Session B61: Fe-Based Superconductors - Mayorana / Topological

Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor

Majorana fermions can be realized as quasiparticle excitations in a topological superconductor, whose
non-Abelian statistics provide a route to developing robust qubits. In this context, there has been a
recent surge of interest in the iron-based superconductor, FeSe_0.5 Te_0.5. Theoretical calculations have
shown that FeSe_0.5 Te_0.5 may have an inverted band structure which may lead to topological surface
states, which can in turn host Majorana modes under certain conditions in the superconducting phase.
Furthermore, recent STM studies have demonstrated the existence of zero-bias bound states inside
vortex cores which have been interpreted as signatures of Majorana modes. While most recent studies
have focused on Majorana bound states, more generally, akin to elementary particles, Majorana
fermions can propagate and display linear dispersion. These excitations have not yet been directly
observed, and can also be used for quantum information processing. This talk is focused on our recent
work in realizing dispersing Majorana modes. I will describe the conditions under which such states can
be realized in condensed matter systems and what their signatures are. Finally, I will describe our
scanning tunneling experiments of domain walls in the superconductor FeSe_0.45 Te_0.55 , which might
potentially be first realization of dispersing Majorana states in 1D.   

Longer-range exchange interaction in iron-based superconductors: First-principles studies

The nature of strong electronic correlations in iron-based superconductors (FeSCs) was shown to be kin to manganites where localized spins and itinerant electrons coexist and are coupled by Hund’s rule interaction, leading to fierce competition between superexchange antiferromagnetism and orbital-degenerate double-exchange ferromagnetism [1,2]. This implies that in a low-energy spin-only description of FeSCs where the itinerant-electron degree of freedom were integrated out, the effective exchange interactions would have been long ranged. The spin dynamics in FeSCs has been interpreted by using such spin-only Heisenberg models with exchange couplings extended to the third nearest neighbors, i.e., the J1-J2-J3 model. Here, we use first-principles calculations on the K2Fe4Se5 and KFeAgTe2 insulators to demonstrate the importance of J4 the effective exchange between the fourth nearest neighbors. We further reveal that the band gap of K2Fe4Se5 or KFeAgTe2 is not of Mott type but the gap of Hund's metal. Our findings shed a new light on the understanding of FeSCs and the puzzling strong magnetic fluctuations in FeSe in particular. [1] PRL 105, 107004 (2010); [2] PRB 86, 081106(R) (2012).   

Quasiparticle self-consistent GW analysis in iron-based superconductors

Since the early theoretical study of iron-based superconductors, the density functional theory (DFT) has given great contributions to understand material properties, e.g. magnetic/orbital structure, pairing mechanism of superconductivity, etc. However, the LDA/GGA exchange-correlation potential in conventional DFT calculations is insufficient to describe the electronic state observed experimentally, such as in the angular resolved photoemission spectroscopy (ARPES) and de Hass van Alphen (dHvA) measurement [1-3]. In this study, we calculated the electronic band structure of iron-based superconductors with the quasiparticle self-consistent GW (QSGW) method. We found that the QSGW can improve the LDA/GGA band structure and Fermi surface in most cases. We will summarize the result and discuss the superconducting gap in the obtained QSGW band structure. [1] A. A. Kordyuk et al., Phys. Rev. B 83 134513 (2011). [2] K. Okazaki et al., Science 337 1314 (2012). [3] T. Terashima et al., J. Phys. Soc. Jpn. 79 053702 (2010).   

Search for evidence of quantum anomalous vortices in Iron-based Topological Superconductor Fe1+yTe1−xSex

Topological superconductivity makes it possible for fault-tolerant quantum computations. Fe-based superconductors are a rich material family of intermetallic compounds for high-temperature superconductivity. The interplay between these two exciting fields creates an emergent new field, marked by recent discoveries of the superconducting Dirac surface state and Majorana bound states at the vortex cores in iron-based superconductors Fe_1+yTe_1−xSe_x. However, the direct electronic transport consequence is not clear out of these topological superconducting states. We are left wondering how to operate these novel excitations. We solve the problem by thermally drive ordinary superconducting vortices around these Majorana zero modes and search for a transverse electrical response. This scheme is the Nernst effect in the superconducting state. A finite Nernst signal is observed at zero fields in the superconducting states of Fe_1+yTe_1−xSe_x. This anomalous Nernst signal shows field-symmetric dependence on the external magnetic field. Our experiments provide the first evidence of broken time-reversal symmetry in topological superconductors and point to a new method to engage Majorana zero mode excitations in transport properties.   

The Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals: I Concept and Symmetries

A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. One of the new features of the concept, is that triplet RVB bonds can resonate into the interior of an atom, where they are supported as Hund's coupled triplet states between orbitals at the same site. Remarkably though, simple symmetry arguments due to P. W. Anderson, mean that such a process can only develop coherence with triplet pairs on the Fermi surfacce, if the there are two symmetry related atoms per unit cell, leading to a state that has staggered structure of onsite pair correlations that can be detected using Josephson tunneling. A natural candidate for this physics are the iron based superconductors, as will be described in the two following talks [1].

[1]P. Coleman, Y. Komijani, E. Konig, arXiv :1910.03168   

Title: The Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals: II Mean-field theory

Triplet resonating valence bond (tRVB) states are entangled states that are produced in anisotropic magnetic environments [1], just like how singlet RVB states arise in frustated antiferromagnetic systems. A single Iron atom in a cubic environment contains miniature triplet states resonating between various t2g orbitals of the d-shell due to the large Hund's coupling. I will discuss how this can be used to derive a local inter-orbital triplet pairing applicable to Iron-based superconductors [2]. While the order parameter contains significant inter-band pairing, the projection on the Fermi surface appears as an odd-parity intra-band triplet pairing which enjoys a weak-coupling instability and gaps out the entire Fermi surface. In analogy with the RVB theory, a Gutzwiller projected variational mean-field is suggested for the ground state. Furthermore, we augment our mean-field theory using a Kotliar-Liu slave-boson approach to include the effect of intra- and inter-orbital interactions. Experimental signatures of the proposed triplet superconductor are discussed in the next talk.

[1] B. Shen, et al, arXiv:1907.10470.
[2] P. Coleman, Y. Komijani, E. Koenig, arXiv:1910.03168.   

The Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals: III Phenomenology in iron based superconductors.

Based on the triplet Resonating Valence Bond concept introduced in the previous two talks, I will discuss the prospects and signatures of this theory in the context of iron based superconductors. I will explicitly concentrate on the spin-triplet, orbital antisymmetric pairing state as derived in part II and on four experimental techniques of fundamental interest: (1) nuclear magnetic resonance, (2) neutron scattering, (3) tunneling spectroscopy, (4) scanning Josephson tunneling microscopy. First, I will demonstrate that this pairing state develops an anisotropic, partial suppression of the Knight shift and discuss existing experimental data on single crystals. Second and third, I will demonstrate that the relative sign between triplet d-vectors of electron and hole pockets crucially affects finite frequency spin-susceptibility and local density of states. I will discuss the consequences thereof for key experimental observables, i.e. a sharp subgap spin-resonance and characteristic quasi-particle interference patterns, that previously were interpreted as evidence for s_+- pairing. Finally, I describe experimental signatures of the staggered order parameter in scanning Josephson microscopy.   

Unconventional superconductivity and Hund's induced electron correlations: a Cooperative mechanism

The phenomenology of iron-based superconductors shows that the normal state is a bad metal characterized by orbital-selective correlations induced by the Hund's exchange coupling, suggesting an important role of the electron-electron interactions. On the other hand theories based on the exchange of bosons (e.g. spin fluctuations) describe correctly a variety of phenomena pointing towardsa more standard pairing mechanism.
To overcome this dychotomy we study how a multiorbital superconducting pairing driven by a generic weak-copuling boson exchange is affected by the presence of correlations. The key novelty of the study is the inclusion of the dynamical properties that make a Hund's metal substantially different with respect to both a weakly interacting metal and to an ordinary correlated metal with a large effective mass renormalization. We unveil the crucial role of the redistribution of spectral weight of the Hund’s metal to promote superconductivity and to enhance the orbital-selective character of the gap functions.   

Hund-enhanced electronic compressibility in LiFeP, LiFeAs and NaFeAs tuned by chemical substitution

We study the electronic structure of LiFeP, LiFeAs and NaFeAs in their paramagnetic metallic phase including dynamical electronic correlations within a density functional theory + slave-spin mean-field framework. Our results show that the three compounds are next to the crossover between a normal and a Hund’s metal, where a region of enhanced electronic compressibility that may be relevant for superconductivity is present in this type of systems. While LiFeP and LiFeAs lie in the normal metallic regime, with LiFeAs in the vicinity of the crossover, NaFeAs is in the Hund’s metal regime, which explains the different behavior observed in these materials. Our findings correlate positively with the experimental trends for doping- and pressure-dependence of superconductivity in these compounds, as well as the predicted mass renormalizations and Sommerfeld coefficients.   

Modified pairing structure due to momentum-dependent correlations in iron-based superconductors

We discuss the influence of momentum-dependent correlation effects arising from particle-hole interactions on the superconducting gap structure of iron-based superconductors. Within the Eliashberg formalism, we obtain a modified linearized gap equation arising from the spin-fluctuation interaction in the weak-coupling regime which includes self-consistent renormalizations of quasiparticle weights. The modification of the particle-particle interaction vertex by particle-hole processes modifies the superconducting gap structure, i.e. momentum-dependent enhancement or suppression of gap amplitude compared to traditional spin-fluctuation pairing calculations. We obtain good agreement with experimentally observed anisotropic gap structures in LiFeAs, indicating that inclusion of non-local correlation effects in the existing weak-coupling theories can account for observed signatures of the correlated iron-based superconductors.   

Systematic derivation of ab initio effective Hamiltonians for iron-based superconductors

Iron-based superconductors have attracted much attentions since its discovery at 2008. Owing to huge amount of studies, more than a dozen iron-based superconductors including related compounds have been found. In this study, combining the first-principles calculations and accurate numerical methods for treating quantum lattice models [1], we systematically obtain and analyze first-principle effective Hamiltonians of more than 20 iron-based superconductor and the related compounds. We perform the band calculation using Quantum ESPRESSO [2], derive the ab initio effective Hamiltonians using RESPACK [3], and analyze the Hamiltonians using mVMC [4]. As a result, we show the materials dependence of the microscopic parameters/physical quantities, and their relations with the superconducting transition temperatures.

[1] M. Imada and T. Miyake, J. Phys. Soc. Jpn. 79, 112001 (2010)
[2] https://www.quantum-espresso.org
[3] https://sites.google.com/view/kazuma7k6r
[4] http://www.pasums.issp.u-tokyo.ac.jp/mvmc/en/   

Topological bands in Fe(Se,Te)

Bulk FeSe_0.45Te_0.55 has recently emerged as a promising candidate to host topological superconductivity on its surface, with experimental signatures for a Dirac surface state and Majorana bound states in vortex cores. However, ARPES measurements of the bulk band structure show essentially no k_z dispersion, in apparent contradiction with DFT predictions for the significant k_z dispersion that drives the band inversion.
We reconcile the observed lack of dispersion with the predicted band inversion using a tight binding model with strongly renormalized inter-layer hopping and reasonable values of spin-orbit coupling. We use symmetry arguments to identify a sharp signature of bulk band inversion in the photon energy dependence of the ARPES matrix elements. We test our prediction for the change in orbital character of the band using ARPES data with a wide range of photon energies covering several Brillouin zones along k_z. We thus provide direct evidence for the non-trivial topology of the bulk bands in Fe(Se,Te), where the band inversion occurs in a nearly flat band due to an interplay of strong correlations and topology.