Controlling ${\mathit{T}}_c$ through Band Structure and Correlation Engineering in Collapsed and Uncollapsed Phases of Iron Arsenides

Recent observations of selective emergence (suppression) of superconductivity in the uncollapsed (collapsed) tetragonal phase of ${\mathrm{LaFe}}_2{\mathrm{As}}_2$ has rekindled interest in understanding what features of the band structure control the superconducting $T_c$. We show that the proximity of the narrow $\mathrm{Fe}\text{−}{d}_{xy}$ state to the Fermi energy emerges as the primary factor. In the uncollapsed phase this state is at the Fermi energy, and is most strongly correlated and a source of enhanced scattering in both single and two particle channels. The resulting intense and broad low energy spin fluctuations suppress magnetic ordering and simultaneously provide glue for Cooper pair formation. In the collapsed tetragonal phase, the $d_{xy}$ state is driven far below the Fermi energy, which suppresses the low-energy scattering and blocks superconductivity. A similar source of broad spin excitation appears in uncollapsed and collapsed phases of ${\mathrm{CaFe}}_2{\mathrm{As}}_2$. This suggests controlling coherence provides a way to engineer $T_c$ in unconventional superconductors primarily mediated through spin fluctuations.

Figure 1

Fermi surface in the $k_z=0$ plane for UT and CT-LFA phases. In the UT phase, the circular pocket around $\mathrm{\Gamma }$ has $\mathrm{Fe}\text{−}{d}_{xy}$ character, while chickpea shaped pockets are of $\mathrm{Fe}\text{−}{d}_{xz,yz}$ character. These pockets disappear in the CT phase, where superconductivity is absent. Simultaneously, the effective band width $W$ of the $\mathrm{Fe}\text{−}3d$ manifold significantly increases in the CT phase ($\sim 4\mathrm{eV}$, in the UT phase $W\sim 2.4\mathrm{eV}$, leading to larger electronic itineracy. Also shown is the partial local density of states projected onto the $\mathrm{Fe}\text{−}3d$ orbitals. The bandwidth $W$ of narrow $d_{xy}$ states gets further narrowed in the UT-LFA phase to mark enhancement in effective correlation ($U/W$), where U is the Hubbard parameter.

Figure 2

Color-weighted electronic $\mathrm{QS}GW$ band structures in LFA (top) and CFA (bottom). CT (UT) phases are displayed on the left (right). All ${\mathrm{t}}_{2g}$ Fe states ($d_{xy}$ in blue, $d_{xz,yz}$ in red) are in close proximity to the Fermi energy, while the Fe-$d_{eg}$ states (depicted in green) are somewhat below. In the CT phase of LFA, the $d_{xy}$ state is pushed below $E_F$, eliminating the hole pocket at $\mathrm{\Gamma }$ and suppressing $T_c$.

Figure 3

Single-particle correlated $\mathrm{QS}GW+\mathrm{DMFT}$ electronic spectral functions $A(q,\omega )$ for CT and UT phases of LF and CFA along high-symmetry lines. The UT-CFA phase is most incoherent, while the CT-LFA phase is most coherent. The presence (absence) of the $\mathrm{Fe}\text{−}{d}_{xy}$ state at Fermi energy appears to be the primary criterion for incoherent (coherent) spectral features.

Figure 4

The energy and momentum resolved spin susceptibility $\mathrm{Im}\chi (q,\omega )$ (in the top panel from left to right) shown for the CT and UT phases, respectively. The $q$ path ($H$, $K$, $L=0$) is chosen along $(0,0)\text{−}(\frac{1}{2},0)\text{−}(\frac{1}{2},\frac{1}{2})\text{−}(0,0)$ in the Brillouin zone corresponding to the two-Fe atom unit cell. The intensity in the CT phase is artificially multiplied by 5 to bring excitations for CT and UT phases to the same scale.

Figure 5

The low energy behavior of $\mathrm{Im}\chi (q,\omega )$ is shown for four candidates at $q=(\frac{1}{2},\frac{1}{2},0)$. The more intense the peak is, higher is the $T_c$. Three different energy cuts at 15, 30, and 60 meV for $\mathrm{Im}\chi (q,\omega )$ are resolved along the $q$ path $(H,K,L=0)=(0,0)\text{−}(\frac{1}{2},0)\text{−}(\frac{1}{2},\frac{1}{2})\text{−}(0,0)$ to stress the low-energy concentration of glue in the superconducting phases. (The intensity of CT-LFA peak is artificially multiplied by five to bring excitations for CT and UT phases to the same scale).

Figure 6

The superconducting instability is absent in the CT-LFA phase. The superconducting instability corresponding to the leading (${\lambda }_1$) and lagging (${\lambda }_2$) eigenvalues of the solutions to the linearized Eliashberg equations, $\mathrm{\Delta }(q,\omega =0)$ are shown for the UT-LFA phase. The evolution of the leading eigenvalue as a function of temperature is shown for CT-CFA, UT-CFA, and UT-LFA in the bottom panel. In the inset we enlarge the low temperature part of the curves to show the estimated $T_c$’s.