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.

Ab initio study of anharmonicity in high pressure Cmca-4 metallic hydrogen

Hydrogen is the only atom for which the Schr odinger equation is solvable. Consisting only of a proton and an electron, hydrogen is the lightest element and, nevertheless, is far from being simple. Under ambient conditions, it forms diatomic molecules H2 in gas phase, but di erent temperature and pressures lead to a complex phase diagram, which is not completely known yet. Solid hydrogen was rst documented in 1899 [1] and was found to be isolating. At higher pressures, however, hydrogen can be metallized. In 1935 Wigner and Huntington predicted that the metallization pressure would be 25 GPa [2], where molecules would disociate to form a monoatomic metal, as alkali metals that lie below hydrogen in the periodic table. The prediction of the metallization pressure turned out to be wrong: metallic hydrogen has not been found yet, even under a pressure as high as 320 GPa. Nevertheless, extrapolations based on optical measurements suggest that a metallic phase may be attained at 450 GPa [3]. The interest of material scientist in metallic hydrogen can be attributed, at least to a great extent, to Ashcroft, who in 1968 suggested that such a system could be a hightemperature superconductor [4]. The temperature at which this material would exhibit a transition from a superconducting to a non-superconducting state (Tc) was estimated to be around room temperature. The implications of such a statement are very interesting in the eld of astrophysics: in planets that contain a big quantity of hydrogen and whose temperature is below Tc, superconducting hydrogen may be found, specially at the center, where the gravitational pressure is high. This might be the case of Jupiter, whose proportion of hydrogen is about 90%. There are also speculations suggesting that the high magnetic eld of Jupiter is due to persistent currents related to the superconducting phase [5]. Metallization and superconductivity of hydrogen has puzzled scientists for decades, and the community is trying to answer several questions. For instance, what is the structure of hydrogen at very high pressures? Or a more general one: what is the maximum Tc a phonon-mediated superconductor can have [6]? A great experimental e ort has been carried out pursuing metallic hydrogen and trying to answer the questions above; however, the characterization of solid phases of hydrogen is a hard task. Achieving the high pressures needed to get the sought phases requires advanced technologies. Diamond anvil cells (DAC) are commonly used devices. These devices consist of two diamonds with a tip of small area; for this reason, when a force is applied, the pressure exerted is very big. This pressure is uniaxial, but it can be turned into hydrostatic pressure using transmitting media. Nowadays, this method makes it possible to reach pressures higher than 300 GPa, but even at this pressure hydrogen does not show metallic properties. A recently developed technique that is an improvement of DAC can reach pressures as high as 600 GPa [7], so it is a promising step forward in high pressure physics. Another drawback is that the electronic density of the structures is so low that X-ray di raction patterns have low resolution. For these reasons, ab initio studies are an important source of knowledge in this eld, within their limitations. When treating hydrogen, there are many subtleties in the calculations: as the atoms are so light, the ions forming the crystalline lattice have signi cant displacements even when temperatures are very low, and even at T=0 K, due to Heisenberg's uncertainty principle. Thus, the energy corresponding to this zero-point (ZP) motion is signi cant and has to be included in an accurate determination of the most stable phase. This has been done including ZP vibrational energies within the harmonic approximation for a range of pressures and at T=0 K, giving rise to a series of structures that are stable in their respective pressure ranges [8]. Very recently, a treatment of the phases of hydrogen that includes anharmonicity in ZP energies has suggested that relative stability of the phases may change with respect to the calculations within the harmonic approximation [9]. Many of the proposed structures for solid hydrogen have been investigated. Particularly, the Cmca-4 structure, which was found to be the stable one from 385-490 GPa [8], is metallic. Calculations for this structure, within the harmonic approximation for the ionic motion, predict a Tc up to 242 K at 450 GPa [10]. Nonetheless, due to the big ionic displacements, the harmonic approximation may not su ce to describe correctly the system. The aim of this work is to apply a recently developed method to treat anharmonicity, the stochastic self-consistent harmonic approximation (SSCHA) [11], to Cmca-4 metallic hydrogen. This way, we will be able to study the e ects of anharmonicity in the phonon spectrum and to try to understand the changes it may provoque in the value of Tc. The work is structured as follows. First we present the theoretical basis of the calculations: Density Functional Theory (DFT) for the electronic calculations, phonons in the harmonic approximation and the SSCHA. Then we apply these methods to Cmca-4 hydrogen and we discuss the results obtained. In the last chapter we draw some conclusions and propose possible future work.

As2Te3-ren isolatzaile topologikorako presiopeko trantsizioaren ab-initio azterketa

Materia kondentsatuko sikan erronka nagusietako bat naturako materialen izaera eza- gutu eta ezaugarritzea da. Orain dela urte batzuk arte ezagutzen genituen material guztiak, eroale, erdieroale edo isolatzaileak ziren, materialeko balentzia elektroien izae- raren arabera. Azken urteotan sikako arlo honetan burututako lanek eman dute bere fruitua, materiaren egoera berri bat aurkitu baita naturan [1]: isolatzaile topologikoa. Isolatzaile topologikoak material isolatzaileak dira baina ertza eroalea dute. Egoera eroale hauek dira material berri honen berezkotasuna. Egoerok sistemaren topologia dela eta existitzen dira eta sistemaren simetriaren bidez babestuta daudenez, deusez- taezinak dira. Hall isolatzaile kuantikoa izan zen isolatzaile topologikoen gaia teorikoki garatzen hasteko inspirazio iturria eta esperimentalki beranduago aurkitu ziren [2]. Lan ugari egiten ari da materiaren egoera berri honen teoria osatu eta era honetako material berriak aurkitzeko. Gaur egun isolatzaile topologiko ezagunenetarikoak kalogenuro fami- liakoak dira. Talde honetakoa da 2008.urtean estrainekoz aurkitu zen hiru dimentsiotako isolatzaile topologikoa: Bi1

Spin-orbita elkarrekintza eta trukatze-korrelazio eremu eskalar eta bektorialaren ab-initio kalkuluak LAPW metodoaren bidez: Bismutoaren adibidea

Gradu amaierako lan honetan, LAPW metodoa aztertu da solidoen propietate elektronikoak era teorikoan ikertzeko eta efektu erlatibistek hauengan duten eragina zenbatesteko tresna teoriko bezala. Konkretuki spin-orbita elkarrekintzan zentratu gara, eta hau konputazionalki inplementatzeko bigarren bariazionalaren metodoa aztertu da. Bestalde, Spin-DFT teoriaren barruan spin-orbita kodifikatzen duen trukatze-korrelazio eremu bektorialaren azterketa labur bat egin da, ekarpen erlatibista beste ikuspuntu batetik aztertu eta informazio osagarria lortzeko asmoz.

La leyenda de la violación de Lucrecia y la articulación del relato del reinado de Tarquinio el Soberbio en Tito Livio ("Ab Urbe Condita" 1.49-60)

[ES] El propósito de este trabajo es el de mostrar cómo Livio elabora el episodio de la violación de Lucrecia de tal manera que se conecta con los restantes episodios del reinado de Tarquinio el Soberbio, formando una unidad tan estrecha y bien dispuesta que éste se convierte en el punto culminante de un proceso que comienza con el inicio del reinado del último monarca romano. Livio no se limita a seleccionar y disponer en una simple secuencia temporal los hechos que la tradición atribuía al segundo Tarquinio, sino que los elabora y ordena con vistas a conseguir un relato efectivo desde la perspectiva literaria y narrativa y, como consecuencia de ello, convincente desde el punto de vista moral, una de sus principales preocupaciones.