Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit

Identifying s-wave pairing symmetry in single-layer FeSe from topologically trivial edge states

Determining the pairing symmetry of single-layer FeSe on SrTiO3 is the key to understanding the enhanced pairing mechanism. It also guides the search for superconductors with high transition temperatures. Despite considerable efforts, it remains controversial whether the symmetry is the sign-preserving s- or the sign-changing s±-wave. Here, we investigate the pairing symmetry of single-layer FeSe from a topological point of view. Using low-temperature scanning tunneling microscopy/spectroscopy, we systematically characterize the superconducting states at edges and corners of single-layer FeSe. The tunneling spectra collected at edges and corners show a full energy gap and a substantial dip, respectively, suggesting the absence of topologically non-trivial edge and corner modes. According to our theoretical calculations, these spectroscopic features can be considered as strong evidence for the sign-preserving s-wave pairing in single-layer FeSe.

Pair density wave state in a monolayer high-Tc iron-based superconductor

The pair density wave (PDW) is an extraordinary superconducting state in which Cooper pairs carry non-zero momentum^1,2. Evidence for the existence of intrinsic PDW order in high-temperature (high-T_c) cuprate superconductors^3,4 and kagome superconductors⁵ has emerged recently. However, the PDW order in iron-based high-T_c superconductors has not been observed experimentally. Here, using scanning tunnelling microscopy and spectroscopy, we report the discovery of the PDW state in monolayer iron-based high-T_c Fe(Te,Se) films grown on SrTiO₃(001) substrates. The PDW state with a period of λ ≈ 3.6a_Fe (a_Fe is the distance between neighbouring Fe atoms) is observed at the domain walls by the spatial electronic modulations of the local density of states, the superconducting gap and the π-phase shift boundaries of the PDW around the vortices of the intertwined charge density wave order. The discovery of the PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform to study the interplay between the correlated electronic states and unconventional Cooper pairing in high-T_c superconductors.

Direct Probing of a Large Spin-Orbit Coupling in the FeSe Superconducting Monolayer on STO

Spin-orbit coupling (SOC) is a fundamental physical interaction, which describes how the electrons' spin couples to their orbital motion. It is the source of a vast variety of fascinating phenomena in nanostructures. Although in most theoretical descriptions of high-temperature superconductivity SOC has been neglected, including this interaction can, in principle, revise the microscopic picture. Here by preforming energy-, momentum-, and spin-resolved spectroscopy experiments we demonstrate that while probing the dynamic charge response of the FeSe monolayer on strontium titanate, a prototype two-dimensional high-temperature superconductor using electrons, the scattering cross-section is spin dependent. We unravel the origin of the observed phenomenon and show that SOC in this two-dimensional superconductor is strong. We anticipate that such a strong SOC can have several consequences on the electronic structures and may compete with other pairing scenarios and be crucial for the mechanism of superconductivity.

Topological transition and Majorana zero modes in 2D non-Hermitian chiral superconductor with anisotropy

We study a non-Hermitian chiral topological superconductor system on two dimensional square lattice, from which we obtained a rich topological phase diagram and established an exact relationship between topological charge flow of exceptional points in generalized Brillouin zone and change of topological properties. Its rich topological phase diagram is the result of competition between anisotropy and non-Hermitian effect. This system belongs to class D according to AZ classification of non-Hermitian systems. Each topological phase can be characterized by a 2DZnumber, which indicates the number of chiral edge modes, and two 1DZ₂numbers, which indicate the existence of zero modes at edge dislocations.

Phase-Manipulation-Induced Majorana Mode and Braiding Realization in Iron-Based Superconductor Fe(Te,Se)

A recent experiment reported the evidence of dispersing one-dimensional Majorana mode trapped by the crystalline domain walls in FeSe_{0.45}Te_{0.55}. Here, we perform the first-principles calculations to show that iron atoms in the domain wall spontaneously form the ferromagnetic order in line with orientation of the wall. The ferromagnetism can impose a π phase difference between the domain-wall-separated surface superconducting regimes under the appropriate width and magnetization of the wall. Accordingly, the topological surface superconducting state of FeSe_{0.45}Te_{0.55} can give rise to one-dimensional Majorana modes trapped by the wall. More interestingly, we further propose a surface junction in the form of FeSe_{0.45}Te_{0.55}-ferromagnet-FeSe_{0.45}Te_{0.55}, which can be adopted to create and fuse the Majorana zero modes through controlling the width or magnetization of the interior ferromagnetic barrier. The braiding and readout of Majorana zero modes can be realized by the designed device. Such surface junction has the potential application in the superconducting topological quantum computation.

Coexistence of Superconductivity and Nontrivial Band Topology in Monolayered Cobalt Pnictides on SrTiO3

As an intrinsically layered material, FeSe has been extensively explored for potentially revealing the underlying mechanisms of high transition temperature (high-T_c) superconductivity and realizing topological superconductivity and Majorana zero modes. Here we use first-principles approaches to identify that the cobalt pnictides of CoX (X = As, Sb, Bi), none of which is a layered material in bulk form. Nevertheless, all can be stabilized as monolayered systems either in freestanding form or supported on the SrTiO₃(001) substrate. We further show that each of the cobalt pnictides may potentially harbor high-T_c superconductivity beyond the Cu- and Fe-based superconducting families, and the underlying mechanism is inherently tied to their isovalency nature with the FeSe monolayer. Most strikingly, each of the monolayered CoX's on SrTiO₃ is shown to be topologically nontrivial, and our findings provide promising new platforms for realizing topological superconductors in the two-dimensional limit.

Superconductivity and nucleation from fractal anisotropy and product-like fractal measure

Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on the position of the electrons. Several physical quantities were found to be position-dependent comparable with those arising in heavy doping and p–n junction. At the boundary of the superconductor, a shrinkage of the magnetic field was observed, leading to a scenario equivalent to the Meissner–Ochsenfeld effect. An enhancement of the London penetration depth is revealed and such an improvement was observed in pnictides at the onset of commensurate spin-density-wave order inside the superconducting phase at zero temperature. The Bardeen–Cooper–Schrieffer theory was also analysed and the appearance of zero-energy states is detected. Nucleation of superconductivity in a bulk was also studied. The system acts as a quantum damped harmonic oscillator and our analysis showed that type-I superconductivity occurs when κ < 2 / ( 1 + α ) , whereas type II occurs for κ > 2 / ( 1 + α ) , where κ is the Ginzburg–Landau parameter. The transition at the passage from the ‘genuine’ to the ‘intermediate’ type-I estimates 0.767767 < α ≤ 1 .

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

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.