Superconductivity of ${\text{Mo}}_3{\text{Sb}}_7$ from first principles

Superconductivity in ${\text{Mo}}_3{\text{Sb}}_7$ is analyzed using the combined electronic structure and phonon calculations, and the electron-phonon coupling constant ${\lambda }_{\text{ph}}=0.54$ is determined from first principles. This value explains the experimental value of the superconducting critical temperature $T_c=2.2\text{K}$. The possible influence of spin fluctuations and spin gap on the superconductivity in ${\text{Mo}}_3{\text{Sb}}_7$ is discussed, and electron-paramagnon interaction is found to be weak.

Figure 1

(Color online) Total and site-decomposed densities of electronic states in ${\text{Mo}}_3{\text{Sb}}_7$ (per formula unit). The inset shows the details of the DOS near $E_F=0$.

Figure 2

(Color online) Phonon dispersions along the high-symmetry directions of the BZ (left) and total and site-decomposed densities of phonon states in ${\text{Mo}}_3{\text{Sb}}_7$ (right). The special points are $\Gamma =\left(0,0,0\right)$, $H=\left(1/2,-1/2,1/2\right)$, $P=\left(3/4,-1/4,3/4\right)$, $\Gamma =\left(1,0,1\right)$, and $N=\left(1,0,1/2\right)$.

Figure 3

(Color online) Critical temperature $T_c$ as a function of Coulomb parameter ${\mu }^{\star }$ for ${\lambda }_{\text{sf}}=0$ and two prefactors in Eq. (3): ${\omega }_{\text{ph}}/1.20$ and $\Theta /1.45$. Parameters: ${\lambda }_{\text{ph}}=0.54$, ${\lambda }_{\text{sf}}=0$, ${\omega }_{\text{ph}}=143\text{K}$, $\Theta =310\text{K}$.

Figure 4

(Color online) Critical temperature $T_c$ as obtained from Eq. (4) for increasing paramagnon frequency ${\omega }_{\text{sf}}$ and for different values of ${\lambda }_{\text{sf}}$. Parameters: ${\lambda }_{\text{ph}}=0.54$, ${\mu }^{\star }=0.09$, ${\omega }_{\text{ph}}=143\text{K}$.