Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)

MoS2 eta WS2 monogeruzen egitura elektroniko eta magnetikoaren ab-initio kalkuloak

Bi dimentsiotako materialetan presente diren propietate elektroniko bereziek betidanik piztu izan dute komunitate zientifikoaren interesa. Idealki atomo bakarreko lodierako materialak diren hauek hasiera batean joku teoriko huts zirela uste bazen ere, A.K. Geim eta K.S. Novoselov-ek kontrakoa frogatu zuten lehenengo aldiz grafenoa sintetizatuz[1]. Grafitoa osatzen duen geruzetako bakoitza den grafenoak guztiz anomaloak diren pro- pietate elektronikoak dauzka, Dirac-en motako sei puntuz besterik ez osatutako Fermi gainazala duelarik. Honen ondorioz, eroapen elektroiak masa gabekoak balira bezala higitzen dira mobilitate elektronikoa areagotuz. Propietate berezi hauetaz baliatuko liratekeen aplikazio teknologiko posibleek[2] material honekiko interesa egun arlo zienti- fikotik at ere hedatzea eragin du. Grafenoaren sintesiaren errekonozimendu gisa Geim eta Novoselov-ek 2010ean fisikaren Nobel saria lortu zuten. Hala ere, grafenoa ez da sintetiza daitekeen material bidimentsional bakarra. Grafenoa lortzeko teknika bera erabiliz (banantze mikromekanikoa), Geim eta Novoselov-ek zu- zendutako taldeak M oS2 eta N bSe2 sintetizatzea lortu zuen[3]. Konkretuki, M oS2 mo- nogeruza erdieroalea izanik transistoreak minimizatzeko prozesuan silizioaren ordezkari gisa jarduteko hautagaia da. Hala ere, hau egin ahal izateko bere propietate elektro- nikoak sakonkiago aztertzea komeni da. Gradu amaierako lan honetan material honen egitura elektronikoaren eta magnetikoaren karakterizazio teorikoan aurrerapauso txiki bat egitea izan dugu helburu. Horrez gain, W S2 materiala ere era berean landu da, tungsteno atomoa pisutsuagoa izatean, spin-orbita elkarrekintzaren eragina nabariagoa izatea espero baita. Modu honetan, lan hau hiru atal nagusitan banatzen da. Lehenengoa teoriari dago- kio, DF T (Dentsitatearen Funtzionalaren Teoria) inplementatzeko oinarri teorikoa lan- du delarik. Magnetizazioa aztertzeko ezinbestekoa den espina inplementatzeko modua ere aztertu da, eta baita egin beharreko hurbilketen eta pseudopotentzialen metodoaren azalpen bat eman ere. Bigarren atalean QuantumEspresso kodea erabiliz burututako ab-initio kalkuluen deskripzio eta emaitzak aurkeztu dira, azkenei dagokien interpreta- zioa eginez. Bertan M oS2 -n bolumenetiketik monogeruzara pasatzeak egitura elektroni- koan duen eragina aztertu da, ondoren M oS2 eta W S2 monogeruzen banda egitura eta magnetizazioan analisi sakonagoa eginez. Azkenengo atalean ateratako ondorioak idatzi dira, etorkizunerako lanetarako ateak zabalduz.

Unconventional spin texture of a topologically nontrivial semimetal Sb(110)

9 p.

Charge and spin transport in graphene devices

170 p.

Electronic properties of graphene grain boundaries

Grain boundaries and defect lines in graphene are intensively studied for their novel electronic and magnetic properties. However, there is not a complete comprehension of the appearance of localized states along these defects. Graphene grain boundaries are herein seen as the outcome of matching two semi-infinite graphene sheets with different edges. We classify the energy spectra of grain boundaries into three different types, directly related to the combination of the four basic classes of spectra of graphene edges. From the specific geometry of the grains, we are able to obtain the band structure and the number of localized states close to the Fermi energy. This provides a new understanding of states localized at grain boundaries, showing that they are derived from the edge states of graphene. Such knowledge is crucial for the ultimate tailoring of electronic and optoelectronic applications.

Acoustic plasmons in extrinsic free-standing graphene

An acoustic plasmon is predicted to occur, in addition to the conventional two-dimensional (2D) plasmon, as the collective motion of a system of two types of electronic carriers coexisting in the same 2D band of extrinsic (doped or gated) graphene. The origin of this novel mode stems from the anisotropy present in the graphene band structure near the Dirac points K and K'. This anisotropy allows for the coexistence of carriers moving with two distinct Fermi velocities along the Gamma K and Gamma K' directions, which leads to two modes of collective oscillation: one mode in which the two types of carriers oscillate in phase with one another (this is the conventional 2D graphene plasmon, which at long wavelengths (q -> 0) has the same dispersion, q(1/2), as the conventional 2D plasmon of a 2D free electron gas), and the other mode found here corresponds to a low-frequency acoustic oscillation (whose energy exhibits at long-wavelengths a linear dependence on the 2D wavenumber q) in which the two types of carriers oscillate out of phase. This prediction represents a realization of acoustic

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.