Session N5: Focus Session: Computational Discovery and Design of New Materials: Electronic properties of 1D and 2D materials

The Virial Theorem in Graphene and other Dirac Materials

The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by $E = \mathcal{B}$/$r_s$ where $r_s a_0$ is the mean radius of the $d$-dimensional sphere containing one particle, with $a_0$ the Bohr radius, and $\mathcal{B}$ is a constant independent of $r_s$. This result implies that, given a linear dispersion and a Coulombic interaction, there is no Wigner crystalization and that calculating $\mathcal{B}$ or measuring at any value of $r_s$ determines the energy and compressibility for all $r_s$. In addition to the total energy we calculate the exact forms of the chemical potential, pressure and inverse compressibility in arbitrary dimension.   

Create Dirac Cones in Your Favorite Materials

We propose a theoretical recipe to create Dirac cones into anyone's favorite materials. The method allows to tailor anisotropy and quantity of cones in any effective one-band two-dimensional lattice. The validity of our theory is demonstrated with two examples on the square lattice, an ``unlikely'' candidate hosting Dirac cones, and show that a graphene-like low-energy electronic structure can be realized. The proposed recipe can be applied in real materials via introduction of vacancy, substitution or intercalation, and also extended to photonic crystal, molecular array, and cold atoms systems.   

Stability of Weyl metals under imuurity scattering

We investigate the effects of bulk impurities on the electronic spectrum of Weyl semimetals, a recently identified class of Dirac-type materials. Using a $T$-matrix approach, we study resonant scattering due to a localized impurity in tight binding versions of the continuum models recently discussed by Burkov, Hook, and Balents, describing perturbed four-component Dirac fermions in the vicinity of a critical point. The impurity potential is described by a strength $g$ as well as a matrix structure $\Lambda$. Unlike the case in $d$-wave superconductors, where a zero energy resonance can always be induced by varying the impurity scalar and/or magnetic impurity strength, we find that for certain types of impurity ($\Lambda$), the Weyl node is protected, and that a scalar impurity will induce an intragap resonance over a wide range of scattering stength. A general framework is developed to address this question, as well as to determine the dependence of resonance energy on the impurity strength.   

A semi-classical analysis of Dirac fermions in 2+1 dimensions

We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices by two generators of the $SU(2)$ group in the $(2S+1)$ dimensional representation and doing a certain scaling, we formulate a $S\rightarrow\infty$ limit where the orbital and the spinor degrees become classical. We solve for the classical trajectories for a free particle on a cylinder and a particle in a constant magnetic field. We compare the semiclassical spectrum, obtained by Bohr-Sommerfeld quantization with the exact quantum spectrum for low values of $S$. For the free particle, the semiclassical spectrum is exact. For the particle in a constant magnetic field, the semiclassical spectrum reproduces all the qualitative features of the exact quantum spectrum at all $S$. The quantitative fit for $S=1/2$ is reasonably good.   

An \textit{Ab Initio Study of the} Interaction between \textit{3d} Transition Metal Atoms and Silicon Carbide Nanotubes

Interaction of \textit{3d-}transition metal atoms with armchair silicon carbide nanotubes (SiCNTs) of chiralities (3,3), (5,5), (7,7), and (9,9) is studied in detail using hybrid density functional PBE0 and an all electron basis set 6-31G**. The results show that the interaction energy between transition metal and SiCNTs depends not only on the number of $d$-electrons but also on the curvature of the nanotubes. Interaction between SiCNTs and transition metals increases with increase in curvature of the nanotubes. To explore the curvature effect in detail, both internal and external adsorption sites were chosen for the functionalization. With the exception for the SiCNTs functionalized by Ni and Zn, all 3d-transition metal-functionalized nanotubes were found to have magnetic ground states. The quenching of magnetism is strongly dependent on the curvature of the nanotubes. Mulliken charge analysis has been performed to study the amount and direction of charge transfer between transition metals and the SiCNTs. SiCNTs doped with transition metals have significantly lower band gaps, in general, than those of bare nanotubes. Transition metal atoms Ni and Zn have the least effect on the band gaps of the SiCNTs.   

Interaction of a single Li atom with SiGe(6,6) nanotubes

A study of the interaction between four types of SiGe(6,6) nanotubes\footnote{P. Wanaguru and A. K. Ray, J. Comp. Theo. Nanosci. (in press).} and a Li atom was performed using the cluster approximation. Full geometry and spin optimizations were performed without any symmetry constraints using the hybrid functional B3LYP, an all electron 6-311G**//3-21G* basis set and the GAUSSIAN 09 suite of software. All possible internal and external adsorption sites were considered and it was found that some tubes were deformed as a result of the adsorption process. Among the nanotubes which retained the tubular shape, most preferred site for the external adsorption was quasi on top of Ge site with the highest adsorption energy being 1.639eV. Also, the band gaps of the systems decreased from the values of pristine SiGe nanotube values, the range being 0.880 to 0.958eV. For inside adsorption, most preferred site was the hollow site. Adsorption energies ranged from 1.606 to 1.657eV and band gaps, from 0.777 to 0.807eV. We will present, In detail, adsorption energies, band gaps, density of states, and the bonding nature of Li to the nanotubes.   

On the possibility of population inversion in strained silicon nanowires: an atomistic study

Density functional theory and Ensemble Monte Carlo studies show the possibility of population inversion in strained silicon nanowires. At room temperature and electric field of 15 KV/cm, a strain induced indirect subband can hold 10 times more electron population compared to the direct subband. The most dominant mechanism which depletes the indirect subband is scattering by longitudinal optical (LO) phonons. At T$=$300K the inter-sub band scattering is almost symmetric with the rate of 10$^{11}$ s$^{-1}$. On the other hand the processes of thermalization to the bottom of the indirect subband (via acoustic phonon emission) and the 2nd order radiative recombination are very slow (10$^{-9}$ sec and 10 sec, respectively). At T$=$77K the LO-phonon absorption rate (indirect to direct subband scattering) drops to 10$^{8}$ s$^{-1}$. This induced asymmetry in scattering leads to the enhanced population difference between indirect and direct subbands even at higher electric fields. The spontaneous emission time is 10$^{-7}$sec and a few seconds for direct and indirect bandgap nanowires, respectively. This study suggests the usability of strained silicon nanowires in nano-lasers.   

Vortices in One Dimension: A Soliton Analysis of Gapped Carbon Nanotubes

We study the optical properties of carbon nanotubes using the bosonization technique. The action has a general sine-Gordon form and the fundamental excitations are solitons and antisolitons. The bound soliton-antisoliton of the system is an exciton. Using a mean-field analysis we find bright and dark excitonic energies that are in good agreement with experimental values. Further, the large energy differences between the exitonic spectra and the single particle spectra agrees with perturbative treatments: Bethe-Salpeter excitonic energies compared to Hatree-Fock single particle energies.   

Berry phase dependent quantum trajectories of electron-hole pairs in semiconductors under intense terahertz fields

Quantum evolution of particles under strong fields can be approximated by the quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand strong-field optics phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz siedeband generation (HSG) [1]. The HSG in semiconductors may have a wealth of physics due to the possible nontrivial ``vacuum'' states of band materials. We find that in a spin-orbit-coupled semiconductor, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field accumulates nontrivial Berry phases. We study the monolayer MoS$_2$ as a model system and find that the Berry phases are given by the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This result demonstrates an interesting Berry phase dependent effect in the extremely nonlinear optics of semiconductors. \\[4pt] [1] B. Zaks, R. B. Liu, and M. S. Sherwin, Nature \textbf{483}, 580 (2012).   

Transport properties of semi-Dirac

Recent theoretical works show the existence of a new type of dispersion relation in both $VO_2/TiO_2$ nanostructures\footnote{V. Pardo and W.E. Pickett, Phys.Rev. Let. 102, 166803 (2009)} and in stressed graphene \footnote{G. Montambaux \emph{et al.}, PRB 80, 153412 (2009)}, where the electrons confined in a plane show a non-relativistic behavior along one direction, and relativistic in the other. This semi-Dirac dispersion $E=\sqrt{(v_F p_x)^2+(p_y^2/2m)^2}$ can be observed in graphene when the Dirac cones of different valleys touch each other because of stress. When stress is increased, a gap is opened, and the graphene turns from a semi-metal to an insulator. We propose to adress this topological phase transition through transport measurements.   

Heat transport and correlations in anharmonic oscillator chains, a molecular dynamics study

It is well known that the anharmonic oscillator chain displays anomalous heat conduction, the most striking feature of which being a thermal conductivity diverging with length as $\kappa \propto L^\alpha$ where $\alpha = 2/5$ or $1/3$. By comparing MD simulations results with an analysis based on the use of the Peierls-Boltzmann equation, we shed light on the mechanisms behind this striking phenomenon in 1D and pseudo-1D systems. The possibility of persistent cross-mode correlations and its consequences were also investigated.   

Extended Electronic States above Diskoid Nanostructures

We demonstrate that charged graphene nanostructures, which can be modeled as charged metallic nanodisks, can support spatially extended electronic states with binding energies of 50-200 meV. In the case of high angular momenta these states can be highly separated from the disk surfaces, in analogy to image states above carbon nanotubes observed experimentally. We present the single-electron and approximate multi-electron wavefunctions.   

Low-energy local density of states of the 1D Hubbard model

We examine the {local} density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations with a remarkably rich structure of the local DOS in space and energy. The results predict signatures of strongly correlated excitations in the tunneling probability along finite quantum wires, such as carbon nanotubes, atomic chains or semiconductor wires in scanning tunneling spectroscopy (STS) experiments. However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. In particular, we find that the effective boundary exponent can be negative in finite wires, which leads to an increase of the local DOS near the edges in contrast to the established behavior in the thermodynamic limit.   

Energy Partitioning of Tunneling Currents into Luttinger Liquids

Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger-liquid parameter $K$), while the partitioning of charge is fully determined by $K$. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in dc experiments on wires contacted by conventional (Fermi-liquid) leads.