Semimetallic Superconductivity in Cubic Nd$_3$In: A First-Principles Insight into Indium-Based Compounds

TL;DR

This work investigates cubic Nd3In as a semimetallic superconductor with nontrivial topology using first-principles methods. DFT+SOC identifies Nd-dominated electronic states with multiple Fermi-surface pockets and nesting that drives strong electron–phonon coupling, quantified as $\lambda = 1.394$. Fully anisotropic Migdal–Eliashberg theory yields a robust $T_c \approx 14$ K at ambient pressure, rising to $\approx 18$ K at $15$ GPa, with a single $s$-wave gap and $2\Delta_0/(k_B T_c) = 3.93$, highlighting strong-coupling superconductivity. The material also exhibits Weyl semimetal topology with Fermi arcs and a strong $\mathbb{Z}_2$ index $(1;100)$, indicating a topological phase coexisting with superconductivity and pointing to prospects in quantum transport and topological quantum computation.

Abstract

The quest for materials that simultaneously exhibit superconductivity and nontrivial topology has drawn significant attention in recent years, driven by their potential to host exotic quantum states. Their unique coexistence often leads to rich physics and potential applications in quantum technologies. Here, we predict cubic Nd$_3$In as an exceptional candidate in this class, combining strong-coupling superconductivity with distinctive topological features. Using first-principles calculations, we find that the strong-coupling superconductivity in Nd$_3$In arises primarily due to pronounced Fermi surface nesting, leading to an electron-phonon coupling constant of $λ= 1.39$. Our fully anisotropic Migdal--Eliashberg analysis predicts a superconducting transition temperature \( T_c \approx 14\ \mathrm{K} \) at ambient pressure, which is the highest value reported so far among cubic semimetallic superconductors. When subjected to a pressure of 15 GPa, \( T_c \) increases further to 18 K. Beyond superconductivity, Nd$_3$In is found to be a Weyl semimetal, as evidenced by the presence of Fermi arcs and nontrivial $\mathbb{Z}_2$ topological invariants, confirming its topological nature. The combination of strong-coupling superconductivity and nontrivial topological states makes Nd$_3$In a promising candidate for quantum transport and topological quantum computation.

Figures (11)

• Figure 1: (a) Crystal structure and (b) Brillouin zone of Nd$_3$In.
• Figure 2: Orbital projected electronic band structure and corresponding density of states (DOS) for Nd$_3$In. The Fermi energy ($E_F$) is set to zero and indicated by the dashed horizontal line. The size of the colored scatter points is proportional to the contribution from the selected atomic orbitals. Several Weyl points are observed in the band structure, among which a few representative points are highlighted. The red-shaded region in the left panel marks the locations of type-I Weyl points, which occur between bands 24 and 25.
• Figure 3: (a) Fermi surface in reciprocal space. (b) Contours of the Fermi surface on the $k_z = 0$ plane, with dashed lines indicating the high symmetry points.
• Figure 4: (a) SOC-induced orbital-projected electronic band structure of Nd$_3$In and (b) the corresponding density of states (DOS). The Fermi energy ($E_F$) is set to zero and indicated by the dashed horizontal line. The size of the colored scatter points in panel (a) reflects the relative contribution of the selected atomic orbitals. (c) Effect of SOC on the band structure. Without SOC (upper inset), three band-touching points divide the spectrum into four regions (I–IV). Inclusion of SOC (lower inset) lifts two of these nodal points, leaving a single Weyl point and partially gapped regions.
• Figure 5: (a) Fermi surface including spin--orbit coupling (SOC) displayed in reciprocal space. (b) Cross-sectional contours of the Fermi surface on the $k_z = 0$ plane, where dashed lines denote high-symmetry points.