The iron-based superconductors (FeSCs) were first discovered in 2008, and displayed transition temperatures (Tc) up to 55 K. Despite sharing some features with the high–Tc cuprates, these materials are unique in that unconventional superconductivity and other ordering phenomena are present in a multi-orbital setting.
While FeSCs can take on a variety of structures, they all share a common building block: FeX layers (where X = As, P, S, Se, Te). These layers are formed by edge-sharing tetrahedrons, with Fe atoms at the tetrahedron centers and X atoms at the corners. The former degeneracy of five 3d orbitals from Fe is lifted under this tetrahedron crystal field and further hybridization. For the undoped case, six valence electrons occupy five 3d orbitals in a high spin state, or selectively occupy four of them (with the uppermost dxy orbital unoccupied) in a low spin state. Therefore, under a tight binding approximation, this orbital configuration produces multiple Fermi surfaces, where multiple bands around the Fermi level possess different symmetries and all play important roles.
In this multi-orbital setting with onsite spin, more interactions come into play — interorbital and intraorbital hopping and repulsion, on-site Hund’s coupling, and off-site exchange interactions. The strengths of these interactions vary relatively when various tuning parameters are adjusted, and the system develops different long-range orders with drastic changes in electronic structure. Therefore, investigation of momentum and orbital dependencies are essential to understand these long-range orders in FeSCs.
The FeSCs are, like the cuprates, an ideal platform for angle-resolved photoemission (ARPES) studies. Similar to the cuprates, their stacked layered structure enables easy in-situ cleavage to expose large flat surfaces. Furthermore, symmetry rules mean that different polarization states of incident photons will select bands with different orbital symmetry. This enables us to verify the orbital characteristics of bands and selectively trace part of them for study. In addition, we also designed an instrument to apply in situ anisotropic strain on the material, which is crucial to disentangle the presence of domain walls (symmetry axes of adjacent domains are not aligned) from the nematic phase (in which tetragonal symmetry is broken in each unit cell).
We mention a few of our experimental results, which have provided insights on many critical problems in the FeSCs. Current projects include investigating the temperature- and doping-dependent evolution of electronic structure, and possible topological superconductivity and enhancement of Tc in monolayer FeSe. The main goal of these projects is to form a unified picture of the physics in FeSCs, and explore its pairing mechanisms.
The normal state serves as a starting point for understanding FeSCs. Although most FeSCs are generally metallic, bad metal behavior in transport indicates non-negligible electron–electron correlations. (In bad metals, electron mean free path appears smaller than lattice spacing, violating the so-called Mott-Ioffe-Regel limit.) The presence of these correlations are confirmed by the strong renormalization of bandwidth observed in our ARPES measurements. After systematically investigating orbital-dependent correlation effects over a wide range of FeSCs, we conclude that:
- Widths of all bands systematically narrow from the phosphides, to the arsenides, and to the chalcogenides, corresponding to an increasing trend in renormalization factor;
- The width of the dxy band narrows at a much more strongly than that of dyz ,evolving from the phosphides to the chalcogenides;
- In iron chalcogenides, where electron correlation is much stronger, we find a temperature-induced crossover from the metallic state at low temperature to an orbital-selective Mott phase (OSMP) at high temperatures.
In a Mott insulator, strong on-site repulsion prevents electrons from hopping across sites (which requires double occupation), forming an insulator even where band theory may predict conducting behavior. The OSMP modifies this in the presence of multiple orbitals and Hund's coupling in the FeSCs. Our experimental observations shows that FeSCs host an orbital selective Mott insulating phase, which provides critical information for further theoretical modeling of FeSCs.
- D.H. Lu et al., Nature 455, 81 (2008)
- M. Yi et al., PNAS 108, 6878 (2011)
- M. Yi et al., Phys. Rev. Lett. 110, 067003(2013)
- Z.K. Liu et al., Phys. Rev. B 92, 235138(2015)
- M. Yi et al., Npj Quantum Materials, 2:57(2017)
Hopping between different orbitals is present in multiple bands near the Fermi levels of FeSCs. This multiband structure becomes more complicated when a further symmetry is broken at the nematic phase transition. In the nematic phase, in-plane tetragonal C4 symmetry is reduced to C2 symmetry, leading to the lifting of degeneracy between dyz and dxz orbitals. In a spin-density wave (SDW), translational symmetry is further broken, and the Brillouin zone is folded. Clarifying the evolution of different bands across these transitions is an important but challenging task. By adopting polarization techniques, we use ARPES to study this complex evolutionary behavior.
Unlike most FeSCs, where the nematic phase arises in a narrow temperature region above an antiferromagnetic (AFM) phase, undoped bulk FeSe has a nematic phase that remains stable over a wide temperature range in the absence of the AFM phase. Therefore, undoped bulk FeSe is a great platform for investigating band evolution across the nematic transition. The top figure above shows a schematic of nematic band reconstruction proposed by M. Yi et al. In the tetragonal phase (a), the degeneracy of dxz and dyz orbitals remains protected by C4 symmetry. In the orthomorphic phase, the degeneracy between dxz and dyz bands is lifted with respect to momentum. Near the Γ point (center of the Brillouin zone), the dxz hole band shifts up, while the dyz hole band top shifts down below EF. However, the dxz band was observed to shift downward along the Γ1–MY path while shifting upward along MY–Γ2. This momentum-dependent shift in band degeneracy indicates the appearance of hybridization between the dxz and dyz orbitals, resulting in a band inversion. The final evolutionary picture is summarized in fig (d) and (e). A detailed discussion is presented in . (Aside: when Te is substituted for Se, a band inversion makes FeTe topological. This does not occur for FeSe.)
A more detailed structure of the nematic order parameter was recently discovered by our group members. We define the nematic order parameter as the energy difference between dxz and dyz bands. H. Pfau et al. investigated electronic bands along Γ–X in both FeSe and BaFe2As2, and found a sign flip of the nematic order parameter along Γ–X. The orbital-dependent nature of the nematic order parameter places a strong constraint on the theoretical modeling of FeSCs.
- M. Yi et al., Phys. Rev. X 9, 041049(2019)
- H. Pfau et al., Phys. Rev. Lett. 123, 066402(2019)
- H. Pfau et al., Phys. Rev. B 99, 035118(2019)
One of the central problems for FeSCs is the nature of the unconventional pairing mechanism for high-temperature superconductivity. Understanding the relationship between different order parameters will provide clues for its pairing symmetry. This pairing symmetry is known to be d-wave for the cuprates, but is unresolved for the FeSCs. The coexistence of spin-density wave (SDW) and superconducting (SC) phases in many iron pnictides has attracted great interest, for it may help us infer this symmetry.
M. Yi et al. carried out ARPES measurements on Ba1-xKxFe2As2. They treated gap sizes (of band gaps induced by SDW and SC) as a measure of the strength of coherent electronic excitations of the corresponding SDW and SC orders. When the system is cooled below the Néel temperature TNéel, the SDW gap opens and saturates. (This is the temperature below which paramagnetism gives way to antiferromagnetism.) However, upon further cooling below the superconducting transition temperature Tc, the SC gap emerges, and SDW gap size correspondingly decreases. They thus proposed a competing picture of SDW and SC phases. Crucially, this coexisting-yet-competing behavior of the two phases excludes the possibility of a conventional s++ pairing mechanism in this FeSC.
- M. Yi et al., Nat. Commun., 5:3711(2014)