arXiv subjects
Publications and source records attributed to Godfrey Gumbs.
In this note we present the Green's functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well know, we hope that their derivation performed in a uniform way is of some pedagogical value.
In this paper, the effect of B and N doping on the phonon induced thermal conductivity of graphene has been investigated. This study is important when one has to evaluate the usefulness of electronic properties of B and N doped graphene. We have performed the calculations by employing density functional perturbation theory(DFPT) to calculate the inter-atomic forces=force constants of pristine/doped graphene. Thermal conductivity calculations have been carried out by making use of linearized Boltzmann transport equations (LBTE) under single-mode relaxation time approximation (RTA). The thermal conductivity of pristine graphene has been found to be of the order of 4000W/mK at 100K, which decreases gradually with an increase in temperature. The thermal conductivity decreases drastically by 96 % to 190 W/mK when doped with 12.5 % B and reduces by 99 % to 30 W/mK with 25 % B doping. When graphene is doped with N, the thermal conductivity decreases to 4 W/mK and 55 W/mK for 12.5 % and 25 % doping concentration, respectively. We have found that the thermal conductivity of doped graphene show less sensitivity to change in temperature. It has also been shown that the thermal conductivity of graphene can be tuned with doping and has a strong dependence on doping concentration.
Using the $α$-T$_3$ model, we carried out analytical and numerical calculations for the static and dynamic polarization functions in the presence of a perpendicular magnetic field. These results were employed to determine the longitudinal dielectric function and the magnetoplasmon dispersion relation. The magnetic field splits the continuous valence, conduction and flat energy subband into discrete Landau levels which present significant effects on the polarization function and magnetoplasmon dispersion. We present results for a doped layer in the integer quantum Hall regime for fixed hopping parameter $α$ and various magnetic fields as well as chosen magnetic field and different $α$ in the random phase approximation.
After having derived boundary conditions for dressed-state electrons in a dice lattice, we investigate the electron tunneling through a square electrostatic potential barrier in both dice lattices and graphene under a linearly-polarized off-resonance and high-frequency dressing field, and demonstrate the anomalous Klein paradox for a nonzero incident angle, resulted from the misalignment of optically-controllable elliptical dispersion for Dirac-cone dressed states and the direction of incoming kinetic particles in our system. This finite incident angle is found depending on the type of light polarization, the light-induced anisotropy in energy dispersion and the strength of electron-light coupling. Meanwhile, we also observe much larger off-peak transmission amplitudes in dice lattices in comparison with graphene. We expect the theoretical results in this paper could be used for wide range of Dirac materials and applied to controlling both coherent tunneling and ballistic transport of electrons for constructing novel optical and electronic nano-scale switching devices.
We predict the occurrence of Bose-Einstein condensation and superfluidity of dipolar magnetoexcitons for a pair of quasi-two-dimensional spatially separated $α$-${\cal T}_3$ layers. We have solved a two-body problem for an electron and a hole for the model Hamiltonian for the $α$-${\cal T}_3$ double layer in a magnetic field. The energy dispersion of collective excitations, the spectrum of sound velocity, and the effective magnetic mass of magnetoexcitons are obtained in the integer quantum Hall regime for high magnetic fields. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition are probed as functions of the excitonic density, magnetic field, and the inter-layer separation.
An extensive analytical and numerical investigation has been carried out to examine the role played by many-body effects on various $α$-$\mathcal{T}_3$ materials under an off-resonance optical dressing field. Additionally, we explore its dependence on the hopping parameter $α$ as well as the electron-light coupling strength $λ_0$. The obtained dressed states due to mutual interaction between Dirac electrons and incident light are shown to demonstrate rather different electronic and optical properties in comparison with those in the absence of incident light. Specifically, various collective transport and optical properties of these electron dressed states are discussed in detail and compared for both single- and double layer $α$-$\mathcal{T}_3$ lattices. All of these novel properties are due to the presence of a middle flat band and the interband transitions between it and an upper conduction band. Also, coupled plasmon dispersions for interacting double layer $α$-$\mathcal{T}_3$ lattices are calculated, revealing a lower acoustic-like plasmon branch with tunable group velocity determined by both the layer separation and Fermi energy of each layer. Finally, a many-body theory is presented within the random-phase approximation for calculating the optical absorbance of doped multi-layered $α$-$\mathcal{T}_3$ lattices in a linearly-polarized light field. We anticipate that the discoveries reported here could impact the design of the next-generation nano-optical and nano-plasmonic devices.
Sodium, magnesium and aluminum adatoms, which, respectively, possess one, two and three valence electrons in terms of 3s, $3s^2$, and ($3s^2$, 3p) orbitals, are very suitable for helping us understand the adsorption-induced diverse phenomena. In this study, the revealing properties of metal (Na/Mg/Al)-adsorbed graphene systems are investigated by mean of the first-principles method. The single- and double-side chemisorption cases, the various adatom concentrations, the hollow/top/valley/bridge sites, and the buckled structures are taken into account. The hollow and valley adsorptions, which, respectively, correspond to the Na/Mg and Al cases, create the extremely non-uniform environments within the Moire superlattices. This lead to diverse orbital hybridizations in Na/Mg/Al-Si bonds, as indicated from the Na/Mg/Al-dominated bands, the spatial charge density distributions and the orbital-projected density of states (DOS). Among three kinds of metal-adatom adsorptions, the Al-adsorption configurations present the strongest chemical modifications. The ferromagnetic configurations are shown to only survive in the specific Mg- and Al-adsorptions, but not the Na-cases. The theoretical predictions could be validated by experimental measurements and the up-to-date potential applications are included. Furthermore, the important similarities and differences with the graphene-related systems are also discussed.
The magneto-transport properties of phosphorene are investigated by employing the generalized tight-binding model to calculate the energy bands. For bilayer phosphorene, a composite magnetic and electric field is shown to induce a feature-rich Landau level (LL) spectrum which includes two subgroups of low-lying LLs. The two subgroups possess distinct features in level spacings, quantum numbers, as well as field dependencies. These together lead to anomalous quantum Hall (QH) conductivities which include a well-shape, staircase and composite quantum structures with steps having varying heights and widths. The Fermi energy-magnetic field-Hall conductivity ($E_{F}-B_{z}-σ_{xy}$) and Fermi energy-electric field-Hall conductivity ($E_{F}-E_{z}-σ_{xy}$) phase diagrams clearly exhibit oscillatory behaviors and cross-over from integer to half-integer QH effect. The predicted results should be verifiable by magneto-transport measurements in a dual-gated system.
The theoretical framework, which is built from the first-principles results, is successfully developed for investigating emergent two-dimensional (2D) materials, as it is clearly illustrated by carbon substitution in silicene. Computer coding with the aid of VASP in conjunction with data analysis from the multi-orbital hybridizations [spin configurations] are thoroughly identified from the optimal honeycomb lattices, the atom-dominated energy spectra, and the spatial charge density distributions. The atom and orbital-decomposed van Hove singularities [the net magnetic moments], being very sensitive to the concentration and arrangements of guest atoms. All the binary 2D silicon-carbon compounds belong to the finite- or zero-gap semiconductors, corresponding to the thoroughly/strongly/slightly modified Dirac-cone structures near the Fermi level. Additionally, there are frequent π and σ band crossings, but less anti-crossing behaviors. Apparently, our results indicate the well-defined π and σ bondings.
A theoretical framework, which is under the first-principles calculations, is developed to fully explore the dramatic changes of essential properties due to the silicon-atom chemical modifications on monolayer graphenes. For the Si-chemisorption and Si-substituted graphenes, the guest-atom-diversified geometric structures, the Si- and C-dominated energy bands, the magnetic moments, the charge transfers, the spatial charge densities, the spin distribution configurations, and the van Hove singularities in the atom- and orbital-projected density of states are investigated thoroughly by the delicate evaluations and analyses. Such fundamental properties are sufficient in determining the critical physical and chemical pictures, in which the accurate multi-orbital hybridizations are very useful in comprehending the diverse phenomena, e.g., the C- and Si-co-dominated energy bands, the semiconducting or metallic behaviors, and the existence/absence of Dirac-cone band structures. This developing model could be generalized to other emergent layered materials.
Dirac-electronic tunneling and nonlinear transport properties with both finite and zero energy bandgap are investigated for graphene with a tilted potential barrier under a bias. For validation, results from a finite-difference based numerical approach, which is developed for calculating transmission and reflection coefficients with a dynamically-tunable (time-dependent bias field) barrier-potential profile, are compared with those of both an analytical model for a static square-potential barrier and a perturbation theory using Wentzel-Kramers-Brillouin (WKB) approximation. For a biased barrier, both transmission coefficient and tunneling resistance are computed and analyzed, indicating a full control of the peak in tunneling resistance by bias field for a tilted barrier, gate voltage for barrier height, and energy for incoming electrons. Moreover, a finite energy gap in graphene is found to suppress head-on transmission as well as skew transmission with a large transverse momentum. For a gapless graphene, on the other hand, filtering of Dirac electrons outside of normal incidence is found and can be used for designing electronic lenses. All these predicted attractive transport properties are expected extremely useful for the development of novel electronic and optical graphene-based devices.
The Hall conductivity $σ_{xy}$ of many condensed matter systems presents a step structure when a uniform perpendicular magnetic field is applied. We report the quantum Hall effect in buckled AB-bottom-top bilayer silicene and its robust dependence on the electronic valley and spin-orbit coupling. With the unique multi-valley electronic structure and the lack of spin degeneracy, the quantization of the Hall conductivity in this system is unlike the conventional sequence as reported for graphene. Furthermore, the conductivity plateaux take different step values for conduction ($2e^2/h$) and valence ($6e^2/h$) bands since their originating valleys present inequivalent degeneracy. We also report the emergence of fractions under significant effect of a uniform external electric field on the quantum Hall step structure by the separation of orbital distributions and the mixing of Landau levels from distinct valleys. The valley- and spin-dependent quantum Hall conductivity arises from the interplay of lattice geometry, atomic interaction, spin-orbit coupling, and external magnetic and electric fields.
In the presence of external off-resonance and circularly-polarized irradiation, we have derived a many-body formalism and performed a detailed numerical analysis for both the conduction and optical currents in $α-\mc{T}_3$ lattices. The calculated complex many-body dielectric function, as well as conductivities of displacement and transport currents, display strong dependence on the lattice-structure parameter $α$, especially approaching the graphene limit with $α\to 0$. Unique features in dispersion and damping of plasmon modes are observed with different $α$ values, which are further accompanied by a reduced transport conductivity under irradiation. The discovery in this paper can be used for designing novel multi-functional nanoelectronic and nanoplasmonic devices.
The effect due to doping by B, Si, N on the magneto-transport properties of graphene is investigated using the generalized tight-binding model in conjunction with the Kubo formula. The crucial electronic and transport properties are greatly diversified by the type of dopant and doping concentration. The contribution from the guest atoms may open a band gap, thereby giving rise to the rich Landau level energy spectra and consequently the unique quantum Hall conductivity. The Fermi energy-dependent quantum Hall effect appears as a step structure having both integer and half-integer plateaus. Doping leads to the occurrence of zero conductivity, unlike the plateau sequence for pristine graphene. The predicted dopant- and concentration-enriched quantum Hall effect for doped graphene should provide useful information for magneto-transport measurements and possible technological applications as well as metrology.
The rich magneto-electronic properties of AA-bottom-top (bt) bilayer silicene are investigated using a generalized tight-binding model. The electronic structure exhibits two pairs of oscillatory energy bands in which the lowest conduction and highest valence states of the low-lying pair are away from the K point. The quantized Landau levels (LLs) are classified into various separated groups by the localization behaviors of spatial distributions. The LLs in the vicinity of Fermi energy do not present simple wave function modes which are quite different from other two-dimensional systems. The geometry symmetry, intralayer and interlayer atomic interactions, and effect of a perpendicular magnetic field are responsible for the peculiar LL energy spectra in AA-bt bilayer silicene. This work provides a better understanding of the diverse magnetic quantization phenomena in 2D condensed-matter materials.
The revealing properties of transition metal (T)-doped graphene systems are investigated with the use of the first-principles method. The detailed calculations cover the bond length, position and height of adatoms, binding energy, atom-dominated band structure, adatom-induced free carrier density as well as energy gap, spin-density distributions, spatial charge distribution, and atom-, orbital- and spin-projected density-of-states (DOS). The magnetic configurations are clearly identified from the total magnetic moments, spin-split energy bands, spin-density distributions and spin-decomposed DOS. Moreover, the single- or multi-orbital hybridizations in T-C, T-T, and C-C bonds can be accurately deduced from the careful analyses of the above-mentioned physical quantities. They are responsible for the optimal geometric structure, the unusual electronic properties, as well as the diverse magnetic properties. All the doped systems are metals except for the low-concentration Ni-doped ones with semiconducting behavior. In contrast, ferromagnetism is exhibited in various Fe/Co-concentrations but only under high Ni-concentrations. Our theoretical predictions are compared with available experimental data, and potential applications are also discussed.
The Berry-phase mediated valley-selected skew scattering in alpha-T3 lattices is demonstrated. The interplay of Lorentz and Berry forces in position and momentum spaces is revealed and analyzed. Many-body screening of the electron-impurity interaction is taken into account to avoid overestimation of back- and skew-scattering of electrons in the system. Triplet peak from skew interactions at two valleys is found in near-vertical and near-horizontal forward- and backward-scattering directions for small Berry phases and low magnetic fields. Magnetic-field dependence in both non-equilibrium and thermal-equilibrium currents is also presented for valley-dependent longitudinal and transverse transports mediated by a Berry phase. Mathematically, two Boltzmann moment equations are employed for computing scattering-angle distributions of non-equilibrium skew currents by using microscopic inverse energy- and momentum-relaxation times. Meanwhile, a valley-dependent unbalanced thermal-equilibrium anomalous Hall current induced by the Berry force in momentum space, due to different mobilities for two valleys, is also computed for comparisons.
A detailed numerical study of the Helmholtz Green's function for the description of scalar wave propagation through a nano-hole on a plasmonic layer is presented here. In conjunction with this, we briefly review the analytic formulation taking the nano-hole radius as the smallest length parameter of the system. Figures exhibiting the numerical results for this Green's function in various ranges of the transmission region are presented.