Competition between electron-phonon coupling and spin fluctuations in superconducting hole-doped CuBiSO

CuBiSO is a band insulator that becomes metallic upon hole doping. Superconductivity was recently reported in doped Cu${}_{1-x}$BiSO and attributed to spin fluctuations as the pairing mechanism. Based on first-principles calculations of the electron-phonon coupling, we argue that the latter is very strong in this material, and probably drives superconductivity. The critical temperature is, however, strongly depressed by the proximity to magnetism. Thus Cu${}_{1-x}$BiSO is a quite unique compound where both a conventional phonon-driven and an unconventional triplet superconductivity are possible, and compete with each other. We argue that, in this material, it may be possible to switch from conventional to unconventional superconductivity by varying such parameters as doping or pressure.

Figure 1

(Top) Band structure of CuBiSO, shaded according to the partial Cu $d_{\mathit{xz}+\mathit{yz}}$ (left) and S $p_{x+y}$ (right) characters: the continuous and dash-dotted lines mark, respectively, the position of the Fermi level in the undoped compound and that corresponding to the filling $d^6$ of Fe pnictides (see text); the corresponding DOS in states/(f.u. spin eV) is also shown. (Bottom) Low-energy band structure: Dotted and dashed lines mark the position of the Fermi level corresponding to the hole dopings $x=0.1$ and $x=0.5$, in RBA.

Figure 2

From top to bottom: Partial phonon density of states (PDOS), Eliashberg spectral function for $x=0.1$, in RBA, and (inset) ratio between the coupling constant and $N_0(x)$ as a function of doping.

Figure 3

Phase diagram of Cu${}_{1-x}$BiSO, defined by ${\lambda }_{\Delta }$ as a function of doping ($x$) and Stoner parameter $I$, whose value is represented by the color scale. The two horizontal dashed lines correspond to $I_{\text{LDA}}$ = 0.53 eV and $I_{\text{GGA}}$ = 0.67 eV. The vertical dashed line indicates the doping for which superconductivity was observed in Ref. 5. In the region (FM) the system shows a FM instability, defined by the condition ($N_{0}I⩾1$); elsewhere the system is paramagnetic (PM). Below the bold line (which marks the condition $T_c^{\text{s}}=T_c^{\text{t}}$) the ground state is a conventional singlet superconductor. Above the bold line a triplet superconducting state is more stable. The isolines ${\lambda }_{\Delta }=0.6$ and ${\lambda }_{\text{sf}}^{\text{t}}=0.6$ indicate the values of $I,x,$ which reproduce the experimental $T_c=5.8$ K of Ref. 5 in the singlet and triplet channels, respectively.