Downfolding electron-phonon Hamiltonians from ab initio calculations: Application to ${\mathrm{K}}_3$ picene

We propose an electron-phonon parametrization which is constructed to reproduce target geometry and harmonic frequencies taken from first principles calculations or experiment. With respect to standard electron-phonon models, it adds a “double-counting” correction, which takes into account the lattice deformation as the system is dressed by low-energy electron-phonon processes. We show the importance of this correction by studying potassium-doped picene (${\mathrm{K}}_3$ picene), recently claimed to be a superconductor with a $T_c$ of up to 18 K. The Hamiltonian parameters are derived from ab initio density functional theory, and the lattice model is solved by dynamical mean-field theory. Our calculations include the effects of electron-electron interactions and local electron-phonon couplings. Even with the inclusion of a strongly coupled molecular phonon, the Hubbard repulsion prevails and the system is an insulator with a small Mott gap of $\approx 0.2$ eV.

Figure 1

Mean-field solution of Eqs. (3) as a function of the deformation potential $\delta V$, taken with respect to the ab initio molecular value $\delta V_{\mathrm{mol}}$. The geometry is constrained to the crystal relaxed DFT solution, and the dressed frequency is set to the crystal DFT ${\omega }_{\mathrm{dressed}}=0.173$ eV, yielding (a) ${\omega }_{\mathrm{bare}}$ and (b) $x^0$.

Figure 2

Paramagnetic spectral functions obtained by (a) ED and (b) CTQMC without phonons at $T=0$ eV (ED) and $0.01$ eV (CTQMC).

Figure 3

(a) $T=0$ ED/DMFT spectral functions including both EE and EP interactions without EP-DC correction. (b) Same as (a), but with the EP-DC correction.