S-wave Superconductor Research Articles

Anisotropic vortex core in the nematic state in electron-doped iron-pnictide superconductors

We investigated the vortex states in the electron-doped BaFe1.8Co0.2As2 using Bogoliubov-de Gennes equations, based on a phenomenological model with competing nematic order and extended s-wave superconductivity. Specifically, we considered the spin-driven nematic order for the optimally doped compound. Our findings suggest that there are no Andreev bound states at the Fermi energy in the nematic phase, and the local density of states exhibits a double-peak structure, consistent with scanning tunneling microscopy experiments. Moreover, we propose an elliptic vortex structure in the local density of states map, which we attribute to the presence of the nematic order.

Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors

Spin chains proximitized by s-wave superconductors are predicted to enter a mini-gapped phase with topologically protected Majorana modes (MMs) localized at their ends. However, the presence of non-topological end states mimicking MM properties can hinder their unambiguous observation. Here, we report on a direct method to exclude the non-local nature of end states via scanning tunneling spectroscopy by introducing a locally perturbing defect on one of the chain’s ends. We apply this method to particular end states observed in antiferromagnetic spin chains within a large minigap, thereby proving their topologically trivial character. A minimal model shows that, while wide trivial minigaps hosting end states are easily achieved in antiferromagnetic spin chains, unrealistically large spin-orbit coupling is required to drive the system into a topologically gapped phase with MMs. The methodology of perturbing candidate topological edge modes in future experiments is a powerful tool to probe their stability against local disorder.

Multi-band analysis on physical properties of superconducting FeSe films

The origins of superconductivity and pairing symmetry of order parameters are still controversial problems for FeSe thin films up to date. Under the Neumann boundary conditions, the electromagnetic properties of this system are investigated using the two-band Ginzburg–Landau theory. We calculate the temperature dependence of upper critical field in arbitrary direction and critical supercurrent density through the FeSe film. It is revealed that the normalized upper critical field is independent of the film thickness and all of our theoretical results are in accordance with the experimental data. These thus strongly indicate the existence of two-gap s-wave superconductivity in this material.

Thermal transport in multiple Majorana edge states of hybrid topological superconductor junctions

The hybrid topological superconductor (TSC) with multiple Majorana edge states can be formed in a system where a magnetic topological insulator (MTI) thin film is coupled with two s-wave superconductors in proximity. The band structure and thermal transport properties of the hybrid TSC hosting chiral and helical Majorana edge states are investigated. By using the nonequilibrium Green’s function method combined with the Landauer–Büttiker formula, the scattering coefficients (i.e., the normal tunneling T, the local Andreev reflection TLAR, the crossed Andreev reflection TCAR) and two-terminal electric thermal conductance κe are calculated. With the change of the exchange field Mz, the system goes through a series of topological phase transitions. The chiral Majorana edge states, the helical Majorana edge states and the multiple Majorana edge states possessing both chiral and helical edge modes are induced at the boundary of TSC. At the boundary of the central TSC, a single Majorana fermion edge state is equivalent to half an ordinary fermion to carry heat, leading to the generation of a half-integer quantized thermal conductance plateau. Thus, half-integer (i.e., 1/2, 3/2) and integer (i.e., 1, 2) quantized thermal conductance plateaus appear in different topological phases. These quantized plateaus that survive well over a certain range of temperatures can be used experimentally to detect chiral and helical Majorana fermions.

Conventional s-wave superconductivity in the non-centrosymmetric compounds Re3W, Re3W0.5Nb0.5, and Re3W0.5Ta0.5

We carried out an investigation of the structural and superconducting properties of Re3W1−xMx alloys, which can crystallize in both a centrosymmetric (CS) hexagonal, and a non-centrosymmetric (NCS) cubic α-Mn phase. The superconducting transition temperatures (Tc) of the CS and NCS phases in pure Re3W are ∼ 9.1 and ∼ 7.7 K, respectively. While boules fast cooled from the melt have a mixture of CS phases, the NCS phase can be stabilized upon annealing at very high temperatures (∼ 1700 °C), or upon the partial substitution of the transition metals M = Ta, or Nb for W. X-ray diffraction and wavelength dispersive X-ray spectroscopy (WDS) data suggest that the optimal composition for the formation of the α-Mn phase directly from the melt in Re3W1−xMx is x ≈ 0.5. A detailed study of the superconducting properties of the Re3W1−xMx solid solutions was carried out by means of measurement of magnetization, ac magnetic susceptibility, electrical transport, and low temperature specific heat. As the M content is increased, the superconducting critical temperature Tc progressively decreases, though the overall superconducting properties remain similar to those of the parent NCS Re3W compound. The partial substitution at the W site does not seem to affect the pairing mechanism. Given the exponentially vanishing character of the electronic specific heat Ce(T) at low temperatures, the superconducting behavior of the NCS alloys is consistent with a nodeless, s-wave superconducting gap symmetry in all NCS samples. These findings add the pseudo-binary Re-M-W systems to the small roll of NCS materials where the pairing symmetry of the superconducting state can be explored.

The mixed-state entanglement in holographic p-wave superconductor model

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

Search for large topological gaps in atomic spin chains on proximitized superconducting heavy-metal layers

One-dimensional systems comprising s-wave superconductivity with meticulously tuned magnetism realize topological superconductors hosting Majorana modes whose stability is determined by the gap size. However, for atomic spin chains on superconductors, the effect of the substrate’s spin-orbit coupling on the topological gap is largely unexplored. Here, we introduce an atomic layer of the heavy metal gold on a niobium surface combining strong spin-orbit coupling and a large superconducting gap with a high crystallographic quality, enabling the assembly of defect-free iron chains using a scanning tunneling microscope tip. Scanning tunneling spectroscopy experiments and density functional theory calculations reveal ungapped Yu–Shiba–Rusinov bands in the ferromagnetic chain despite the heavy substrate. By artificially imposing a spin spiral state, the calculations indicate minigap opening and zero-energy edge state formation. The methodology enables a material screening of heavy-metal layers on elemental superconductors for ideal systems hosting Majorana edge modes protected by large topological gaps.

Surface structure and multigap superconductivity of V3Si (111) revealed by scanning tunneling microscopy

V3Si, a classical silicide superconductor with relatively high T_{mathrm{C}} (∼16 K), is promising for constructing silicon-based superconducting devices and hetero-structures. However, real space characterization on its surfaces and superconducting properties are still limited. Here we report the first low-temperature scanning tunnelling microscopy (STM) study on cleaned V3Si (111) single crystal surface. We observed a sqrt{3} times sqrt{3} superstructure which displays mirror symmetry between adjacent terraces, indicating the surface is V-terminated and reconstructed. The tunneling spectrum shows full superconducting gap with double pairs of coherence peaks, but has a relatively small gap size with comparing to bulk T_{mathrm{C}}. Impurity induced in-gap state is absent on surface defects but present on introduced magnetic adatoms. Upon applying magnetic field, a hexagonal vortex lattice is visualized. Interestingly, the vortex size is found to be field dependent, and the coherence length measured from single vortex at low field is significantly larger than estimated value from bulk H_{c2}. These results reflect V3Si is a multi-band, s-wave superconductor.

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi2 Te3 Interface.

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe0.55 Se0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. Here superconductivity is reported in monolayer (ML) FeTe1-y Sey (Fe(Te,Se)) grown on Bi2 Te3 by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi2 Te3 heterostructures. For y= 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi2 Te3 TIS and the desired spin-momentum locking is not observed. In contrast, for y= 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi2 Te3 system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

Bandwidth-controlled quantum phase transition between an easy-plane quantum spin Hall state and an s -wave superconductor

The quantum spin Hall state can be understood in terms of spontaneous O(3) symmetry breaking. Topological skyrmion configurations of the O(3) order parameter vector carry a charge 2e, and as shown previously, when they condense, a superconducting state is generated. We show that this topological route to superconductivity survives easy-plane anisotropy. Upon reducing the O(3) symmetry to O(2)$\times$ Z$_2$, skyrmions give way to merons that carry a unit charge. On the basis of large-scale auxiliary field quantum Monte Carlo simulations, we show that at the particle-hole symmetric point, we can trigger a continuous and direct transition between the quantum spin Hall state and s-wave superconductor by condensing pairs of merons. This statement is valid in both strong and weak anisotropy limits. Our results can be interpreted in terms of an easy-plane deconfined quantum critical point. However, in contrast to the previous studies in quantum spin models, our realization of this quantum critical point conserves $U(1)$ charge, such that skyrmions are conserved.

Induced superconductivity in the two-dimensional topological insulator phase of cadmium arsenide

Hybrid structures between conventional, s-wave superconductors, and two-dimensional topological insulators (2D TIs) are a promising route to topological superconductivity. Here, we investigate planar Josephson junctions fabricated from hybrid structures that use thin films of cadmium arsenide (Cd3As2) as the 2D TI material. Measurements of superconducting interference patterns in a perpendicular magnetic field are used to extract information about the spatial distribution of the supercurrent. We show that the interference patterns are distinctly different in junctions with and without mesa-isolation. In mesa-defined junctions, the bulk of the 2D TI appears to be almost completely shunted by supercurrent flowing along the edges, whereas the supercurrent is much more uniform across the junction when the Cd3As2 film extends beyond the device. We discuss the possible origins of the observed behaviors.

Multi-Band Analysis on Physical Properties of the Quasi-Two-Dimensional Superconductor NbSe2

The discovery of quasi-two-dimensional superconductors bears consequences for both basic research and practical applications. However, the mechanism of superconductivity and the form of order parameters are still controversial problems for the transition metal dichalcogenide NbSe2 thin film. Under the Neumann boundary condition, the physical properties of this compound are investigated within the two-component Ginzburg–Landau theory. We compute the upper critical field in an arbitrary direction and the temperature dependence of critical supercurrent density through this layered system. All of our theoretical calculations fit the experimental measurements well; thus, this study strongly provides evidence of two-gap s-wave superconductivity in the NbSe2 thin film.

Holographic p-Wave Superconductor with Excited States in 4D Einstein–Gauss–Bonnet Gravity

We construct a holographic p-wave superconductor with excited states in the 4D Einstein–Gauss–Bonnet gravity using the Maxwell complex vector field model. In the probe limit, we observe that, the higher curvature correction or the higher excited state can hinder the vector condensate to be formed in the full parameter space, which is different from the holographic s-wave superconductor. Regardless of the choice of the vector mass by selecting the value of m2L2 or m2Leff2, we note that the critical chemical potential becomes evenly spaced for the number of nodes and that the difference of the critical chemical potential between the consecutive states depends on the curvature correction. Moreover, we find that the higher curvature correction or the higher excited state will alter the universal relation of the gap frequency, and the pole and delta function of the conductivity for the excited states can be broadened into the peaks with the finite width as the curvature correction increases.

Ginzburg–Landau Analysis on the Physical Properties of the Kagome Superconductor CsV3Sb5

The kagome lattice consisting of corner-sharing triangles has been studied in the context of quantum physics for more than seventy years. For the novel discovered kagome superconductor CsV3Sb5, identifying the pairing symmetry of order parameter remained an elusive problem until now. Based on the two-band Ginzburg–Landau theory, we study the temperature dependence of upper critical field and magnetic penetration depth for this compound. All theoretical results are consistent with the experimental data, which strongly indicates the existence of two-gap s-wave superconductivity in this system. In addition, it is worth noting that the anisotropy of effective masses in the band with large (or small) gap is about 70 (or 2.4). With the calculation of the Kadowaki–Woods ratio as 0.58×10−5μΩ cm mol2 K2 mJ−2, the semi-heavy-fermion feature is suggested in the compound CsV3Sb5.

Flow equation and fermion gap in the holographic superconductors

We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.

Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors

Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this work, we show that the existence of sublattice degrees of freedom can enrich the tunability of bound states on the boundary and hence lift the constraint on their locations. We take the Kane-Mele model with honeycomb-lattice structure to illustrate the underlying physics. With the introduction of an in-plane exchange field to the model, we find that the boundary Dirac mass induced by the exchange field has a sensitive dependence on the boundary sublattice termination. We find that the sensitive sublattice dependence can lead bound states to emerge at a specific type of boundary defects named as sublattice domain walls if the exchange field is of ferromagnetic nature, even in the absence of any sharp corner on the boundary. Remarkably, this sensitive dependence of the boundary Dirac mass on the boundary sublattice termination allows the positions of bound states to be manipulated to any place on the boundary for an appropriately-designed sample. With a further introduction of conventional s-wave superconductivity to the model, we find that, no matter whether the exchange field is ferromagnetic, antiferromagnetic, or ferrimagnetic, highly controllable Majorana zero modes can be achieved at the sublattice domain walls. Our work reshapes the understanding of boundary physics in second-order topological phases, and meanwhile opens potential avenues to realize highly controllable bound states for potential applications.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

Antiferromagnetism-driven two-dimensional topological nodal-point superconductivity

Magnet/superconductor hybrids (MSHs) hold the promise to host emergent topological superconducting phases. Both one-dimensional (1D) and two-dimensional (2D) magnetic systems in proximity to s-wave superconductors have shown evidence of gapped topological superconductivity with zero-energy end states and chiral edge modes. Recently, it was proposed that the bulk transition-metal dichalcogenide 4Hb-TaS2 is a gapless topological nodal-point superconductor (TNPSC). However, there has been no experimental realization of a TNPSC in a MSH system yet. Here we present the discovery of TNPSC in antiferromagnetic (AFM) monolayers on top of an s-wave superconductor. Our calculations show that the topological phase is driven by the AFM order, resulting in the emergence of a gapless time-reversal invariant topological superconducting state. Using low-temperature scanning tunneling microscopy we observe a low-energy edge mode, which separates the topological phase from the trivial one, at the boundaries of antiferromagnetic islands. As predicted by the calculations, we find that the relative spectral weight of the edge mode depends on the edge’s atomic configuration. Our results establish the combination of antiferromagnetism and superconductivity as a novel route to design 2D topological quantum phases.

Majorana zero modes in a double-stranded DNA with s-wave superconductor

We propose a setup consisting of a double-stranded DNA (dsDNA) with s-wave superconductor which can be used to investigate the topological properties. Based on the transport calculations, we find that Majorana zero modes (MZMs) can be formed at the end of dsDNA with a Zeeman field paralleling to the helix direction. A novel nontrivial topological phase can be induced by a gate field. The MZMs in the topological superconducting dsDNA are stable when the weak Anderson disorder is considered. With the assistance of Green's function method, we calculated the differential conductance through the dsDNA with MZMs and proposed an effective method for probing MZM in dsDNA.

Influence of magnetic field on the transport properties of ferromganet/ferromagnet/s-wave superconductor junctions formed on the surface of a three-dimension topological insulator

We study the influence of magnetic field on the transport properties of ferromagnetic metal (FM)/ferromagnetic insulator (FI)/s-wave superconductor (s-wave SC) junctions and FM/FM/s-wave SC junctions formed on the surfaces of three dimensional topological insulators (3DTI), where the magnetic field is applied perpendicular to the s-wave SC surfaces. For a broad range of the magnetic field strength, the conductance is investigated. Unlike the preceding studies, we apply the magnetic field to the superconductor surfaces of the junctions instead of the magnetization induced by the ferromagnets adjacent to their surfaces. We determine the dependence of conductance on the magnetic field for the cases of parallel and antiparallel magnetizations and reveal that the magnetoresistance sensitively depends on the magnitude of the magnetic field for the biases below the renormalized gap. The results obtained in this work will find applications in superconductor spintronics.