State Of Iron-based Superconductors Research Articles

Dislocation Majorana bound states in iron-based superconductors

We show that lattice dislocations of topological iron-based superconductors such as FeTe1−xSex will intrinsically trap non-Abelian Majorana quasiparticles, in the absence of any external magnetic field. Our theory is motivated by the recent experimental observations of normal-state weak topology and surface magnetism that coexist with superconductivity in FeTe1−xSex, the combination of which naturally achieves an emergent second-order topological superconductivity in a two-dimensional subsystem spanned by screw or edge dislocations. This exemplifies a new embedded higher-order topological phase in class D, where Majorana zero modes appear around the “corners” of a low-dimensional embedded subsystem, instead of those of the full crystal. A nested domain wall theory is developed to understand the origin of these defect Majorana zero modes. When the surface magnetism is absent, we further find that s± pairing symmetry itself is capable of inducing a different type of class-DIII embedded higher-order topology with defect-bound Majorana Kramers pairs. We also provide detailed discussions on the real-world material candidates for our proposals, including FeTe1−xSex, LiFeAs, β-PdBi2, and heterostructures of bismuth, etc. Our work establishes lattice defects as a new venue to achieve high-temperature topological quantum information processing.

Correlation-corrected band topology and topological surface states in iron-based superconductors

Iron-based superconductors offer an ideal platform for studying topological superconductivity and Majorana fermions. In this paper, we carry out a comprehensive study of the band topology and topological surface states of a number of iron-based superconductors using a combination of density functional theory (DFT) and dynamical mean field theory. We find that the strong electronic correlation of Fe 3d electrons plays a crucial role in determining the band topology and topological surface states of iron-based superconductors. Electronic correlation not only strongly renormalizes the bandwidth of Fe 3d electrons, but also shifts the band positions of both Fe 3d and As/Se p electrons. As a result, electronic correlation moves the DFT-calculated topological surface states of many iron-based superconductors much closer to the Fermi level, which is crucial for realizing topological superconducting surface states and observing Majorana zero modes as well as achieving practical applications, such as quantum computation. More importantly, electronic correlation can change the band topology and make some iron-based superconductors topologically nontrivial with topological surface states whereas they have trivial band topology and no topological surface states in DFT calculations. Our paper demonstrates that it is important to take into account electronic correlation effects in order to accurately determine the band topology and topological surface states of iron-based superconductors and other strongly correlated materials.

Topological Superconductivity in an Extended s -Wave Superconductor and Its Implication to Iron-Based Superconductors

In the presence of both space and time reversal symmetries, an s-wave A1g superconducting state is usually topologically trivial. Here we demonstrate that an exception can take place in a type of nonsymmorphic lattice structures. We specify the demonstration in a system with a centrosymmetric space group P4/nmm, the symmetry group that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by 2Z degenerate Dirac cones on the (1,0) edge, and Z pairs of Majorana modes at the intersection between the (1,1) and (1,-1) edges. The topological invariance and Fermi surface criterion for the topological state are provided. Moreover, we point out that the previously proposed s-wave state in iron-based superconductors, which features a sign-changed superconducting order parameter between two electron pockets, is such a topological state. Thus, these results not only open a new route to pursue topological superconductivity, but also establish a measurable quantity to settle one long-lasting debate on the pairing nature of iron-based superconductors.

Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals

In the presence of certain symmetries, three-dimensional Dirac semimetals can harbor not only surface Fermi arcs, but also surface Dirac cones. Motivated by the experimental observation of rotation-symmetry-protected Dirac semimetal states in iron-based superconductors, we investigate the potential intrinsic topological phases in a $C_{4z}$-rotational invariant superconducting Dirac semimetal with $s_{\pm}$-wave pairing. When the normal state harbors only surface Fermi arcs on the side surfaces, we find that an interesting gapped superconducting state with a quartet of Bogoliubov-Dirac cones on each side surface can be realized, even though the first-order topology of its bulk is trivial. When the normal state simultaneously harbors surface Fermi arcs and surface Dirac cones, we find that a second-order time-reversal invariant topological superconductor with helical Majorana hinge states can be realized. The criteria for these two distinct topological phases have a simple geometric interpretation in terms of three characteristic surfaces in momentum space. By reducing the bulk material to a thin film normal to the axis of rotation symmetry, we further find that a two-dimensional first-order time-reversal invariant topological superconductor can be realized if the inversion symmetry is broken by applying a gate voltage. Our work reveals that diverse topological superconducting phases and types of Majorana modes can be realized in superconducting Dirac semimetals.

Unveiling non-Abelian statistics of vortex Majorana bound states in iron-based superconductors using fermionic modes

Motivated by the recent experiments that reported the discovery of vortex Majorana bound states (vMBSs) in iron-based superconductors, we establish a portable scheme to unveil the non-Abelian statistics of vMBSs using normal fermionic modes. The unique non-Abelian statistics of vMBSs is characterized by the charge flip signal of the fermions that can be easily read out through the charge sensing measurement. In particular, the charge flip signal will be significantly suppressed for strong hybridized vMBSs or trivial vortex modes, which efficiently identifies genuine vMBSs. To eliminate the error induced by the unnecessary dynamical evolution of the fermionic modes, we further propose a correction strategy by continually reversing the energy of the fermions, reminiscent of the quantum Zeno effect. Finally, we establish a feasible protocol to perform non-Abelian braiding operations on vMBSs.

NMR investigations toward understanding the variety of ground states in iron-based superconductors

We report NMR experiments on heavily electron-doped Fe-based superconductor in comparison with the results on the parent Fe-based compounds. The typical parent Fe-based compound LaFe(As1-x′P x′)O exhibits the re-emergent antiferromagnetic (AFM) order at x′ ~ 0.6 (AFM2) separated from the parent AFM order at x′ =0 (AFM1). Systematic 31P-NMR study on [Sr4Sc2O6]Fe2(As1−x P x )2 (SrSc42622), which has local lattice parameters of iron-pnictogen (FePn) layer similar to the series of LaFe(As1−x′/P x′)O, also revealed that the presence of AFM1 order is universal for most of parent Fe-based compounds. In contrast, the static AFM2 order was absent in this series, however, the dynamical low-energy AFM spin fluctuations are enhanced at around x ~ 0.8, indicating that the onset of the static AFM2 is quite sensitive to the local lattice parameters of FePn layer. In order to elucidate the further universality and diversity, we have carried out 77Se-NMR measurement on Li x (NH3)yFe2−δ Se2 (Tc = 44 K) in heavily electron-doped regime. Although the spin fluctuations at low energies does not significantly develops upon cooling, the moderate spin fluctuations were extracted at high temperatures from comparison of the temperature (T) dependences of Knight shift and nuclear relaxation rate (1/T 1 T). We discuss the universality and diversity of the relationship between the Tc and the characteristics of the spin fluctuations in the Fe-based compounds from a microscopic point of the NMR measurements.

Decisive proofs of the transition in the temperature dependence of the magnetic penetration depth

One of the features of the unconventional state in iron-based superconductors is possibility to transform to the s ++ state with the increase of the nonmagnetic disorder. Detection of such a transition would prove the existence of the state. Here we study the temperature dependence of the London magnetic penetration depth within the two-band model for the and s ++ superconductors. By solving Eliashberg equations accounting for the spin-fluctuation mediated pairing and nonmagnetic impurities in the T-matrix approximation, we have derived a set of specific signatures of the transition: (1) sharp change in the behavior of the penetration depth λ L as a function of the impurity scattering rate at low temperatures; (2) before the transition, the slope of increases as a function of temperature, and after the transition this value decreases; (3) the sharp jump in the inverse square of the penetration depth as a function of the impurity scattering rate, , at the transition; (4) change from the single-gap behavior in the vicinity of the transition to the two-gap behavior upon increase of the impurity scattering rate in the superfluid density ρ s (T).

The transport properties of iron-based superconductors

There are a variety of order states in iron-based pnictides, such as electronic nematic phase, spin density wave, and so on, which leads to plenty of novel physical phenomena. The measurements of transport properties can provide extremely useful information for understanding of the low-energy excitations of iron-based superconductors. Due to the multi-band electronic structure in iron-based pnictides, the temperature dependence of resistivity and Hall coefficient varies with different systems, however, there are no evidence for the pseudo-gap opening in the normal state which is a common feature in underdoped high-<inline-formula><tex-math id="M2">\begin{document}$T_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M2.png"/></alternatives></inline-formula> cuprates. In the hole-doped iron-based superconductors, the Hall coefficient changes its sign in low temperatures, and meanwhile the resistivity shows a broad hump in the same temperature range. Such a behavior is proposed as a crossover from incoherent to coherent transport. The Seebeck coefficients of iron-based superconductors also show remarkable differences from the cuprates. In iron-based superconductors, the absolute value of Seebeck coefficients in the normal state becomes the largest at the optimally doping point with highest <inline-formula><tex-math id="M3">\begin{document}$T_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M3.png"/></alternatives></inline-formula>, which is probably related to the strong inter-band scattering. The Nernst effect in the normal state of iron-based superconductors indicates that superconducting phase fluctuations is not obvious above <inline-formula><tex-math id="M4">\begin{document}$T_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201836_M4.png"/></alternatives></inline-formula>, which is also significantly different from the cuprates. These unusual thermoelectric properties observed in iron-based superconductors have not been observed in the nickel-based pnictide superconductors with the analogous structure, i.e., LaNiAsO, and the nickel-based superconductors behave more like a usual metal. All these results above illustrate that these unusual transport properties of iron-based superconductors are inherently associated with their high temperature superconductivity, and these factors should be taken into account in the theory on its superconducting mechanism.

Topological ultranodal pair states in iron-based superconductors

Bogoliubov Fermi surfaces are contours of zero-energy excitations that are protected in the superconducting state. Here we show that multiband superconductors with dominant spin singlet, intraband pairing of spin-1/2 electrons can undergo a transition to a state with Bogoliubov Fermi surfaces if spin-orbit coupling, interband pairing and time reversal symmetry breaking are also present. These latter effects may be small, but drive the transition to the topological state for appropriate nodal structure of the intra-band pair. Such a state should display nonzero zero-bias density of states and corresponding residual Sommerfeld coefficient as for a disordered nodal superconductor, but occurring even in the pure case. We present a model appropriate for iron-based superconductors where the topological transition associated with creation of a Bogoliubov Fermi surface can be studied. The model gives results that strongly resemble experiments on FeSe1−xSx across the nematic transition, where this ultranodal behavior may already have been observed.

Multiple topological states in iron-based superconductors

Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even though the principal combination of topological bands and superconductivity promises exotic unprecedented avenues of superconducting states and Majorana bound states (MBSs), the central building block for topological quantum computation. Along with progressing laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) towards high energy and momentum resolution, we have resolved topological insulator (TI) and topological Dirac semimetal (TDS) bands near the Fermi level ($E_{\text{F}}$) in the iron-based superconductors Li(Fe,Co)As and Fe(Te,Se), respectively. The TI and TDS bands can be individually tuned to locate close to $E_{\text{F}}$ by carrier doping, allowing to potentially access a plethora of different superconducting topological states in the same material. Our results reveal the generic coexistence of superconductivity and multiple topological states in iron-based superconductors, rendering these materials a promising platform for high-$T_{\text{c}}$ topological superconductivity.

Ultrafast destruction and recovery of the spin density wave order in iron-based pnictides: A multipulse optical study

We report on systematic excitation-density dependent all-optical femtosecond time resolved study of the spin-density wave state in iron-based superconductors. The destruction and recovery dynamics are measured by means of the standard and a multi-pulse pump-probe technique. The experimental data are analyzed and interpreted in the framework of an extended three temperature model. The analysis suggests that the optical-phonons energy-relaxation plays an important role in the recovery of almost exclusively electronically driven spin density wave order.

Stabilization of s -wave superconductivity through arsenic p -orbital hybridization in electron-doped BaFe2As2

Using random-phase approximation spin-fluctuation theory, we study the influence of the hybridization between iron $d$-orbitals and pnictide $p$-orbitals on the superconducting pairing state in iron-based superconductors. The calculations are performed for a 16-orbital Hubbard-Hund tight-binding model of BaFe$_2$As$_2$ that includes the As-$p$ orbital degrees of freedom in addition to the Fe-$d$ orbitals and compared to calculations for a 10-orbital Fe-$d$ only model. In both models we find a leading $s^\pm$ pairing state and a subleading $d_ {x^2-y^2}$-wave state in the parent compound. Upon doping, we find that the $s^\pm$ state remains the leading state in the 16-orbital model up to a doping level of 0.475 electrons per unit cell, at which the hole Fermi surface pockets at the zone center start to disappear. This is in contrast to the 10-orbital model, where the $d$-wave state becomes the leading state at a doping of less than 0.2 electrons. This improved stability of $s^\pm$ pairing is found to arise from a decrease of $d_{xy}$ orbital weight on the electron pockets due to hybridization with the As-$p$ orbitals and the resulting reduction of near $(\pi,\pi)$ spin-fluctuation scattering which favors the competing $d$-wave state. These results show that the orbital dependent hybridization of Fermi surface Bloch states with the usually neglected $p$-orbital states is an important ingredient in an improved itinerant pairing theory.

Nontrivial Role of Interlayer Cation States in Iron-Based Superconductors.

Unconventional superconductivity in iron pnictides and chalcogenides has been suggested to be controlled by the interplay of low-energy antiferromagnetic spin fluctuations and the particular topology of the Fermi surface in these materials. Based on this premise, one would also expect the large class of isostructural and isoelectronic iron germanide compounds to be good superconductors. As a matter of fact, they, however, superconduct at very low temperatures or not at all. In this work we establish that superconductivity in iron germanides is suppressed by strong ferromagnetic tendencies, which surprisingly do not originate from changes in bond angles or bond distances with respect to iron pnictides and chalcogenides, but are due to changes in the electronic structure in a wide range of energies happening upon substitution of atom species (As by Ge and the corresponding spacer cations). Our results indicate that superconductivity in iron-based materials may not always be fully understood based on d or d-p model Hamiltonians only.

Collective magnetic excitations of C4 -symmetric magnetic states in iron-based superconductors

We study the collective magnetic excitations of the recently discovered $C_{4}$ symmetric spin-density wave states of iron-based superconductors with particular emphasis on their orbital character based on an itinerant multiorbital approach. This is important since the $C_{4}$ symmetric spin-density wave states exist only at moderate interaction strengths where damping effects from a coupling to the continuum of particle-hole excitations strongly modifies the shape of the excitation spectra compared to predictions based on a local moment picture. We uncover a distinct orbital polarization inherent to magnetic excitations in $C_{4}$ symmetric states, which provide a route to identify the different commensurate magnetic states appearing in the continuously updated phase diagram of the iron-pnictide family.

Electronic vortex structure of Fe-based superconductors: Application to LiFeAs

Detailed tunneling spectroscopy of vortex core states can provide important insight to the momentum structure of the superconducting order parameter. We present a theoretical study of vortex bound states in iron-based superconductors by use of a realistic five-band model relevant to these systems, and superconductivity stabilized by spin-fluctuation generated pairing vertices yielding an $s\pm$ gap structure. The computed local density of states agrees remarkably well with both the bias dependence of the local conductance and the spatial structure of the low-bias conductance as obtained by scanning tunneling microscopy measurements on LiFeAs [T. Hanaguri et al., Phys. Rev. B 85, 214505 (2012)].

Properties of the zero-energy Andreev bound state in a two-sublattice SNS junction

We study properties of the zero energy Andreev bound state in a superconductor-normal metal-superconductor (SNS) junction consisting of two intrinsic degrees of freedom. The superconductors on either sides of the normal metal are assumed to have two sublattices with an intra-sublattice pairing with a phase equal to zero or π between the two sublattices. In addition, we add a uniform inter-sublattice pairing and study its effect on the local density of states (LDOS). In particular, we find that as the inter-sublattice pairing is turned on, the zero-bias peak (ZBP) is unstable (robust) when the phase difference across the sublattices is π (zero). We discuss the relevance of our results to the recently proposed odd-parity η pairing ground states in iron-based superconductors (FeSCs).

ChemInform Abstract: Antiferromagnetism and Its Origin in Iron‐Based Superconductors (Review Article)

AbstractReview: 129 refs.

Antiferromagnetism and its origin in iron-based superconductors (Review Article)

In iron-based superconductors, unravelling the origin of the antiferromagnetism is a crucial step towards understanding the high-Tc superconductivity as it is widely believed that the magnetic fluctuations play important roles in the formation of the Cooper pairs. Therefore, in this paper, we will briefly review experimental results related to the antiferromagnetic state in iron-based superconductors and focus on a review of the theoretical investigations which show applicability of the itinerant scenario to the observed antiferromagnetism and corresponding phase transitions in various families of the iron-based superconductors. A proposal of coupling between frustrated and unfrustrated bands for understanding the reduced magnetic moment typically observed in iron pnictides is also reviewed. While all the above theoretical investigations do not rule out a possible existence of localized electrons in iron-based superconductors, these results strongly indicate a close relation between itinerant electrons and the magnetically ordered state and point out the importance of taking into account the orbital degrees of freedom.

Iron-Based Superconductors as Odd-Parity Superconductors

Parity is a fundamental quantum number used to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd-parity s-wave spin-singlet pairing state in a single trilayer FeAs=Se, the building block of the materials. In a low-energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of an s-wave normal pairing between two sublattices and an s-wavepairing within the sublattices. The state has a fingerprint with a real-space sign inversion between the top and bottom As=Se layers. The results suggest that iron-based super- conductors are a new quantum state of matter, and the measurement of the odd parity can help to establish high-temperature superconducting mechanisms. DOI: 10.1103/PhysRevX.3.031004 Subject Areas: Condensed Matter Physics, Superconductivity Symmetry plays the central role in the search for beauty in physics. It controls the structure of matter and allows us to simplify a complicated problem. The gauge principle is a fundamental principle in physics. Models formulated in different gauge settings are equivalent. Symmetry and gauge principles together provide the foundations of mod- ern physics that allow us to solve complicated problems. The recently discovered iron-based high-temperature superconductors (high T c )( 1-3) are layered materials with complicated electronic structures. Their complexity causes a major difficulty in understanding pairing symme- try, which arguably is the most important property and clue to determine the pairing mechanism (4,5). In a strongly correlated electron system, major physics is determined locally in real space. Important properties, such as pairing symmetry in a superconducting state, are ex- pected to be robust against small variations of Fermi surfaces in reciprocal space. Although the superconducting mechanism related to high-temperature superconductors (high Tc) has not yet been determined, the robust d-wave pairing symmetry in cuprates (6) can be understood under this principle. Does this principle still hold for iron-based supercon- ductors? Namely, do all iron-based superconductors pos- sess one universal pairing state? Unlike cuprates, the answer to this question is highly controversial because different theoretical approaches have provided different answers and no universal state has been identified (5). Nevertheless, as local electronic structures in all families of iron-based superconductors are almost identical and phase diagrams are smooth against doping (4,5), it is hard to argue that the materials can approach many differ- ent superconducting ground states.

From d-wave to s-wave pairing in the iron-pnictide superconductor (Ba,K)Fe2As2

The nature of the pairing state in iron-based superconductors is the subject of much debate. Here we argue that in one material, the stoichiometric iron pnictide KFe2As2, there is overwhelming evidence for a d-wave pairing state, characterized by symmetry-imposed vertical line nodes in the superconducting gap. This evidence is reviewed, with a focus on thermal conductivity and the strong impact of impurity scattering on the critical temperature Tc. We then compare KFe2As2 to Ba0.6K0.4Fe2As2, obtained by Ba substitution, where the pairing symmetry is s-wave and the Tc is ten times higher. The transition from d-wave to s-wave within the same crystal structure provides a rare opportunity to investigate the connection between band structure and the pairing mechanism. We also compare KFe2As2 with the nodal iron-based superconductor LaFePO, for which the pairing symmetry is probably not d-wave, but more likely s-wave with accidental line nodes.