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 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 Fermi surface. Noteworthy, many properties of our proposed basis set are also shared by the Fermi Surface Harmonics (FSH) introduced by Philip B. Allen [Physical Review B 13, 1416 (1976)], 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 demonstrates very robust in handling problems with any crystal structure or topology of the Fermi surface, 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).Comment: Accepted for publication in New Journal of Physics (NJP). 28 pages, 9 figure

Relativistic effects and fully spin-polarized Fermi surface at the Tl/Si(111) surface

We present a detailed analysis of the relativistic electronic structure and the momentum dependent spin-polarization of the Tl/Si(111) surface. Our first principle calculations reveal the existence of fully spin-polarized electron pockets associated to the huge spin-splitting of metallic surface bands. The calculated spin-polarization shows a very complex structure in the reciprocal space, strongly departing from simple theoretical model approximations. Interestingly, the electronic spin-state close to the Fermi surface is polarized along the surface perpendicular direction and reverses its orientation between different electron pockets

Spin-flip transitions and departure from the Rashba model in the Au(111) surface

We present a detailed analysis of the spin-flip excitations induced by a periodic time-dependent electric field in the Rashba prototype Au(111) noble metal surface. Our calculations incorporate the full spinor structure of the spin-polarized surface states and employ a Wannier-based scheme for the spin-flip matrix elements. We find that the spin-flip excitations associated with the surface states exhibit an important angular modulation which is completely absent in the standard Rashba model \cite{rashba}. Furthermore, we demonstrate that the maximum of the calculated spin-flip absorption rate is about twice the model prediction. These results show that although the Rashba model accurately describes the spectrum and spin polarization, it does not fully account for the dynamical properties of the surface states

Characterisation of cosmic defects using field theory and analytical models

159 p. (eng); 163 p. (eus.)Kosmologiaren eredu estandarraren eta partikulen eredu estandarraren arteko zubi-lana egiteko hautagai interesgarrienetakoak defektu kosmikoak dira. Ondorioz, defektu kosmiko hauen ezaugarritze zehatzak berebiziko garrantzia dauka. Izan ere ezaugarri hauetatik eratorritako behagarriak behaketa esperimentalekin konparatuz bi teorien arteko zubiaren osagaien berri izan baikenezake. Tesi honetan zehar defektu kosmiko mota desberdinen ezaugarrien azterketan sakondu dugu. Alde batetik, energiarekiko portaera berezia daukaten bi ereduren ezaugarri grabitazionalak aztertu ditugu, eredu hauek izan ditzaketen behagarri grabitazionalen azterketari ateak irekiz. Bestalde, defektu kosmologikoen eboluzioa deskribatzen duten eremu-teorien simulazio numerikoak gauzatu ditugu. Defektu mota desberdinentzat burutu ditugu simulazio hauek eta informazio desberdina aztertu dugu kasu bakoitzean. Lehenik eta behin, monopolo globalen simulazioak burutu ditugu eta defektu hauen abiadura zehaztu dugu. Ondoren, soka erdilokalak simulatu ditugu eta defektu hauen eboluzioaren ezaugarritze zehatza burutu dugu. Azkenik, soka globalen eta monopolo globalen zenbakizko simulazioak gauzatu ditugu hauek sor dezaketen CMB seinalearen deskribapena lortzeko eta deskribapen hauek datuekin konparatu ditugu

Characterisation of cosmic defects using field theory and analytical models

159 p. (eng); 163 p. (eus.)Kosmologiaren eredu estandarraren eta partikulen eredu estandarraren arteko zubi-lana egiteko hautagai interesgarrienetakoak defektu kosmikoak dira. Ondorioz, defektu kosmiko hauen ezaugarritze zehatzak berebiziko garrantzia dauka. Izan ere ezaugarri hauetatik eratorritako behagarriak behaketa esperimentalekin konparatuz bi teorien arteko zubiaren osagaien berri izan baikenezake. Tesi honetan zehar defektu kosmiko mota desberdinen ezaugarrien azterketan sakondu dugu. Alde batetik, energiarekiko portaera berezia daukaten bi ereduren ezaugarri grabitazionalak aztertu ditugu, eredu hauek izan ditzaketen behagarri grabitazionalen azterketari ateak irekiz. Bestalde, defektu kosmologikoen eboluzioa deskribatzen duten eremu-teorien simulazio numerikoak gauzatu ditugu. Defektu mota desberdinentzat burutu ditugu simulazio hauek eta informazio desberdina aztertu dugu kasu bakoitzean. Lehenik eta behin, monopolo globalen simulazioak burutu ditugu eta defektu hauen abiadura zehaztu dugu. Ondoren, soka erdilokalak simulatu ditugu eta defektu hauen eboluzioaren ezaugarritze zehatza burutu dugu. Azkenik, soka globalen eta monopolo globalen zenbakizko simulazioak gauzatu ditugu hauek sor dezaketen CMB seinalearen deskribapena lortzeko eta deskribapen hauek datuekin konparatu ditugu

Breakdown of the Peierls substitution for the Haldane model with ultracold atoms

We present two independent calculations of the tight-binding parameters for a specific realization of the Haldane model with ultracold atoms. The tunneling coefficients up to next-to-nearest neighbors are computed ab-initio by using the maximally localized Wannier functions, and compared to analytical expressions written in terms of gauge invariant, measurable properties of the spectrum. The two approaches present a remarkable agreement and evidence the breakdown of the Peierls substitution: (i) the phase acquired by the next-to-nearest tunneling amplitude $t_{1}$ presents quantitative and qualitative differences with respect to that obtained by the integral of the vector field A, as considered in the Peierls substitution, even in the regime of low amplitudes of A; (ii) for larger values, also $|t_{1}|$ and the nearest-neighbor tunneling $t_{0}$ have a marked dependence on A. The origin of this behavior and its implications are discussed.Comment: 5 pages, 5 figure