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Computational theory in Condensed Matter Physics

Summary and research lines

Our group develops new computational tools of interest for many-body problems in Solid State Physics. We focus on the theoretical study of low-energy electron excitations (electron-phonon interaction, superconductivity, impurities, etc.) and their influence on properties such as transport of charge and spin. We have ten-year experience in the development of tools based on Wannier functions for the efficient calculation of electron-phonon matrix elements.

An outstanding recent contribution of our group is a new theoretical framework based on Fermi Surface Harmonics (FSH). This revolutionary methodology has the potential to reduce by several orders of magnitude the computational demand of various problems in Condensed Matter Physics. We are currently making the FSH technique known in the community by its application to a number of problems: spin and charge transport on surfaces as well as in the bulk, electron-state renormalization and electron-phonon theory, superconductivity, magnetic impurities and scattering problems, magnetic anisotropy, non-perturbative methods, etc.

In particular, we are working on these research lines:

  • Fermi Surface Harmonics (FSH) applied to Solid State Physics problems.

  • Magnetic anisotropy and magnetic ordering.

  • Applications of non-pertubative methods: Renormalization Group, Quantum Monte Carlo, and exact diagonalization.

  • Electronic response in the relativistic regime and spin plasmons.

  • Green functions theory applied to many-body problems: electron-phonon interaction at the surface and bulk of materials.

  • The problem of charge and spin transport at the surface and bulk of materials.

  • Quasi-particles, renormalization and self-consistent theory for electron excitations.

  • Magnetic impurities and scattering problems: T-matrix formalism and multiple scattering.

  • First-principles calculations: electronic and magnetic properties of surfaces and adsorbates.

 

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Highlights from recent publications

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Band structure of the two-dimensional compound YbAu2 grown on Au(111), where Yb behaves mainly as a divalent ion. Background: ARPES band dispersion in the ΓK direction of the first Brillouin zone. Green horizontal line: non-interacting binding energy of the Yb-4f_7/2 manifold. Blue: parabolic approximation of the non-interacting two-dimensional band with character Yb(d_xy)-Au(s) (label C). Hybridization of this band with the 4f orbital results in valence fluctuations with lifetime ~0.2 ps, manifested in the ARPES spectrum as an anticrossing feature (red). [From: L. Fernández, M. Blanco-Rey, et al. Nanoscale, 12, 22258-22267 (2020)].

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Efficient representation of anisotropic Fermi-surface quantities through the Helmholtz Fermi-surface harmonics (HFSH) basis set. The two-index electron-phonon mass enhancement parameter λ_k,k’ of MgB_2 requires a fine sampling of momentum space (~10^3-4 k-points) to capture its anisotropy, as shown on the left panel. After transforming it through the symmetric HFSH basis functions (shown on the center), a much more compact representation is obtained, in which only the first few λ_L,L’ coefficients are significant, as shown on the right panel. [J Lafuente-Bartolome, I. G. Gurtubay, and A. Eiguren. Phys. Rev. B 102, 165113 (2020).]

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Density plot of the spectral function accounting for the electron-phonon interactions of the MoS_2 monolayer for the A'_1 phonon mode within the small momentum regime along the ΓK direction obtained by means of ab initio calculations (left) and an Einstein-like model (right) for the electron-doping concentrations ρ=0.015 (a), 0.030 (b), 0.045 (c), 0.060 (d), 0.075 (e), 0.090 (f), 0.105 (g), 0.120 e/u.c. (h). The color code scale represents the height of the spectral function. Dashed black lines represent the adiabatic phonon dispersion relations. Solid gray lines bound the electron-hole excitation damping continuum for the Einstein-like model. [P. Garcia-Goiricelaya, J. Lafuente-Bartolome, I. G. Gurtubay, and A. Eiguren. Phys. Rev. B 101, 054304 (2020)]

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Induced magnetization for the second lowest energy acoustic phonon mode at q = K involving pure out of plane displacements of W atoms. a) Real-space representation of the magnetization in the plane of the W atoms for 4 × 4 unit cells along the hexagonal axes of WSe_2 for the second lowest energy mode at q = K. In this mode the W atoms (filled circles) displace along the perpendicular direction (see color-bar) and the Se atoms above (filled triangle up) and below (filled triangle down) the W plane rotate clockwise with opposite phase around their equilibrium positions (crosses) in their respective planes. The colored vector-field is proportional to the in-plane magnetization at each point in real space, with yellow/light (blue/dark) arrows representing the largest (smallest) values. These arrows as well as the displacements of the Se atoms have been scaled to make them visible. b) The colored arrows give the z displacement of the W atoms along the q = K direction (dotted magenta line in a) according to the color-bar. The dashed line describes the propagation of the vibration along several unit-cells in real space. Note that K = [1/3, 1/3, 0] in crystal axes, and hence the periodicity of the wave. c) Side view of the WSe_2 formula-unit in the lower left corner unit-cell. The names of the atoms display their displacements from the equilibrium positions, denoted as in a. This figure is a snapshot of the time evolution of the induced magnetization for this mode [From I.G. Gurtubay, A. Iturbe-Beristain, and A. Eiguren. Commun Phys 3, 22 (2020)]

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Strongly renormalized multiple quasiparticle spectra on the doped monolayer MoS_2. (a) Spectral function calculated from first principles including electron-phonon interaction effects. (b) Zoom of the spectral function of the outer spin-split band on the area highlighted in (a) with the same color code. (c) Three dimensional representation of (b). (d) Imaginary part of the electron self-energy ImΣ(ω) (right panel) for an electron with spin-up and momentum k_A close K. The onsets of the rectangular maxima are at ω_MA and ω_MO, the energies of the acoustic and optical phonons at q=M, while their width is related to the enhanced density of states (DOS) at the occupied Q′ pockets (yellow shaded area in left panel). (e) Dispersion of the three quasi-particle poles found for the outer band. The quasiparticle energies with respect to the momentum are shown by the blue (n=1), green (n=2), and red (n=3) dots, respectively. The length of the bars represent the spectral weight of each pole, given by the real part of their residues Re(Zn_qp), while the imaginary part of the residues are represented by the rotation of the bars, Im(Zn_qp)=1 giving a rotation of θn_qp=π radians. (f) Contribution to the spectral function coming from each complex quasi-particle pole. The good agreement with (c) allows for the faithful interpretation of the signatures in the spectral function as multiple quasiparticle excitations. [From P. Garcia-Goiricelaya, J. Lafuente-Bartolome, I. G. Gurtubay, and  A. Eiguren. Communications Physics 2, 81 (2019).]