Bilayer Iron-Based Superconductors

• Bilayer iron-based superconductors are layered materials with two Fe-based planes separated by spacer layers, yielding distinct bonding and antibonding electronic states.
• Interlayer coupling combined with spin–orbit interactions leads to sharp spin resonance mode splitting and anisotropic magnetic excitations that directly probe exchange strengths.
• These materials display multigap superconductivity with potential topological states and evidence of Majorana zero modes, offering a platform for quantum device engineering.

A bilayer iron-based superconductor is a layered material system in which the fundamental structural building block is two iron-pnictide (or iron-chalcogenide) layers (such as FeAs or FeSe) linked via intercalated metallic or insulating spacer layers, yielding a crystallographic or electronic “bilayer” unit. Prototypical bilayer iron-based superconductors—including CaKFe₄As₄ (“1144” type), KCa₂Fe₄As₄F₂ and CsCa₂Fe₄As₄F₂ (“12442” type), and artificially engineered Fe/Ba-122 heterostructures—exhibit distinctive collective excitations and multiband phenomena arising from the interplay of interlayer coupling, orbital physics, and spin–orbit interaction. These systems serve as an ideal platform to study the consequences of bilayer symmetry, spin-resonance mode splitting, interlayer pairing, band-selective superconductivity, and topological effects including Majorana zero modes.

1. Crystal and Electronic Structure of Bilayer Iron-Based Superconductors

Bilayer iron-based superconductors crystallize in tetragonal (P4/mmm or I4/mmm) lattices with alternating sequences of Fe–As (sometimes Fe–Se, Fe–Te) layers separated by spacer blocks, such that each primitive unit cell includes two symmetry-inequivalent Fe-based planes. In CaKFe₄As₄, the stacking order is …Ca–FeAs–K–FeAs–Ca–… so the Fe–As bilayers are sandwiched between Ca and K, breaking glide-mirror symmetry relative to the conventional 122 structure (Liu et al., 2022, Xie et al., 2018, Liu et al., 2019). In the 12442 family, as exemplified by KCa₂Fe₄As₄F₂ and CsCa₂Fe₄As₄F₂, double FeAs layers are separated by insulating Ca₂F₂ blocks and alkali metals, yielding as much as 5.9 Å intra-bilayer and 9–10 Å inter-bilayer spacings (Wu et al., 2020, Wang et al., 12 Jan 2026, Xu et al., 2019). This symmetry reduction and quasi-two-dimensionality generate a multiplicity of Fe 3d-derived Fermi sheets split into bonding (even symmetry) and antibonding (odd symmetry) combinations by the finite interlayer hopping and electronic hybridization.

Electronic structure studies (including ARPES with energy resolution down to 1 meV and angular precision of 0.3°, corresponding to ~0.004 Å⁻¹ in momentum space), resolve multiple hole-like and electron-like Fermi pockets centered on high-symmetry points, typically three to five around Γ and one to two around M. Resolving bilayer splitting, particularly in the α and γ sheets of the 12442 compounds, requires direct evaluation of the momentum-dependent band separation ΔE(k), which for KCa₂Fe₄As₄F₂ measures 15–20 meV along the Γ–X direction (Wu et al., 2020, Wang et al., 12 Jan 2026).

The “bilayer spin exciton” model describes the interlayer (bilayer) coupling via a minimal magnetic Hamiltonian

$$H_{\perp} = J_{\perp} \sum_{i} \mathbf{S}_{i,1} \cdot \mathbf{S}_{i,2}$$

where $J_{\perp}$ is the bilayer exchange, and the two layers within each bilayer are labeled by 1,2 (Liu et al., 2022, Xie et al., 2018). This coupling is precisely reflected in the neutron spin resonance spectra as an odd–even mode splitting that quantifies $J_{\perp}$.

2. Spin Resonance Modes and Spin-Orbit Coupling Effects

A hallmark of bilayer iron-based superconductors is the occurrence of sharp, $L$-modulated neutron spin resonance modes in the superconducting state, classified by their symmetry with respect to the bilayer: odd and even. For CaKFe₄As₄, three distinct resonance energies are observed below $T_c$ at 9.5 meV, 13.0 meV (odd modes), and 18.3 meV (even mode), all showing well-defined sinusoidal modulation with respect to the out-of-plane wavevector $L$ as $\sin^2(\pi zL)$ (odd) and $\cos^2(\pi zL)$ (even), where $z$ is the bilayer position fraction (Xie et al., 2018, Xie et al., 2020, Liu et al., 2022). This sharp bilayer mode splitting resolves the long-standing question of spin resonance broadening in doped 122 pnictides and underscores the analogy to bilayer cuprates, which exhibit odd/even magnetic excitations associated with intra-unit-cell pairing (Xie et al., 2018).

Spin-orbit coupling (SOC) is central in dictating the spin-resonance polarization. In both CaKFe₄As₄ and its Ni-substituted variant, the low-energy odd modes are predominantly $c$-axis polarized below $T_c$, i.e. magnetic fluctuations $\chi''_c \gg \chi''_{a,b}$, whereas the high-energy even mode remains isotropic (Xie et al., 2020, Liu et al., 2022). SOC lifts the degeneracy of in-plane and out-of-plane spin excitations, coupling specific orbital channels ($d_{xz}$, $d_{yz}$, $d_{z^2}$) to $c$-axis spin fluctuations and thereby enhancing the $c$-axis magnetic resonance amplitude. The robust $c$-axis polarization is observed to persist even in the paramagnetic state at elevated temperatures and is present regardless of whether the static magnetism is collinear-stripe, vortex-type, or $c$-axis-oriented (Liu et al., 2022).

Odd/even resonance mode energies provide a direct experimental probe of $J_{\perp}$; for instance, a resonance energy splitting of $E_{even} - E_{odd} \approx 8$ meV implies $J_{\perp} \sim 4$ meV in a simple RPA context (Liu et al., 2022).

3. Bilayer Splitting, Interlayer Pairing, and Multigap Superconductivity

ARPES and optical spectroscopy establish the existence of bilayer-split Fermi surfaces and superconducting gaps. In KCa₂Fe₄As₄F₂, for example, five hole pockets appear at Γ, with the innermost (α and γ) bands resolved as bonding–antibonding pairs (maximum $\Delta k \sim 0.017$ Å⁻¹, energy splitting 15–20 meV). Distinct superconducting gap magnitudes are observed on these split bands—e.g., α₁: 8.0 meV, α₂: 6.8 meV (Wu et al., 2020)—which are well-captured only by including a $k_z$-dependent (interlayer) term in the gap function:

$$\Delta_{i}(\mathbf{k}) = \left| \Delta_{0,i} \,\tfrac{1}{2}(\cos k_x + \cos k_y) - \Delta_{z,i} \cos k_z \right|$$

where $\Delta_{0,i}$ and $\Delta_{z,i}$ parameterize intra- and interlayer pairing, respectively. The largest $\Delta_{z,i}$ occurs on the α bands (up to 4 meV), indicative of strong interlayer (bilayer) pairing analogous to the Bi-2212 cuprates (Wu et al., 2020).

In the 12442 systems, multiband superconductivity can manifest as either conventional BCS-like behavior (single $T_c$, nearly locked gaps for all bands, as seen in CsCa₂Fe₄As₄F₂) or as band-selective decoupling (distinct $T_c$ on bilayer-split bands, as in KCa₂Fe₄As₄F₂). The latter is quantitatively modeled by a two-band Eilenberger formalism:

$$\Delta_i(T) = 2\pi T \sum_{\omega_n>0} \sum_{j=1}^2 \lambda_{ij} \frac{\Delta_j(T)}{\sqrt{\omega_n^2 + \Delta_j(T)^2}}$$

with pairing matrix elements $\lambda_{ij}$ and densities of states $N_j$, such that for $|\lambda_{12}| \ll |\lambda_{11}|, |\lambda_{22}|$ the inter-band coupling is sufficiently weak to yield two apparent superconducting transition temperatures (Wang et al., 12 Jan 2026). This regime unlocks the possibility of unusual pairing states, including relative-phase order, time-reversal symmetry breaking, and possible fractional vortex phenomena.

Optical conductivity of CsCa₂Fe₄As₄F₂ reveals sharply distinct clean- and dirty-limit superconductivity on the two bilayer-derived Drude bands: one ultra-clean (scattering rate $1/\tau_n \sim 23$ cm⁻¹), the other dirty ($1/\tau_b \sim 1400$ cm⁻¹), yet both with isotropic, nodeless superconducting gaps ($2\Delta \simeq 14$ meV) (Xu et al., 2019). Thus, the bilayer motif serves as a natural vehicle for probing intertwined disorder, multi-gap, and anisotropy effects.

4. Dimensionality, Layer-Dependent $T_c$, and Phase Stiffness

Bilayer iron-based superconductors display pronounced quasi-2D physics, yet retain ample three-dimensionality due to sizable interlayer coherence length ($\xi_c$) and moderate anisotropy ($\gamma = \rho_c/\rho_{ab}$). Ultrathin flakes (down to monolayer) of CsCa₂Fe₄As₄F₂ and CaKFe₄As₄ exhibit a clear reduction in $T_c$ relative to their respective bulks: $T_c(1~\mathrm{L})\approx24.0$ K vs $T_c(\mathrm{bulk})\approx30.5$ K for Cs-12442 (−21%), and $T_c(3~\mathrm{L})\approx19.0$ K vs $T_c(\mathrm{bulk})\approx35.2$ K for CaKFe₄As₄ (−46%) (Meng et al., 2023). A universal scaling collapses the fractional suppression $-\Delta T_c/T_{c,\mathrm{bulk}}$ onto a logarithmic function of $\xi_c/d_{\rm mono}$ (coherence length over monolayer thickness):

$$-\Delta T_c / T_{c,\mathrm{bulk}} \approx 0.12 \ln(\xi_c/d_{\rm mono})$$

This framework generalizes to other quasi-2D superconductors (e.g., Bi-2212, NbSe₂) and implies that, for sufficiently small interlayer coherence, superconductivity is robust to dimensional reduction—a principle critical for device and heterostructure design (Meng et al., 2023).

5. Topological Superconductivity and Majorana Zero Modes

The breaking of glide-mirror symmetry and enhanced bilayer hybridization in CaKFe₄As₄ yield a topological band inversion at the Brillouin zone center, with a 0.5 eV hybridization gap and a 20–30 meV SOC-induced topological gap between folded As-$p_z$ and Fe-$d_{xz/yz}$ states (Liu et al., 2019). ARPES measurements detect sharp superconducting gaps on both topological surface states (Dirac-like) and trivial bulk sheets, with coherence peaks at $\Delta_{SC}=5.9$ meV (surface) and 7.5 meV (bulk) (Liu et al., 2019).

Scanning tunneling spectroscopy under applied magnetic field identifies discrete Caroli–de Gennes–Matricon bound states within vortex cores, including a zero-bias conductance peak attributed to a Majorana zero mode, whose spatial decay (coherence length $\xi \simeq 6.0$ nm) and level spacing ($\Delta E \sim1.2$ meV) are consistent with theoretical calculations for a Dirac surface BdG Hamiltonian (Liu et al., 2019). The presence of such well-resolved vortex MZMs, enabled by bilayer-induced topological band structure, positions these materials as a solid-state Majorana platform.

6. Artificial Bilayer and Interface Engineering

Artificially fabricated bilayer heterostructures—such as Fe/Ba(Fe₁₋ₓCoₓ)₂As₂ on MgO or LSAT substrates—demonstrate that the metallic FeAs tetrahedron can form atomically coherent, epitaxial interfaces with metallic Fe, preserving near-bulk $T_c$ in the superconducting layer (e.g., $T_{c,90}\sim24.4-24.8$ K for $x \sim 0.08–0.10$) (Thersleff et al., 2010). Transmission electron microscopy reveals that Fe(001) directly bonds to the basal Fe plane of the Ba-122 tetrahedron, and lattice misfits can be minimized (<3%) by appropriate orientation and substrate selection.

Such coherence at the interface provides a promising route for integrating superconductivity with ferromagnetism, realizing superconductor/ferromagnet proximity effects, and engineering devices for superconducting spintronics. The generic nature of the FeAs tetrahedron further enables this architecture to be extended to other iron pnictide and chalcogenide systems (Thersleff et al., 2010).

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Table: Representative Bilayer Iron-Based Superconductors

Compound	Structural Type	Bilayer Separation (Å)	$T_c$ (K)
CaKFe₄As₄	1144	$\sim$5.85	35.2
KCa₂Fe₄As₄F₂	12442	$\sim$5.9	33.5
CsCa₂Fe₄As₄F₂	12442	$\sim$6.0	29
Ba(Fe₁₋ₓCoₓ)₂As₂/Fe	Artificial	—	24–25

This table highlights structural and superconducting characteristics across key bilayer iron pnictides (Xie et al., 2018, Wu et al., 2020, Xu et al., 2019, Thersleff et al., 2010).

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Bilayer iron-based superconductors exemplify the entanglement of structural symmetry, interlayer hybridization, spin–orbit coupling, and multiband effects. These features manifest in sharp spin-resonance mode splitting, highly anisotropic and tunable superconductivity, and emergent topological phenomena—offering both a platform for fundamental condensed matter exploration and opportunities for material engineering through atomic-scale design (Wang et al., 12 Jan 2026, Liu et al., 2019, Meng et al., 2023).