer graphene, which takes into account the charged impurity scattering, acoustic phonon scattering, and surface polar phonon scattering as three main scattering mechanisms. The surface polar optical phonon scattering of carriers in supported bilayer graphene is thoroughly studied using the Rode iteration method. By considering the metal–BLG contact resistance as the only one free fitting parameter, we find that the carrier density dependence of the calculated total conductivity agrees well with that observed in experiment under different temperatures. The conductivity results also suggest that in high carrier density range, the metal–BLG contact resistance can be a significant factor in determining the BLG conductivity at low temperature, and both acoustic phonon scattering and surface polar phonon scattering play important roles at higher temperature, especially for BLG samples with a low doping concentration, which can compete with charged impurity scattering.     

Lattice relaxation of graphene under high magnetic field

We investigate the n = 0 Landau level (LL) in monolayer graphene with high magnetic field. We find that the energy gap is opened in the n = 0 LL by the magnetic-field-dependent lattice relaxation originating from the interactions between the electrons (holes) and longitudinal-deformation-acoustic phonon. Both the linear and square-foot dependence of the energy gap on the magnetic field are obtained depending on the choice of the Debye cut-off wave number for the acoustic phonon. The relations of the Huang-Rhys parameter (lattice relaxation strength) and the transition linewidths with the magnetic field are also discussed. Our results agree with the current experiments on graphene in high magnetic field, and provide an alternative explanation for the experimental measurements.     

多空穴错位分布对石墨纳米带中热输运的影响

利用非平衡格林函数方法研究了石墨纳米带中三空穴错位分布对热输运性质的影响.研究结果发现:三空穴竖直并排结构对低频声子的散射较小,导致低温区域三空穴竖直并排时热导最大,而在高频区域,三空穴竖直并排结构对高频声子的散射较大,导致较高温度区域三空穴竖直并排时热导最小;三空穴的相对错位分布仅能较大幅度地调节面内声学模高频声子的透射概率,而三空穴的相对错位分布能较大幅度地调节垂直振动膜高频声子和低频声子的透射概率,导致三空穴的相对错位分布不仅能大幅调节面内声学模和垂直振动模的高温热导,也能大幅调节垂直振动模的低温热导.研究结果阐明了空穴位置不同的石墨纳米带的热导特性,为设计基于石墨纳米带的热输运量子器件提供了有效的理论依据.     

Infrared spectroscopy of Landau levels of graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.     

Phonon dispersion of quasi-freestanding graphene on Pt(111)

High-resolution electron energy loss spectroscopy has been used to probe phonon dispersion in quasi-freestanding graphene epitaxially grown on Pt(111). Loss spectra clearly show different dispersing features related to both acoustic and optical phonons. The present results have been compared with graphene systems which strongly interact with the substrate, i.e. the nearly-flat monolayer graphene (MLG)/Ni(111) and the corrugated MLG/Ru(0001). We found that the phonon dispersion of graphene/Pt(111) reproduces well the behavior of pristine graphite. This could be taken as an indication of the negligible interaction between the graphene sheet and the underlying Pt substrate. The softening of out-of-plane modes observed for interacting graphene/metal interfaces does not occur for the nearly-free-standing graphene/Pt(111).     

Density of states and zero Landau Level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.     

Thickness and stacking geometry effects on high frequency overtone and combination Raman modes of graphene

We investigate two high frequency Raman overtone and combination modes of graphene named 2D' and 2D + G bands, and located at ~3240 and ~ 4260 cm^–1, respectively. The graphene thickness and stacking geometry effects for these two modes are systematically studied. The features of the 2D' band, which arises from intravalley double resonance, are not sensitive to the variation of thickness with single Lorentzian peak and fixed linewidth. We explain it theoretically by calculating the phonon dispersion mode in k‐space and find that the flat band region of longitudinal optical phonon near Γ point is the mechanism leading to the 2D' band nonsplit. With the thickness increasing, the band position exhibits blueshift and the linewidth increases for the 2D + G band. With changing thickness and stacking geometry of graphene, the intensities of these two high‐frequency bands show obvious different evolution compared with that of G band. Copyright © 2012 John Wiley & Sons, Ltd.     

Phonon anharmonicities in graphite and graphene

We determine from first principles the finite-temperature properties-linewidths, line shifts, and lifetimes-of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E(2g) mode is found to decrease with temperature; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate infrared-active E(1u) mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.     

Resonant phonon scattering in quantum Hall systems driven by dc electric fields

Using dc excitation to spatially tilt Landau levels, we study resonant acoustic phonon scattering in two-dimensional electron systems. We observe that dc electric field strongly modifies phonon resonances, transforming resistance maxima into minima and back into maxima. Further, phonon resonances are enhanced dramatically in the nonlinear dc response and can be detected even at low temperatures. Most of our observations can be explained in terms of dc-induced (de)tuning of the resonant acoustic phonon scattering and its interplay with inter-Landau level impurity scattering. Finally, we observe a resistance maximum when the electron drift velocity approaches the speed of sound and a dc-induced zero-differential resistance state.     

Unconventional quasiparticle lifetime in graphene

We address the question of how large can the lifetime of electronic states be at low energies in graphene, below the scale of the optical phonon modes. For this purpose, we study the many-body effects at the K point of the spectrum, which induce a strong coupling between electron-hole pairs and out-of-plane phonons. We show the existence of a soft branch of hybrid states below the electron-hole continuum when graphene is close to the charge neutrality point, leading to an inverse lifetime proportional to the cube of the quasiparticle energy. This implies that a crossover should be observed in transport properties, from such a slow decay rate to the lower bound given at very low energies by the decay into acoustic phonons.     

Carrier kinetics and population inversion in Landau level system in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau levels population for various values of pumping intensity (tunneling time), magnetic field and the structure doping were carried out. The effect of various scattering mechanisms, as two-electron (electron–electron scattering) as single-electron (acoustic phonon and interface roughness scattering) ones on level population was studied. The population inversion between the zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength thus providing the possibility of wide range tunable stimulated terahertz emission.     

Electrical and optical properties of parabolic semiconducting quantum wells

We investigate theoretically the optical and electrical properties of parabolic semiconducting quantum well structures. In our calculations, we assume that the confinement of the carriers is in an infinite parabolic well. We show that the carrier mobility in the plane perpendicular to the direction of confinements is directly proportional to the harmonic oscillator length λ whose value depends upon the partitioning of the band gap discontinuity between the conduction and valence bands. We have also calculated the linewidth for intra-subband resonances which should occur for electromagnetic radiation polarized in the direction of carrier confinement and show that the linewidth is inversely proportional to λ and directly proportional to the temperature when the linewidth is dominated by acoustic phonon scattering. The absorption coefficient for interband optical transitions shows equally spaced steps as a function of photon energy where the value of the spacing between adjacent steps depends upon the partitioning of the band gap discontinuity. Carrier freeze-out in the intrinsic conduction occurs due to the presence of zero point energies in the conduction and valence bands arising from the carrier confinement. These zero point energies also are found to depend upon the partitioning of the band gap discontinuities. Therefore, information about the partitioning of the energy band gap discontinuity between the conduction and valence bands can be obtained by measuring these various optical and electrical transport properties of a parabolic quantum well semiconducting structure under those conditions when the model of an infinite parabolic well approximates the real system.     

Interaction of longitudinal phonons with discrete breather in strained graphene

We numerically analyze the interaction of small-amplitude phonon waves with standing gap discrete breather (DB) in strained graphene. To make the system support gap DB, strain is applied to create a gap in the phonon spectrum. We only focus on the in-plane phonons and DB, so the issue is investigated under a quasi-one-dimensional setup. It is found that, for the longitudinal sound waves having frequencies below 6 THz, DB is transparent and thus no radiation of energy from DB takes place; whereas for those sound waves with higher frequencies within the acoustic (optical) phonon band, phonon is mainly transmitted (reflected) by DB, and concomitantly, DB radiates its energy when interacting with phonons. The latter case is supported by the fact that, the sum of the transmitted and reflected phonon energy densities is noticeably higher than that of the incident wave. Our results here may provide insight into energy transport in graphene when the spatially localized nonlinear vibration modes are presented.     

Quantum theory of cavity-assisted sideband cooling of mechanical motion

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.     

N型4H-SiC低温拉曼光谱特性

利用拉曼散射技术对N型4H-SiC单晶材料进行了30～300 K温度范围的光谱测量。实验结果表明,随着温度的升高,N型4H-SiC单晶材料的拉曼峰峰位向低波数方向移动,峰宽逐渐增宽。分析认为,晶格振动随着温度的升高而随之加剧,其振动恢复力会逐渐减小,使振动频率降低;原子相对运动会随温度的升高而加剧,使得原子之间及晶胞之间的相互作用减弱,致使声学模和光学模皆出现红移现象。随着温度的升高,峰宽逐渐增宽。这是由于随着温度的升高声子数逐渐增加,增加的声子进一步增加了散射概率,从而降低了声子的平均寿命,而声子的平均寿命与峰宽成反比,因此随着温度的升高峰宽逐渐增宽。声子模强度随温度升高呈现不同规律,E₂(LA),E₂(TA),E₁(TA)和A₁(LA)声子模随着温度升高强度单调增加,而E₂(TO),E₁(TO)和A₁(LO)声子模强度出现了先增后减的明显变化,在138 K强度出现极大值。分析认为造成原因是由于当温度高于138 K时,高能量的声子分裂成多个具有更低能量的声子所致。     

Resonance Raman scattering in graphene: Probing phonons and electrons

In this work, by using different laser excitation energies, we obtain important electronic and vibrational properties of mono- and bi-layer graphene. For monolayer graphene, we determine the phonon dispersion near the Dirac point for the in-plane transverse optical (iTO) mode. This result is compared with recent calculations that take into account electron–electron correlations for the phonon dispersion around the K point. For bilayer graphene we extract the Slonczewski–Weiss–McClure band parameters and compare them with recent infrared measurements. We also analyze the second-order feature in the Raman spectrum for trilayer graphene.     

Magnetic field dependence of cyclotron resonance linewidth for acoustic polarons in the extreme quantum limit

The magnetic field dependence of cyclotron resonance linewidth (CRLW) due to electron-acoustic phonon interactions in the extreme quantum limit is obtained on the basis of Kubo's formula and Fujita's diagram method. The 2-dimensional electron-piezoelectric phonon interaction generates a finite maximum CRLW as a function of magnetic field while CRLW for all other acoustic polarons increase with the magnetic field.     

Raman spectroscopy of magneto-phonon resonances in graphene and graphite

The magneto-phonon resonance or MPR occurs in semiconductor materials when the energy spacing between Landau levels is continuously tuned to cross the energy of an optical phonon mode. MPRs have been largely explored in bulk semiconductors, in two-dimensional systems and in quantum dots. Recently there has been significant interest in the MPR interactions of the Dirac fermion magneto-excitons in graphene, and a rich splitting and anti-crossing phenomena of the even parity $E_{2g}$ long wavelength optical phonon mode have been theoretically proposed and experimentally observed. The MPR has been found to crucially depend on disorder in the graphene layer. This is a feature that creates new venues for the study of interplays between disorder and interactions in the atomic layers. We review here the fundamentals of MRP in graphene and the experimental Raman scattering works that have led to the observation of these phenomena in graphene and graphite.