Pressure induced evolution of anisotropic superconductivity and Fermi surface nesting in a ternary boride

TL;DR

This work uses Migdal-Eliashberg theory implemented in EPW to characterize anisotropic, phonon-mediated superconductivity in Ta(MoB)_2, showing a single-gap superconducting state dominated by Mo-d states coupling to in-plane Mo vibrations with Tc ≈ 19.3 K at ambient pressure. The material remains dynamically stable under hydrostatic pressure up to 76.69 GPa, but its electronic structure and phonon spectrum evolve such that Tc initially decreases (P ≤ 59.71 GPa) due to a reduced N_F and stiffened phonons, followed by a Lifshitz transition at 76.69 GPa that sharpens Fermi surface nesting and abruptly increases Tc, yielding a V-shaped Tc(P) response. The absence of strong CDW signatures is linked to weak nesting and lack of phonon softening, while the Lifshitz transition provides a mechanism for pressure-induced enhancement of superconductivity. Overall, the paper highlights how Fermi surface topology and nesting interplay with EPC under pressure to govern superconductivity in a metastable ternary boride, with predictions amenable to high-pressure experiments.

Abstract

Using Migdal-Eliashberg theory implemented in Electron Phonon Wannier (EPW) code, we have investigated anisotropic superconductivity in a ternary boride $\mathrm{Ta(MoB)_2}$. It is a single-gap, anisotropic, phonon-mediated superconductor having a critical temperature $\mathrm{T_c}\sim \, 19.3$ K. A dominant contribution to superconductivity arises from the robust coupling between electronic states, primarily created by the $\mathrm{d_{xy}}$,$\mathrm{d_{x^2 - y^2}}$ orbitals of Mo atoms and the in-plane vibrations of Mo atoms. A weak Fermi surface nesting and a small electron-phonon coupling cannot induce charge density wave-like instabilities, as evidenced by the lack of a significant peak in the real part of the total Lindhard susceptibility and the absence of phonon softening. Furthermore, we have studied its electronic and superconducting properties under hydrostatic pressure up to 76.69 GPa, owing to its low bulk modulus and metastability. The persistent reduction in the density of states at the Fermi level, Fermi surface nesting and the stiffening of phonon modes lead to a diminution of superconductivity under pressure up to 59.71 GPa. At 76.69 GPa, a modification in the topology of the Fermi surface, namely a Lifshitz transition, occurs resulting in a sudden enhancement of nesting. This enhanced nesting, in turn, induces an abrupt stabilisation of superconductivity at 76.69 GPa, resulting in a V-shaped response to pressure.

Figures (7)

• Figure 1: (a) Crystal structure of $\mathrm{Ta(MoB)_2}$ at ambient pressure, (b) Birch-Murnaghan equation fitting for finding bulk modulus and its pressure derivative
• Figure 2: (a) Electronic band structure and desnity of states at ambient pressure, (b) phonon band structure and color plot of $\mathrm{\lambda_{q\nu} \omega_{q\nu}}$ on the phonon bands at ambient pressure. Right panel describes corresponding phonon density of states and isotropic Eliashberg spectral function, cumulative electron-phonon coupling strength, (c) First Brillouin zone of $\mathrm{Ta(MoB)_2}$ (tetragonal lattice having space group p4/mbm). There are four bands that cross the Fermi level at ambient pressure. Fermi surface plot of $\mathrm{Ta(MoB)_2}$ at ambient pressure corresponding to (d),(e),(f) and (g) individual bands (two different colours have been used for two opposite faces), (h) merged bands
• Figure 3: (a) Main: Fermi nesting function of $\mathrm{Ta(MoB)_2}$ at ambient pressure along high symmetry q points, Inset: zoomed version, (b),(c) color plots of Nesting function at $\mathrm{k_z = 0}$ and $\mathrm{k_z = \frac{1}{2}}$ (boundary wall along $\mathrm{k_z}$ axis) planes of first Brillouin zone respectively, (d) Real part of the bare static Lindhard charge susceptibility of $\mathrm{Ta(MoB)_2}$ at ambient pressure along high symmetry q points, Main: for all possible bands combination ($\mathrm{m = n}$ and $\mathrm{m \neq n}$), Left inset: for intra bands only ($\mathrm{m = n}$), Right inset: for inter bands only ($\mathrm{m \neq n}$), (e),(f) color plots of the real part of the bare static Lindhard charge susceptibility at $\mathrm{k_z = 0}$ and $\mathrm{k_z = \frac{1}{2}}$ planes of first Brillouin zone respectively
• Figure 4: (a) Distribution function of electron-phonon coupling strength $\mathrm{\lambda_k}$ for $\mathrm{Ta(MoB)_2}$, (b) quasi-particle density of states in the superconducting state relative to the density of states in the normal state as a function of frequency (For three different temperatures). The dashed black line is the density of states in the normal state, normalized to 1 at the Fermi level, (c) anisotropic superconducting gap on the Fermi surface of $\mathrm{Ta(MoB)_2}$ as a function of temperature
• Figure 5: Electronic band structure and density of states of $\mathrm{Ta(MoB)_2}$ at different pressure (a) 31.28 GPa, (c) 59.71 GPa and (e) 76.69 GPa. Phonon dispersion, phonon density of states and color plot of $\mathrm{\lambda_{q\nu} \omega_{q\nu}}$ on the phonon bands of $\mathrm{Ta(MoB)_2}$ at different pressure (b) 31.28 GPa, (d) 59.71 GPa and (f) 76.69 GPa.