Plasmon assisted superconductivity in LiTi$_2$O$_4$

Abstract

We combine $GW$ plus extended dynamical mean field theory ($GW$+EDMFT) with the density functional theory for superconductors (SCDFT) framework to study the electronic properties of LiTi$_2$O$_4$. Excellent agreement with experiment is obtained for the density of states, mass enhancement, Sommerfeld coefficient and superconducting $T_c$, if the dynamical nature of the screened Coulomb interaction is taken into account. Our results show that the coupling to collective charge fluctuations (plasmons) plays an important role in the pairing mechanism and explains the remarkably high $T_c$ of this moderately correlated spinel compound.

Figures (5)

• Figure 1: Local $GW$+EDMFT spectral function at the stoichiometric filling (solid line). The dashed and dotted lines show the local spectral functions in the CF basis with two-fold degenerate occupied orbitals ($A^{2,3}$) and an almost empty orbital ($A^{1}$). The shaded region indicates the DFT DoS.
• Figure 2: Electronic properties as a function of the total filling of the Ti-$d$ shell, $n^\text{Ti}$. Top panel: density imbalance $\Delta n$ between the singly and doubly degenerate local levels (circles) and impurity polarization $\mathcal{P}$ (squares). The inset reports the insulating local spectral function at the $d^1$ configuration. Bottom panel: $Z$ factor (circles) and the Sommerfeld coefficient (squares) as a function of $n^\text{Ti}$. The labels indicate the value of the local interacting spectral function at the Fermi level (states eV$^{-1}$ atom$^{-1}$).
• Figure 3: Upper panel: Eliashberg function $\alpha^2F(\omega)$ of LTO. Bottom panel: diagonal components of the contributions to the SCDFT Kernel $\mathcal{K}$ computed at $T=0.05$ K.
• Figure 4: Gap amplitude $\Delta(T,0)$ of stoichiometric LTO as a function of temperature (solid line), yielding $T_c=7.2$ K. The dashed line shows the result obtained with only the static interaction, which clearly underestimates $T_c$. Inset: energy structure of the low temperature BCS order parameter $\Delta(T=0.05~\mathrm{K},\varepsilon)$. The structure near $\varepsilon=0.8$ is likely of plasmonic origin, since it is not present in the calculation with static kernel. All dashed lines are $\times 10$ magnified for clarity.
• Figure 5: Superconducting dome of LiTi$_2$O$_4$. The thick line indicates the critical temperature, while the dashed line shows the BCS order parameter. The gray horizontal line represents the BCS ratio for the $d$ shell occupations with a superconducting solution.