Magnetic impurity chains on top of conventional superconductors are promising platforms to realize Majorana modes. Iron-based high-temperature superconductors are known in the vicinity of magnetic states due to the strong Hund's coupling in iron atoms. Here we propose that the line defects with missing Te/Se anions in Fe(Se,Te) superconductors provide the realization of intrinsic antiferromagnetic(AFM) chains with Rashba spin-orbit coupling. Against conventional wisdom, Majorana zero modes (MZMs) can be robustly generated at these AFM chain ends. These results can consistently explain the recent experimental observation of zero-energy end states in line defects of monolayer Fe(Te,Se)/SrTiO$_3$ by scanning tunneling microscopy (STM) measurements. Our research not only demonstrates an unprecedented interplay among native line defect, emergent magnetism and topological superconductivity but also explores a high-temperature platform for Majorana fermions.
Helical Majorana edge states at the 2D boundaries of 3D topological superconductors can be gapped by a surface Zeeman field. Here we study the effect nested defects imprinted on the Zeeman field can have on the edge states. We demonstrate that depending on the configuration of the field we can induce dimensional reduction of gapless Majorana modes from 2D to 1D or quasi-0D at magnetic domain walls. We determine the nature of the Majorana localisation on these defects as a function of the magnitude and configuration of the Zeeman field. Finally, we observe a generalisation of the index theorem …
Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$…
According to Ginzburg-Landau theory, it has been generally accepted that the diamagnetic property decreases after the lower critical field. However, we found that (Fe, Ti) particle doped MgB2 specimens reveal the Delta H = Delta B section in the magnetization curves, which are not following the theory. We present whether this phenomenon appears to be only confined to (Fe, Ti) particle doped Magnesium diborid superconductor, whether there is a theoretical basis and why it does not appear in other superconductors. We have understood that the cause of the Delta H = Delta B section is the pinning …
Majorana zero-energy bound states (ZEBSs) have been proposed to exist at the ends of one-dimensional Rashba nanowires proximity-coupled to an s-wave superconductor in an external magnetic field induced Zeeman field. Such hybrid structures have been a central platform in the search for non-Abelian Majorana zero modes (MZMs) toward fault-tolerant topological quantum computing. Here we report the discovery of ZEBSs simultaneously appearing at each end of a one-dimensional atomic line defect in monolayer iron-based high-temperature superconductor FeTe0.5Se0.5 films grown on SrTiO3(001) substrates.…
Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$ cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an overdoped (Bi,Pb)$_2$Sr$_2$CuO$_{6+x}$ sample, we apply scanning tunneling microscopy to explore local properties of the charge order. The ordering wavevector is non-dispersive with energy, which can be confirmed and determined. By extracting its order-parameter field, we identify dislocations in the stripe structure of the electronic modulation, which correspond …
In recent years, there were a number of experimental developments and discoveries of novel superconducting materials which exhibit multicomponent, many-body degrees of freedom. These superconductors, that are described by several superconducting condensates, feature many new interesting phenomena that are absent in their single-component counterparts. Several of these new aspects of multicomponent superconductivity are addressed in this report.
Using Indium on Si(111) as an atomically thin superconductor platform, and by systematically controlling the density of nano-hole defects (nanometer size voids), we reveal the impacts of defects density and defects geometric arrangements on superconductivity at macroscopic and microscopic length scales. When nano-hole defects are uniformly dispersed in the atomic layer, the superfluid density monotonically decreases as a function of defect density (from 0.7% to 5% of the surface area) with minor change in the transition temperature Tc, measured both microscopically and macroscopically. With a …
Recently it was discovered that the non-uniform Meissner current flowing around the pinning sites in the type-II superconductor induces the unconventional vortex-antivortex pairs with the non-quantized magnetic flux [J.-Y. Ge, et al., Nat. Commun. 6, 6573 (2015)]. Here we provide the theory of this phenomenon showing that the vortex-like structures originate from the perturbation of the current streamlines by the non-superconducting defect, which results in the generation of the localized magnetic field. The position and the shape of such vortex dipoles are shown to be very sensitive to the de…
The symmetry of the pairing state in iron pnictide superconductor $\mathrm{Ba_{1-x}K_xFe_2As_2}$ is still controversial. At optimal doping ($x \approx 0.4$), it is very likely $s$-wave, but for $x=1$ there are experimental and theoretical arguments for both $s$-wave and $d$-wave. Depending on the choice for $x=1$, intermediate $s+is$ and $s+id$ states have been proposed for intermediate doping $ 0.4 < x < 1$. In both states, the time reversal symmetry is broken and a spontaneous magnetization is allowed. In this work we study a spontaneous magnetization induced by a nonmagnetic defect in the $…
The search for topological superconductors which support Majorana fermion excitations has been an important topic in condensed matter physics. In this work, we propose a new experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on top of a superconductor with Rashba spin-orbit coupling, topological superconducting phases can be achieved without fine-tuning the chemical potential. Moreover, superconductors with different Chern numbers can be obtained by changing the superlattice structure of the or…
The generalized time-dependent Ginzburg-Landau (GTDGL) theory was first proposed to describe better gap superconductors and the phenomenon of thermal phase-slips (PSs) in defect-free systems. However, there is a lack of information about studies involving PSs in mesoscopic superconductors with surface defects. Thus, in this work, we simulated samples with two co-linear surface defects consisting of a lower $T_c$ superconductor narrowing the sample in its central part. The non-linear GTDGL equations were solved self-consistently under variable applied currents and by considering both gapless an…
Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topological interface buried deep beneath the surface. Here, we propose an alternative approach to realize topological superconductivity without SPE. In a Pb(111) thin fil…
Microwave Conductivity due to Scattering from Extended Linear Defects in d-Wave Superconductors
最近的微波电导率测量的解孪晶，高纯度，稍微过掺杂的YBa $_{2}$ Cu $_{3}$ O $_{6.993}$晶体揭示了一个线性的温度依赖性和近Drude线的形状的温度之间的1和20 K和频率范围从1到75 GHz。先前的理论工作表明，d波超导体中点缺陷（杂质）散射的简单模型与这些结果不一致。因此，有人建议，散射扩展缺陷，如孪晶界残留物，从退孪过程中留下的，也可能是重要的。我们计算的自洽玻恩近似（包括顶点校正）的d-波超导体中存在的散射从扩展的线性缺陷的自能和微波电导率。我们发现，在实验相关的限制（$Ω, 1/τ\ll T \ll Δ_{0}$），由此产生的微波电导率有一个线性的温度依赖性和一个近Drude频率依赖性，符合实验。
We studied a qubit based on flux-pinning effects in $Δ$H=$Δ$B region of a superconductor. When volume defects are many enough in a superconductor, $Δ$H=$Δ$B region on M-H curve is formed, which is the region that increased applied magnetic field ($Δ$H) is the same as increasing magnetic induction ($Δ$B). Magnetization (M) is constant in the region by 4$π$M = B - H. Here we show that the behavior of fluxes in $Δ$H=$Δ$B region can be a candidate of qubit. Pinned fluxes on volume defects would move as a bundle in the region by repeating flux-pinning and pick-out depinning process from the surface…
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topol…
Whereas there are two critical fields that are H$_{c1}$ and H$_{c2}$ in the ideal type II superconductor, there is another critical field H$_{c1}'$ defined as the field showing the maximum diamagnetic property in the real type II superconductor. We would present that H$_{c1}'$ is able to be proved theoretically and experimentally. We have derived an equation based on flux-pinning effect of volume defects. MgB$_2$ bulks which were synthesized by Mg and B are similar to this model. The number of quantum fluxes pinned at a defect of radius r, a pinning penetration depth, magnetic flux penetration…
We study the zero-temperature transport properties of one-dimensional normal-superconductor (NS) junctions with topological superconductors across their topological transitions. Working within the Blonder-Tinkham-Klapwijk (BTK) formalism generalized for topological NS junctions, we analytically calculate the differential conductance for tunneling into two models of a topological superconductor: a spinless intrinsic $p$-wave superconductor and a spin-orbit-coupled $s$-wave superconductor in a Zeeman field. In both cases we verify that the zero-bias conductance is robustly quantized at $2e^2/h$ …
We investigate the structure of quasiparticle states localized in a core of an Abrikosov vortex in a clean layered superconductor in the presence of planar defects. It is shown that even a highly transparent defect opens a minigap at the Fermi energy. Its magnitude, $E_g\simΔ\sqrt{R}$, exceeds the mean level spacing for the chiral branch, $ω_0\simΔ^2/E_F$, already for very small values of the reflection coefficient off the defect, $R\ll1$ ($Δ$ is the bulk gap). For $R\gtrsim\sqrt{Δ/E_F}$, formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in …
The electronic structure of a vortex pinned by an insulating columnar inclusion in a type-II chiral $p_x \pm i p_y$ superconductor is studied within the Bogolubov-de Gennes theory. The structure of the anomalous spectral branch is shown to be strongly affected by the mutual orientations of the angular momenta of the center of mass and the relative motion of the two electrons in the Cooper pair. Being only slightly perturbed by the scattering at the defect for the zero sum of these angular momenta the anomalous spectral branch appears to change dramatically in the absence of such compensation. …
Correlated electron systems, particularly iron-based superconductors, are extremely sensitive to strain, which inevitably occurs in the crystal growth process. Built-in strain of this type has been proposed as a possible explanation for experiments where nematic order has been observed at high temperatures corresponding to the nominally tetragonal phase of iron-based superconductors. Strain is assumed to produce linear defect structures, e.g. dislocations, which are quite similar to O vacancy chainlets in the underdoped cuprate superconductor YBCO. Here we investigate a simple microscopic mode…
Recently, Majorana Fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation (TQC). They are proposed to exist in various two-dimensional (2D) topological systems, such as px+ipy topological superconductor and nanowire-superconducting hybridization system. In this paper, two types of Majorana Fermions with different polygon sign rules are pointed out. A "smoking gun" numerical evidence to identify MF's classification is presented through looking for the signature of a first order topological quantum phase trans…
Observation of unconventional band topology in a superconducting doped topological insulator, Cux-Bi2Se3: Topological Superconductor or non-Abelian superconductor?
最近发现掺铜的拓扑绝缘体Bi $_2$ Se $_3$在冷却时经历超导转变，这提高了它是第一个已知的“拓扑超导体”或实现新的非阿贝尔超导状态的可能性。它的真正性质取决于关键的体和表面状态带拓扑结构。我们提出了第一个光电子能谱的结果，通过检查在许多不同的铜掺杂值的能带拓扑，我们发现，拓扑保护的自旋螺旋表面状态保持良好的保护和分离的费米能级，其中铜配对发生在最佳掺杂的拓扑绝缘体的体狄拉克带。铜的加入导致非线性电子掺杂和强重整化的拓扑表面态。这些极不寻常的观测结果强烈地表明，在Cu $_x$ Bi $_2$ Se $_3$的拓扑表面上的超导性不能是任何常规类型的一般拓扑理论。首次报道了三维体狄拉克能带结构的超导掺杂态和拓扑不变性质，这将有助于为这种新型超导体制定一个具体的理论。
Majorana zero modes are usually attributed to topological superconductors. We study a class of two-dimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.
One-dimensional systems proximity-coupled to a superconductor can be driven into a topological superconducting phase by an external magnetic field. Here, we investigate the effect of vortices created by the magnetic field in a type-II superconductor providing the proximity effect. We identify different ways in which the topological protection of Majorana modes can be compromised and discuss strategies to circumvent these detrimental effects. Our findings are also relevant to topological phases of proximitized quantum Hall edge states.
