First-principles evidence for conventional superconductivity in a quasicrystal approximant

TL;DR

This work demonstrates, from first principles, that superconductivity in the Al13Os4 decagonal quasicrystal approximant is conventional and electron–phonon mediated. The authors reproduce the experimental Tc and superconducting gap using fully ab initio Migdal–Eliashberg theory, validating the predictive power of the el–ph framework for ACs and supporting its relevance for QCs. They further show that alloying Al13Os4 with Re or Ir, modeled via the generalized quasichemical approximation, can tune Tc: Al13Re4 is dynamically stable and predicted to reach $T_c \approx 4.7$ K (≈30% higher than Al13Os4), while Al13Ir4 is dynamically unstable. By establishing a practical in silico route to optimize Tc in ACs, the work provides a blueprint for discovering high-Tc QC superconductors and sets bounds on the Tc of their quasicrystalline counterparts.

Abstract

Quasicrystals (QCs) host long-range order without translational symmetry, a regime in which the very foundations of BCS theory are not straightforwardly applicable, yet experiments on QCs and their approximant crystals (ACs) point to conventional, $s$-wave, electron-phonon coupled superconductivity. With this work we directly address this seeming contradiction from first principles. Using state-of-the-art \textit{ab initio} methods, we compute the superconducting properties of the recently discovered AC Al$_{13}$Os$_4$ and quantitatively reproduce its bulk $T_\text{c}$. This constitutes, to our knowledge, the first \emph{ab initio} determination of $T_\text{c}$ for an AC and establishes that the electron-phonon framework is predictive in these systems as well. Using the generalized quasichemical approximation for alloy modeling in the decagonal Al-Os family, we predict tunable superconductivity in Al$_{13}$Os$_{4-x}$Re$_x$ and Al$_{13}$Os$_{4-x}$Ir$_x$; in particular, Al$_{13}$Re$_4$ is dynamically stable and estimated to have a $T_\text{c}$ about 30% above Al$_{13}$Os$_4$. Finally, we argue that $T_\text{c}$ obtained for ACs provides practical bounds for the $T_\text{c}$ of their parent QCs, suggesting that the quasicrystalline counterparts of Al$_{13}$Os$_4$ and Al$_{13}$Re$_4$ could harbor the highest $T_\text{c}$ among QCs yet.

Figures (5)

• Figure 1: Crystal structure of Al$_{13}$Os$_{4}$. (a) Primitive cell (1 formula unit) of Al$_{13}$Os$_{4}$. Aluminum is represented as blue spheres and osmium as red spheres. (b) The y = 0 layer of Al$_{13}$Os$_4$ with one unit cell indicated as thin black lines. (c) The y = 1/2 layer of Al$_{13}$Os$_4$. (d) Variations of the smaller and larger tilings can be used in the quasicrystal Al$_{70}$Ni$_{15}$Co$_{15}$ as marked. Projections of the quasicrystal's 5 basis axes are also shown.
• Figure 2: Electronic properties of Al$_{13}$Os$_4$. (a) Orbital-projected band structure along the selected high-symmetry path (thin black lines). Each marker’s hue is a combination of the colors assigned to the contributing orbitals, with coefficients given by their fractional projections at that state; the marker opacity encodes the total projected weight. Vertical guidelines indicate the high-symmetry points. Total electronic density of states (black, light fill) and orbital-resolved partial DOS for Al-$p$ (blue), Os-$d$ (red), and Al-$s$ (green) are also displayed. (b) Electron localization function (ELF) isosurfaces at selected values. (c) Fermi-surface sheets projected onto the Al-$p$ and Os-$d$ character.
• Figure 3: El–ph interactions and superconducting properties of Al$_{13}$Os$_{4}$. (a) Left: Phonon dispersion along a high-symmetry path in the BZ. Superimposed circles indicate the mode-resolved el–ph coupling $\lambda_{\nu\textrm{q}}$ at selected $q$ points; colors and marker size encode $\lambda_{\nu\textrm{q}}$. Middle: Atom-projected phonon density of states $F(\hbar\omega)$ in meV$^{-1}$ for Al (blue) and Os (red). Right: Eliashberg spectral function $\alpha^2F(\hbar\omega)$ (orange line) and the cumulative total electron–phonon coupling parameter $\lambda$. (b) Superconducting gap $\Delta_0$ as a function of temperature obtained by solving the isotropic Migdal–Eliashberg equations within the full-bandwidth approximation.
• Figure 4: (left) All supercell configurations obtained by substituting Os with Re or Ir in Al$_{13}$Os$_{4}$. (right) Total electronic DOS of Al$_{13}$Os$_{4-x}$Ir$_x$ and of Al$_{13}$Os$_{4-x}$Re$_x$ as a function of composition $x$, computed within the GQCA framework.
• Figure 5: Electronic, el-ph and superconducting properties of Al$_{13}$Re$_4$. (a) Orbital-projected band structure, total electronic density of states (black, light fill), and orbital-resolved partial DOS for Al-$p$ (blue) and Re-$d$ (red). Each marker’s hue in the electronic dispersion is a combination of the colors assigned to the contributing orbitals, with coefficients given by their fractional projections at that state; the marker opacity encodes the total projected weight. (b) Fermi surface projected onto the Al-$p$ and Re-$d$ states. (c) Left: Phonon dispersion along the same high-symmetry path. Superimposed circles indicate the mode-resolved el–ph coupling $\lambda_{\nu\textrm{q}}$ at selected $q$ points; colors and markers size correlate to the values of $\lambda_{\nu\textrm{q}}$. Middle: Atom-projected phonon density of states $F(\hbar\omega)$ for Al (blue) and Re (green). Right: Eliashberg spectral function $\alpha^2F(\hbar\omega)$ (orange line) and the cumulative total el–ph coupling parameter $\lambda$. (d) Superconducting gap $\Delta_0$ as a function of temperature obtained by solving the isotropic Migdal–Eliashberg equations within the full-bandwidth approximation.