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Fermi surface and topology of multiband superconductor BeAu

Riccardo Vocaturo, Klaus Koepernik, Dániel Varjas, Oleg Janson, Maia G. Vergniory, Jeroen van den Brink

Abstract

The chiral material BeAu was recently identified as a multiband type-I superconductor with a critical temperature of 3.2 K. As a member of the B20 crystal family (space group $P2_13$), its band structure hosts multifold fermions at high-symmetry points, unpaired Weyl points and even nodal surfaces. This renders BeAu an appealing system to investigate the interplay between superconductivity and topology. Here we present a comprehensive first-principles analysis of BeAu's electronic structure focusing on its Fermi surface's topology and the implications for superconductivity. Together with the presence of four- and six-fold fermions at high-symmetry points, we identify several additional isolated Weyl points near the Fermi level. We also determine the associated topological edge states -- the surface Fermi arcs. Computing the Chern number associated to different Fermi surface sheets, we show that BeAu harbors a $ν= 4$ topological superconducting phase in the presence of $s$-wave pairing of alternating sign ($s_\pm$ pairing). Notably, we also identify a Fermi surface with a Chern number of +6; the highest value reported to date. Finally, our analysis reveals strong inhomogeneity in the orbital character of electronic states at the Fermi level, suggesting a link to the observed multigap superconductivity.

Fermi surface and topology of multiband superconductor BeAu

Abstract

The chiral material BeAu was recently identified as a multiband type-I superconductor with a critical temperature of 3.2 K. As a member of the B20 crystal family (space group ), its band structure hosts multifold fermions at high-symmetry points, unpaired Weyl points and even nodal surfaces. This renders BeAu an appealing system to investigate the interplay between superconductivity and topology. Here we present a comprehensive first-principles analysis of BeAu's electronic structure focusing on its Fermi surface's topology and the implications for superconductivity. Together with the presence of four- and six-fold fermions at high-symmetry points, we identify several additional isolated Weyl points near the Fermi level. We also determine the associated topological edge states -- the surface Fermi arcs. Computing the Chern number associated to different Fermi surface sheets, we show that BeAu harbors a topological superconducting phase in the presence of -wave pairing of alternating sign ( pairing). Notably, we also identify a Fermi surface with a Chern number of +6; the highest value reported to date. Finally, our analysis reveals strong inhomogeneity in the orbital character of electronic states at the Fermi level, suggesting a link to the observed multigap superconductivity.
Paper Structure (9 sections, 2 equations, 5 figures)

This paper contains 9 sections, 2 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Crystal structure
  3. Electronic structure
  4. Topological multifold crossings and Fermi arcs
  5. Unpaired Weyl crossings
  6. Fermi Surface
  7. Implications for superconductivity
  8. Conclusions
  9. Acknowledgements

Figures (5)

  • Figure 1: (a) Scalar- (without SOC) and full-relativistic (with SOC) GGA band structures of BeAu. (b) Atomic-resolved full-relativistic band structure, highlighting the relative Au and Be contributions. (c-f) Zoom-in on the multifold band crossing at high-symmetry points carrying non-trivial Chern numbers (full-relativistic band structure). In (d) we color in pink the band carrying $C=5$ (see discussion in the main text for details).
  • Figure 2: Spectral function $A(\mathbf{k}, \omega)$ at fixed energy, evaluated at a depth of 10 Bohr radii (5.29 Å) for the (001) surface termination. In panel (a), $A(\mathbf{k}, \omega)$ is shown at the Fermi level, while panels (b), (c), (d), and (e) correspond to $\omega = 0.006,\ 0.10,\ 0.15$, and 0.2 eV, respectively. The red, green, and blue arrows highlight the change of connectivity between Fermi arcs, as discussed in the main text. Panel (f) displays the band structure of a 10-layer slab along the dashed path indicated in panel (e). Bulk states are shown in gray, while surface states are colored according to the expectation value of $\hat{S}_z$. We define a surface state as a band whose atomic weight on the first layer exceeds 30%. Surface states associated with the opposite termination are not shown.
  • Figure 3: Unpaired WPs at generic $k$-points in the energy window of $\sim \pm 50$ meV around the Fermi level. (a) Projection onto the $k_z=0$ plane of the WP positions belonging to the irreducible BZ. The asterix (triangle) marks correspond to positive(negative) chirality. (b) WPs' energy dependece on external pressure. (c) Exact 3-dimensional position (units of $2 \pi / a$) of the nodes, with corresponding energy and chirality. The "band number" refers to our Wannier-projected Hamiltonian. We further label the same bands according to the order in which they appear at the four-fold fermion at $\Gamma$ in Fig. \ref{['fig:e_str']}(a): $N+2$ corresponds to the highest eigenvalue.
  • Figure 4: All full-relativistic Fermi surfaces of BeAu computed with GGA and SOC with the de Haas--van Alphen module of FPLO. We used a $24\times24\times24$$k$-mesh with additional 3 bisections. The color gradient represents the Fermi velocity intensity (units not shown), ranging from low (blue) to high (orange) values.
  • Figure 5: On the left the table summarizes the Fermi surface's Chern number as computed numerically from Eq. \ref{['eq:chern_number']}. In the first line we make explicit that S$_1$ and S$_3$ have multiplicity of 3 because there are 3 symmetry-related M points. For bookkeeping purposes, we have group them together in all previous plots. In the second line, we decided to group S$_2$ and S$_4$ together because it was too demanding to computationally resolve the very small band gap (shown on the right).