Orbital Selectivity Enhanced by Nematic Order in FeSe

Review of Single Crystal Synthesis of 11 Iron-Based Superconductors

The 11 system in the iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity, due to their simple structure and rich physical properties. Many exotic properties, such as multiband electronic structure, electronic nematicity, topology and antiferromagnetic order, provide strong support for the theory of high-temperature superconductivity, and have been at the forefront of condensed matter physics in the past decade. One noteworthy aspect is that a high upper critical magnetic field, large critical current density and lower toxicity give the 11 system good application prospects. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe_1-xTe_x, FeSe_1-xS_x and FeTe_1-xS_x. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique. High-quality single crystals serve as invaluable tools for advancing both the theoretical understanding and practical utilization of high-temperature superconductivity.

Is the Orbital-Selective Mott Phase Stable against Interorbital Hopping?

The localization-delocalization transition is at the heart of strong correlation physics. Recently, there is great interest in multiorbital systems where this transition can be restricted to certain orbitals, leading to an orbital-selective Mott phase (OSMP). Theoretically, the OSMP is widely studied for kinetically decoupled orbitals, but the effect of interorbital hopping remains unclear. Here, we show how nonlocal interorbital hopping leads to local hybridization in single-site dynamical mean-field theory (DMFT). Under fairly general circumstances, this implies that, at zero temperature, the OSMP, involving the Mott-insulating state of one orbital, is unstable against interorbital hopping to a different, metallic orbital. We further show that the coherence scale below which all electrons are itinerant is very small and gets exponentially suppressed even if the interorbital hopping is not overly small. Within this framework, the OSMP with interorbital hopping may thus reach down to extremely low temperatures T, but not to T=0. Accordingly, it is part of a coherence-incoherence crossover and not a quantum critical point. We present analytical arguments supported by numerical results using the numerical renormalization group as a DMFT impurity solver. We also compare our findings with previous slave-spin studies.

Pressure induced superconductivity in MnSe

The rich phenomena in the FeSe and related compounds have attracted great interests as it provides fertile material to gain further insight into the mechanism of high temperature superconductivity. A natural follow-up work was to look into the possibility of superconductivity in MnSe. We demonstrated in this work that high pressure can effectively suppress the complex magnetic characters of MnSe, and induce superconductivity with T_c ~ 5 K at pressure ~12 GPa confirmed by both magnetic and resistive measurements. The highest T_c is ~ 9 K (magnetic result) at ~35 GPa. Our observations suggest the observed superconductivity may closely relate to the pressure-induced structural change. However, the interface between the metallic and insulating boundaries may also play an important role to the pressure induced superconductivity in MnSe.

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.

Observation of an electronic order along [110] direction in FeSe

Multiple ordered states have been observed in unconventional superconductors. Here, we apply scanning tunneling microscopy to probe the intrinsic ordered states in FeSe, the structurally simplest iron-based superconductor. Besides the well-known nematic order along [100] direction, we observe a checkerboard charge order in the iron lattice, which we name a [110] electronic order in FeSe. The [110] electronic order is robust at 77 K, accompanied with the rather weak [100] nematic order. At 4.5 K, The [100] nematic order is enhanced, while the [110] electronic order forms domains with reduced correlation length. In addition, the collective [110] order is gaped around [−40, 40] meV at 4.5 K. The observation of this exotic electronic order may shed new light on the origin of the ordered states in FeSe.

Understanding the relation of different electronic orders in high temperature superconductors is of fundamental interest. Here, the authors observe a checkerboard charge order along [110] direction of FeSe.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Magnetotransport studies of Fe vacancy-ordered Fe4+δSe5 nanowires

We studied the electrical transport of Fe4+δSe5 single-crystal nanowires exhibiting √5 × √5 Fe-vacancy order and mixed valence of Fe. Fe4+δSe5 compound has been identified as the parent phase of FeSe superconductor. A first-order metal-insulator (MI) transition of transition temperature T MI ∼ 28 K is observed at zero magnetic fields (B). Colossal positive magnetoresistance emerges, resulting from the magnetic field-dependent MI transition. T MI demonstrates anisotropic magnetic field dependence with the preferred orientation along the c axis. At temperature T < ∼17 K, the state of near-magnetic field-independent resistance, which is due to spin polarized even at zero fields, preserves under magnetic fields up to B = 9 T. The Arrhenius law shift of the transition on the source-drain frequency dependence reveals that it is a nonoxide compound with the Verwey-like electronic correlation. The observation of the magnetic field-independent magnetoresistance at low temperature suggests it is in a charge-ordered state below T ∼ 17 K. The results of the field orientation measurements indicate that the spin-orbital coupling is crucial in √5 × √5 Fe vacancy-ordered Fe4+δSe5 at low temperatures. Our findings provide valuable information to better understand the orbital nature and the interplay between the MI transition and superconductivity in FeSe-based materials.

Local orbital degeneracy lifting as a precursor to an orbital-selective Peierls transition

Fundamental electronic principles underlying all transition metal compounds are the symmetry and filling of the d-electron orbitals and the influence of this filling on structural configurations and responses. Here we use a sensitive local structural technique, x-ray atomic pair distribution function analysis, to reveal the presence of fluctuating local-structural distortions at high temperature in one such compound, CuIr₂S₄. We show that this hitherto overlooked fluctuating symmetry-lowering is electronic in origin and will modify the energy-level spectrum and electronic and magnetic properties. The explanation is a local, fluctuating, orbital-degeneracy-lifted state. The natural extension of our result would be that this phenomenon is likely to be widespread amongst diverse classes of partially filled nominally degenerate d-electron systems, with potentially broad implications for our understanding of their properties.

A common feature of many transition metal materials is global symmetry breaking at low temperatures. Here the authors show that such materials are characterized by fluctuating symmetry-lowering distortions that exist pre-formed in higher temperature phases with greater average symmetry.

Anisotropic spin fluctuations in detwinned FeSe

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

Imaging orbital-selective quasiparticles in the Hund's metal state of FeSe

Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Z_m of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Z_m appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that [Formula: see text], consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.