Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ? ^?1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level E _F. The dependence on E _F is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrödinger” electrons has been revealed.     

Abnormal electronic transport in disordered graphene nanoribbon

We investigate the conductivity σ of graphene nanoribbons with zigzag edges as a function of Fermi energy E_F in the presence of the impurities with different potential range. The dependence of σ(E_F) displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of σ(E_F) and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao et al. [Science 317 (2007) 1530 (SOM)].     

Capacitance spectroscopy of a system of gapless Dirac fermions in a HgTe quantum well

Information on the density of states of two-dimensional Dirac fermions in a 6.6-nm-thick HgTe quantum well that corresponds to a transition from the direct to inverted spectrum is obtained for the first time by means of capacitance measurements. It is found that the density of states of Dirac electrons is a linear function of the Fermi energy at E _F > 30 meV with the corresponding velocity vDF = 8.2 × 10⁵ m/s. At lower energies, this dependence deviates from the linear law, indicating a strong effect of disorder, which is associated with fluctuations of a built-in charge, on the density of states of the studied system near the Dirac point. At negative energies, a sharp increase in the density of states is observed, which is associated with the tail of the density of states of valleys of heavy holes. The described behavior is in agreement with the proposed model, which includes both the features of the real spectrum of Dirac fermions and the effect of the fluctuation potential.     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.     

Gauge group breaking by Wilson loops

We examine the breaking of gauge symmetries by Wilson loops in the Hosotani-Toms model by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions. For anti-periodic fermions, all gauge groups remain unbroken. For periodic fermions, the groups G₂, F₄ and E₈ are broken by quantum corrections due to fermions in any irreducible representation, whereas E₆, E₇ and the classical groups only break if the fermion representation is in the same congruency class as the adjoint.     

The effect of gradually constricted channel on the I–V characteristics of graphene sheets

Ideal graphene is a gapless semiconductor consisting of a single layer of carbon atoms regularly arranged in a honeycomb lattice having infinite spatial extent in the (x,y)-plane, in which electrons behave as Dirac massless fermions. Even neglecting interactions with the anchoring substrate, a graphene sheet in real world has finite extent, leading to distinctive features in the conductivity of a given sample. In this letter we study the effect of a gradual channel constriction in graphene nanoribbons on their I–V characteristics, using non-equilibrium Green's function formalism. The constriction width and the border cutting angle are the main parameters to be varied. We found that transmission through the channel is considerably affected by these parameters, presenting sharp peaks at specific energies, which can be attributed to a resonance due to the tuning of energy eigenvalues.     

Coherent transmission of nodal Dirac fermions through a graphene-based superconducting double barrier junction

Transport characteristics of relativistic electrons through graphene-based d-wave superconducting double barrier junction and ferromagnet/d-wave superconductor/normal metal double junction have been investigated based on the Dirac–Bogoliubov–de Gennes equation. We have first presented the results of superconducting double barrier junction. In the subgap regime, both the crossed Andreev and nonlocal tunneling conductance all oscillate with the bias voltage due to the formation of Andreev bound states in the normal metal region. Moreover, the critical voltage beyond which the crossed Andreev conductance becomes to zero decreases with increasing value of superconducting pair potential α. In the presence of the ferromagnetism, the MR through graphene-based ferromagnet/ d-wave superconductor/normal metal double junction has been investigated. It is shown that the MR increases from exchange splitting h ₀=0 to h ₀=E _F (Fermi energy), and then it goes down. At h ₀=E _F, MR reaches its maximum 100. In contrast to the case of a single superconducting barrier, Andreev bound states also manifest itself in the zero bias MR, which result in a series of peaks except the maximum one at h ₀=E _F. Besides, the resonance peak of the MR can appear at certain bias voltage and structure parameter. Those phenomena mean that the coherent transmission can be tuned by superconducting pair potential, structure parameter, and external bias voltage, which benefits the spin-polarized electron device based on the graphene materials.     

石墨带的晶格动力学研究

基于晶格动力学理论,采用力常数模型,计算了石墨带的声子色散关系、振动模式密度和比热.计算结果表明,石墨带的声子谱特征介于一维碳纳米管和二维石墨片之间.扶手椅型和锯齿型石墨带的中、高频声子支分别与锯齿型和扶手椅型碳纳米管的类似.由于声子限域效应,低频声子支随着石墨带带宽的改变出现明显的频移现象.振动模式密度在高频区几乎不敏感于带宽,而低频区的峰位随着带宽的增加而逐渐向低频移动.此外,无论是在低温还是高温,比热都随着带宽的增加而逐渐降低,呈现量子尺寸效应.在300K时,比热可以拟合成C_V=C_Vg+A/n,其中C_Vg为石墨片的热容,而A/n项反映了石墨带中边缘效应对比热的影响. 关键词： 石墨带 声子色散关系 比热     

Dynamics of Dirac quasi-particles in lattice vibration and anomalous phonon frequency shift of graphene

By exact solution of time-dependent Schrödinger equation of electron in graphene under interaction with E_2g phonons, we investigate the dynamical behavior of Dirac quasi-particle in the process of lattice vibration. Due to the global geometric phases acquired by electron during lattice vibration, an anomalous shift of the vibration frequency is obtained. We calculate the Fermi energy dependence of frequency shift which is in consistence with experiment in case of small doping density.     

Influence of the boundary conditions on the fermi energy and density of states in a free-electron solid of sub-micron dimensions

Asymptotic expressions for the distribution of the eigenvalues of the Helmholtz-Schrödinger equation are used to anlyze the dependence of the Fermi energy, E_F, and the density of states, ρ(E), on sample size, shape, and electron density, in a free-electron model with Dirichlet boundary conditions. It is found that for very small samples E_F is increased relative to its asymptotic (i.e., bulk) value and ρ(E) is decreased relative to its bulk value. These effects are more pronounced for samples with low electron density and with a large surface-to-volume ratio. In general E_F and ρ(E_F) deviate significantly from their bulk values only for systems with fewer than 50,000 electrons and/or with linear dimensions of 100 Å or less. The use of smoothing functions to represent the density of states obtained from the exact eigenvalue distribution is also discussed. It is shown that an oscillating density of states leads to small cusps in the plot of E_F as a function of sample size. This is in qualitative agreement with the results of experiments on size-dependent oscillations in field emission from thin metallic films. Comparison is also made between photoemission experiments from thin films and other results obtained in this study.     

Quantum size effects in the fermi energy and electronic density of states in a finite square well thin film model

The dependence of the Fermi energy, E_F, and the electronic density of states, ρ(E), of thin metallic films (L_z ≲ 50 Å) on film thickness, electron density, and potential well depth, is systematically investigated in a free-electron, finite square well model. Two size-dependent effects are observed: (1) oscillations in E_F and ρ(E) due to the size-quantization of the energy levels, and (2) changes in the mean values of these quantities, averaged over several oscillation periods, relative to their bulk values. The mean value of E_F is increased relative to its bulk value by as much as 5%–10% for physically reasonable well depths and typical metallic electron densities. For the special case in which the top energy level in the well is occupied, the mean value of E_F is equal to its bulk value. The mean value ofρ(E_F) can be either greater than or less than its bulk value, depending on the well depth. In contrast to the small amplitude oscillations in E_F, the oscillations in ρ(E_F) may have an amplitude as large as 25% of the mean value for sufficiently thin films. Accurate analytic expressions for the thickness dependence of the Fermi energy and density of states are derived.     

Electroabsorption in TlInS2

Electroabsorption spectra of single crystals have been studied near the fundamental absorption edge at 77 and 300 K. At 300 K two positive peaks (2.34 and 2.42 eV) and a negative peak (2.38 eV) are observed in the electroabsorption spectrum. At liquid-nitrogen temperature a fine structure corresponding to the formation of a parabolic exciton (2.503 eV) is observed.Values of the width of the forbidden gap E_g, the n = 1 exciton positions, the exciton activation energy ΔE_b, the effective Bohr radius a_exc, the reduced effective mass of an electron-hole pair μ, and the exciton ionization field F(E_g = 2.535 eV, E_exc = 2.503 eV, E_b = 32 meV, $\text{a}{}_{\mathrm{<mtext>exc</mtext>}}\text{=}\text{28}\text{A}\text{A;}\text{;}$;, μ = 0.15 m₀, and F = 1.2 × 10⁵ V cm^-1) have been determined from the electroabsorption spectrum.     

Dirac quasiparticle tunneling in a NG/ferromagnetic barrier/SG graphene junction

We study the tunneling conductance in a spin dependent barrier NG/F_B/SG graphene junction, where NG, F_B and SG are normal graphene, gate ferromagnetic graphene barrier with thickness d and the graphene s-wave superconductor, respectively. In our work, the quasiparticle scattering process at the interfaces is based on quasi particles governed by the Dirac Bogoliubov–de Gennes equation with effective speed of light v_F ∼ 10⁶ m/s. The conductance of the junction is calculated based on Blonder–Tinkham–Klapwijk (BTK) formalism. The oscillatory conductance under varying gate potential and exchange energy in F_B and the conductance induced by specular Andreev reflection are studied. By taking into account both effects of barrier strengths due to the gate potential χ_G∼V_Gd/?v_F${\chi }_{\text{G}}\sim V_{\text{G}}d/?v_{\text{F}}$ and the exchange energy χ_ex∼E_exd/?v_F${\chi }_{\text{ex}}\sim E_{\text{ex}}d/?v_{\text{F}}$ in the F_B region, we find that the zero bias conductance of junction depends only on the ferromagnetic barrier strength χ_ex in F_B, when the Fermi energy in SG is very much larger than that the Fermi energy in NG (E_FS ? E_FN). The oscillatory conductance peaks can be controlled by either varying χ_ex or χ_G. In the limiting case, by setting E_ex = 0, the conductance in a NG/N_B/SG graphene junction, where SG is the s-wave superconductor, is also studied in order to compare with two earlier contradicted data. Our result agrees with what was obtained by Linder and Sudbo [J. Linder, A. Sudbo, Phys. Rev. B 77 (2008) 64507], which confirms the contradiction to what was given by Bhattacharjee and Sengupta [S. Bhattacharjee, K. Sengupta, Phys. Rev. Lett. 97 (2006) 217001].     

Energy of bonding an adsorbed atom with a single-layer graphene

The change in the local density of states δρ _g of a single-sheet graphene due to adsorption of a single atom has been calculated in the framework of the M model proposed earlier. The dependence of the local density of states δρ _g on the position of the adatom energy level ɛ _a with respect to the Dirac point and other parameters of the problem has been analyzed. It has been shown that the largest changes in the local density of states δρ _g are caused by adatoms with the ɛ _a levels lying in the vicinity of the Dirac point, so that the minimum density of states of graphene remains equal to zero. An analytical expression has been derived for the energy of bonding W _ads of the adatom with graphene. The obtained estimates of the bonding energy W _ads in the weak and strong adatom-substrate bonding regimes are presented. Atoms of alkali metals and halogens have been considered as specific adsorbates.     

Similarities between normal- and super-currents in topological insulator magnetic tunnel junctions

This work compares the normal-current in a NM/Fi/NM junction with the super-current in a SC/Fi/SC junction, where both are topological insulator systems. NM and Fi are normal region and ferromagnetic region of thickness d with exchange energy m playing a role of the mass of the Dirac electrons and with the gate voltage V_G, respectively. SC is superconducting region induced by a s-wave superconductor. We show that, interestingly, the critical super-current passing through a SC/Fi/SC junction behaves quite similar to the normal-current passing through a NM/Fi/NM junction. The normal-current and super-current exhibit N-peak oscillation, found when currents are plotted as a function of the magnetic barrier strength χ ∼ md  /?$?$v_F. With the barrier strength Z ∼ V_Gd  /?$?$v_F, the number of peaks N is determined through the relation Z ∼ Nπ + σπ (with 0 < σ?1$\sigma ?1$ for χ < Z). The normal- and the super-currents also exhibit oscillating with the same height for all of peaks, corresponding to the Dirac fermion tunneling behavior. These anomalous oscillating currents due to the interplay between gate voltage and magnetic field in the barrier were not found in graphene-based NM/Fi/NM and SC/Fi/SC junctions. This is due to the different magnetic effect between the Dirac fermions in topological insulator and graphene.     

Surface states of charge carriers in epitaxial films of the topological insulator Bi2Te3

The galvanomagnetic properties of p-type bismuth telluride heteroepitaxial films grown by the hot wall epitaxy method on oriented muscovite mica substrates have been investigated. Quantum oscillations of the magnetoresistance associated with surface electronic states in three-dimensional topological insulators have been studied in strong magnetic fields ranging from 6 to 14 T at low temperatures. The cyclotron effective mass, charge carrier mobility, and parameters of the Fermi surface have been determined based on the results of analyzing the magnetoresistance oscillations. The dependences of the cross-sectional area of the Fermi surface S(k _F), the wave vector k _F, and the surface concentration of charge carriers n _s on the frequency of magnetoresistance oscillations in p-type Bi₂Te₃ heteroepitaxial films have been obtained. The experimentally observed shift of the Landau level index is consistent with the value of the Berry phase, which is characteristic of topological surface states of Dirac fermions in the films. The properties of topological surface states of charge carriers in p-type Bi₂Te₃ films obtained by analyzing the magnetoresistance oscillations significantly expand fields of practical application and stimulate the investigation of transport properties of chalcogenide films.     

Temperature relaxation and energy loss of hot carriers in graphene

The temperature relaxation and energy loss of hot Dirac fermions are investigated theoretically in graphene with carrier–optical phonon scattering. The time evolutions of temperature and energy loss for hot Dirac fermions in graphene are calculated self-consistently. It shows that the carrier–optical phonon coupling results in the energy relaxation of hot carriers excited by an electric field, and the relaxation time for temperature is about 0.5–1 ps and the corresponding energy loss is about 10–25 nW per carrier for typically doped graphene samples with a carrier density range of 1–5×10¹² cm^?2. Moreover, we analyze the dependence of temperature and energy relaxation on initial hot carrier temperature, lattice temperature and carrier density in detail.     

Dependence on substrate bias of the effective mass and dingle temperature of electrons in the surface inversion layer of silicon

The amplitude of the quantum oscillations in the magnetoconductance of a silicon inversion layer has been studied as a function of gate voltage V_g, for different values of the temperature T, applied magnetic field strength H and substrate bias V_s. By analyzing the amplitude of the oscillations at fixed V_g and V_g as a function of T and H, the dependence of the cyclotron effective mass m¹ and the Dingle temperature T_D on V_g and V_s can be obtained. The dependence of m¹ on V_g for different values of V_s is compared with the prediction of theory.