Two-dimensional Superconductors Research Articles

Proposal for Plasmon Spectroscopy of Fluctuations in Low-Dimensional Superconductors.

We propose to employ an optical spectroscopy technique to monitor the superconductivity and properties of superconductors in the fluctuating regime. This technique is operational close to the plasmon resonance frequency of the material, and it intimately connects with the superconducting fluctuations slightly above the critical temperature T_{c}. We find the Aslamazov-Larkin corrections to ac linear and dc nonlinear electric currents in a generic two-dimensional superconductor exposed to an external longitudinal electromagnetic field. First, we study the plasmon resonance of normal electrons near T_{c}, taking into account their interaction with superconducting fluctuations, and show that fluctuating Cooper pairs reveal a redshift of the plasmon dispersion and an additional mechanism of plasmon scattering, which surpasses both the electron-impurity and the Landau dampings. Second, we demonstrate the emergence of a drag effect of superconducting fluctuations by the external field resulting in considerable, experimentally measurable corrections to the electric current in the vicinity of the plasmon resonance.

Universal mechanical exfoliation of large-area 2D crystals

Two-dimensional materials provide extraordinary opportunities for exploring phenomena arising in atomically thin crystals. Beginning with the first isolation of graphene, mechanical exfoliation has been a key to provide high-quality two-dimensional materials, but despite improvements it is still limited in yield, lateral size and contamination. Here we introduce a contamination-free, one-step and universal Au-assisted mechanical exfoliation method and demonstrate its effectiveness by isolating 40 types of single-crystalline monolayers, including elemental two-dimensional crystals, metal-dichalcogenides, magnets and superconductors. Most of them are of millimeter-size and high-quality, as shown by transfer-free measurements of electron microscopy, photo spectroscopies and electrical transport. Large suspended two-dimensional crystals and heterojunctions were also prepared with high-yield. Enhanced adhesion between the crystals and the substrates enables such efficient exfoliation, for which we identify a gold-assisted exfoliation method that underpins a universal route for producing large-area monolayers and thus supports studies of fundamental properties and potential application of two-dimensional materials.

Superfluid Properties of Superconductors with Disorder at the Nanoscale: A Random Impedance Model

Some two-dimensional superconductors like, e.g., LaAlO 3 /SrTiO 3 heterostructures or thin films of transition metal dichalcogenides, display peculiar properties that can be understood in terms of electron inhomogeneity at the nanoscale. In this framework, unusual features of the metal-superconductor transition have been interpreted as due to percolative effects within a network of superconducting regions embedded in a metallic matrix. In this work we use a mean-field-like effective medium approach to investigate the superconducting phase below the critical temperature T c at which the resistivity vanishes. Specifically, we consider the finite frequency impedance of the system to extract the dissipative part of the conductance and the superfluid stiffness in the superconducting state. Intriguing effects arise from the metallic character of the embedding matrix: upon decreasing the temperature below T c proximity effects may rapidly increase the superfluid stiffness. Then, a rather fragile superconducting state, living on a filamentary network just below T c , can be substantially consolidated by additional superconducting regions induced by proximity effect in the interstitial metallic regions. This mean-field prediction should call for further theoretical analyses and trigger experimental investigations of the superconducting properties of the above systems.

Highly Stable Two-Dimensional Iron Monocarbide with Planar Hypercoordinate Moiety and Superior Li-Ion Storage Performance.

Stable planar hypercoordinate motifs have been recently demonstrated in two-dimensional (2D) confinement systems, while perfectly planar hypercoordinate motifs in 2D carbon-transition metal systems are rarely reported. Here, by using comprehensive ab initio computations, we discover two new iron monocarbide (FeC) binary sheets stabilized at 2D confined space, labeled as tetragonal-FeC (t-FeC) and orthorhombic-FeC (o-FeC), which are energetically more favorable compared with the previously reported square and honeycomb lattices. The proposed t-FeC is the global minimum configuration in the 2D space, and each carbon atom is four-coordinated with four ambient iron atoms, considered as the quasi-planar tetragonal lattice. Strikingly, the o-FeC monolayer is an orthorhombic phase with a perfectly planar pentacoordinate carbon moiety and a planar seven-coordinate iron moiety. These monolayers are the first example of a simultaneously pentacoordinate carbon and planar seven-coordinate Fe-containing material. State-of-the-art theoretical calculations confirm that all these monolayers have significantly dynamic, mechanical, and thermal stabilities. Among these two monolayers, the t-FeC monolayer shows a higher theoretical capacity (395 mAh g-1) and can stably adsorb Li up to t-FeCLi4 (1579 mAh g-1). The low migration energy barrier is predicted as small as 0.26 eV for Li, which results in the fast diffusion of Li atoms on this monolayer, making it a promising candidate for lithium-ion battery material.

Unconventional superconducting phases in multilayer films with layer-dependent Rashba spin-orbit interactions

We present resistivity measurements of bilayer and trilayer films with layer-dependent Rashba spin-orbit interactions. A sharp upturn is observed in the temperature dependence of the parallel upper critical field. We show that it corresponds to a transition from a complex-stripe phase to a helical phase. Moreover, we propose the phase diagram of a multilayer system, which is obtained from experimental observations with the support of numerical calculations. These results pave the way for the clarification of non-trivial superconducting states in multilayer systems composed of two-dimensional Rashba superconductors.

Quantum and classical ratchet motions of vortices in a two-dimensional trigonal superconductor

Dynamical behavior of vortices plays central roles in the quantum phenomena of two-dimensional (2D) superconductors. Quantum metallic state, for example, showing an anomalous temperature-independent resistive state down to low-temperatures, has been a common subject in recently developed 2D crystalline superconductors, whose microscopic origin is still under debate. Here, we unveil a new aspect of the vortex dynamics in a noncentrosymmetric 2D crystalline superconductor of MoS$_{2}$ through the nonreciprocal transport measurement. The second harmonic resistance $R^{2w}$ at low temperature with high current indicates the classical vortex flow accompanying the ratchet motion. Furthermore, we found that $R^{2w}$ is substantially suppressed in the quantum metallic state with low current region, allowing identification of the quantum and classical ratchet motions of vortices by the magnitude of the second harmonic generation. This suggests that nonreciprocal transport measurement can be a powerful tool to probe the vortex dynamics in noncentrosymmetric 2D superconductors.

Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants introduced by Benalcazar et al. We thus establish when a topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity. Our approach is based on stacked Dirac Hamiltonians, using which we relate transitions between topological phases to the transformation properties between adjacent gapped boundaries. We find that in addition to the bulk rotational invariants, the presence of Majorana boundary bound states in a given geometry depends on the interplay between weak topological invariants and the location of the rotation center relative to the lattice. We provide numerical examples for our predictions and discuss possible extensions of our approach.

Universal phase diagram of topological superconductors subjected to magnetic flux

We perform a theoretical study of the orbital effect of a magnetic field on a proximity-coupled islands array of $p_{x}+ip_{y}$ topological superconductors. To describe the system, we generalize the tight-binding model of the Hofstadter butterfly to include the effect of the superconducting islands. The quantum Hall topological phases, appearing in the absence of superconductivity, are characterized by integer fermionic Chern numbers corresponding to the number of occupied bulk Landau levels. As the strength of the superconducting pairing increases a series of transitions occurs, with one less chiral Majorana edge mode at each consecutive phase, leading to a reduction of the fermionic Chern number by a half. When the pairing potential exceeds the tight-binding model bandwidth, Cooper pairs are localized in the islands, the Chern number is zero, and there are no low-energy edge modes. We identify domains in the model's parameter space for which the system is topological and supports an odd number of chiral Majorana edge modes. While the precise shape of the domains depends on the details of the model, the general structure of the phase diagram is robust, and it is obtained numerically and in several simplified traceable analytical models. We discuss the relevance of this study to recent experimental research of two-dimensional superconductor arrays on semiconductor systems.

Topological Braiding of Non-Abelian Midgap Defects in Classical Metamaterials.

Nontrivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one- and two-dimensional topological superconductors. Here, we generate such representations with topologically protected domain-wall modes in a classical analog of the Kitaev superconducting chain, with a particle-holelike symmetry and a Z_{2} topological invariant. The midgap modes are found to exhibit distinct fusion channels and rich non-Abelian braiding properties, which are investigated using a T-junction setup. We employ the adiabatic theorem to explicitly calculate the braiding matrices for one and two pairs of these midgap topological defects.

Magnetic flux periodicity in second order topological superconductors

The magnetic flux periodicity of $\frac{hc}{2e}$ is a well known manifestation of Cooper pairing in typical s-wave superconductors. In this paper we theoretically show that the flux periodicity of a two-dimensional second-order topological superconductor, which features zero-energy Majorana modes localized at the corners of the sample, is $\frac{hc}{e}$ instead. We further show that the periodicity changes back to $\frac{hc}{2e}$ at the transition to a topologically trivial superconductor, where the Majorana modes hybridize with the bulk states, demonstrating that the doubling of periodicity is a manifestation of the non-trivial topology of the state.

Emergent superconductivity in two-dimensional NiTe2 crystals

Despite growing interest in them, highly crystalline two-dimensional superconductors derived from exfoliated layered materials are few. Employing the anisotropic Migdal-Eliashberg formalism based on {\it ab initio} calculations, we find monolayer NiTe$_{2}$ to be an intrinsic superconductor with a $T_{\text c}\sim$5.7~K, although the bulk crystal is not known to superconduct. Remarkably, bilayer NiTe$_{2}$ intercalated with lithium is found to display two-gap superconductivity with a critical temperature $T_{\text{c}}\sim 11.3$~K and superconducting gap of $\sim$3.1~meV, arising from a synergy of electronic and phononic effects. The comparatively high $T_\text{c}$, substrate independence and proximity tunability will make these superconductors ideal platforms for exploring intriguing correlation effects and quantum criticality associated two-dimensional superconductivity.

Transport through a network of two-dimensional NbC superconducting crystals connected via weak links

Recent progresses in the growth and fabrication techniques for preparing crystalline two-dimensional (2D) superconductors have stimulated intense interest in the studies of the electronic properties of these systems. Here we investigate the superconducting transport properties based on chemical vapor deposition-grown thin NbC crystals consisting of network structures. The 2D character of the superconductivity in individual NbC crystals is revealed by examining the angular dependence of magnetotransport measurements. At low temperatures, the samples show nonmonotonic double-step superconducting transitions as a function of temperature and magnetic field. We demonstrate that the observed transport characteristics can be understood in terms of coupled Josephson junctions forming between isolated NbC crystals, including the effects of Josephson and quasiparticle tunneling. In particular, detailed analysis of the magnetic field-driven transition suggests the existence of quantum flux-creep regime at low temperatures and small magnetic fields in such thin NbC superconducting crystals. Our work underlines the importance of the morphology on the transport properties of 2D superconducting crystals, providing a comprehensive understanding of crystalline 2D superconductors.

Enhanced phase-coherent multifractal two-dimensional superconductivity

We study the interplay of superconductivity and disorder by solving numerically the Bogoliubov-de-Gennes equations in a two dimensional lattice of size $80\times80$ which makes possible to investigate the weak-coupling limit. In contrast with results in the strong coupling region, we observe enhancement of superconductivity and intriguing multifractal-like features such as a broad log-normal spatial distribution of the order parameter, a parabolic singularity spectrum, and level statistics consistent with those of a disordered metal at the Anderson transition. The calculation of the superfluid density, including small phase fluctuations, reveals that, despite this intricate spatial structure, phase coherence still holds for sufficiently weak disorder. It only breaks down for stronger disorder but before the insulating transition takes place.

Angle dependence of Hc2 with a crossover between the orbital and paramagnetic limits

This paper establishes the angle dependence of the upper critical field H${}_{c2}$ of a two-dimensional Ising superconductor NbSe${}_{2}$. The experimental results demonstrate the cusp-like behavior around the parallel magnetic fields even at the lowest temperature where H${}_{c2}$ should be determined by the pure paramagnetic effect. Those results are well described by the formula that includes contributions both from the orbital and paramagnetic effects.

Surface Bound States and Spontaneous Edge Currents in Chiral Superconductors: Effect of Spatially Varying Order Parameter

We use the quasiclassical theory of superconductivity and examine the surface bound states and edge currents in two-dimensional chiral superconductors by focusing on the effect of spatially varying...

Phase Transition across Anisotropic NbS3 and Direct Gap Semiconductor TiS3 at Nominal Titanium Alloying Limit.

Alloying selected layered transitional metal trichalcogenides (TMTCs) with unique chain-like structures offers the opportunities for structural, optical, and electrical engineering thus expands the regime of this class of pseudo-one-dimensional materials. Here, the novel phase transition in anisotropic Nb(1- x ) Tix S3 alloys is demonstrated for the first time. Results show that Nb(1- x ) Tix S3 can be fully alloyed across the entire composition range from triclinic-phase NbS3 to monoclinic-phase TiS3 . Surprisingly, incorporation of a small concentration of Ti (x ≈ 0.05-0.18) into NbS3 host matrix is sufficient to induce triclinic to monoclinic transition. Theoretical studies suggest that Ti atoms effectively introduce hole doping, thus rapidly decreases the total energy of monoclinic phase and induces the phase transition. When alloyed, crystalline and optical anisotropy are largely preserved as evidenced by high resolution transmission electron microscopy and angle-resolved Raman spectroscopy. Further Raman measurements identify Raman modes to determine crystalline anisotropy direction and offer insights into the degree of anisotropy. Overall results introduce Nb(1- x ) Tix S3 as a new and easy phase change material and mark the first phase engineering in anisotropic van der Waals (vdW) trichalcogenide systems for their potential applications in two-dimensional superconductivity, electronics, photonics, and information technologies.

Atomic line defects and zero-energy end states in monolayer Fe(Te,Se) high-temperature superconductors

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. The spectroscopic properties of the ZEBSs, including the temperature and tunneling barrier dependences, as well as their fusion induced by coupling on line defects of different lengths are found to be robust and consistent with those of the MZMs. These observations suggest a realization of topological Shockley defects at the ends of an atomic line defect in a two-dimensional s-wave superconductor that can host a Kramers pair of MZMs protected by time-reversal symmetry along the chain. Our findings reveal an unprecedented class of topological line defect excitations in two-dimensional superconductor FeTe0.5Se0.5 monolayer films and offer an advantageous platform for generating topological zero-energy excitations at higher operating temperatures, in a single material, and under zero external magnetic field.

Tunable nonlocal valley-entangled Cooper pair splitter realized in bilayer-graphene van der Waals spin valves

We investigate the Cooper pair splitting based on crossed Andreev reflection in a two-dimensional narrow superconductor coupled to two leads, where the two leads are van der Waals (vdW) spin valves formed by inserting bilayer graphene (BLG) between two antiparallel insulating ferromagnetic layers. In this BLG-based $n$-type vdW spin valve/superconductor/$p$-type vdW spin valve junction with edge-contact geometry, when controlling the Fermi energy and the interlayer electric field in BLG independently by top- and bottom-gate voltages in the vdW spin valve region, we first demonstrate that the two electrons of perfect Cooper pair splitting can remain nonlocal valley entanglement. This effect can be explained as follows: When both the two antiparallel insulating ferromagnetic layers and the interlayer electric field are taken into account, BLG exhibits a spin-splitting but valley-degenerate band gap near the Dirac point. Thus, our setups allow the Cooper pair in the BCS scenario to serve as a natural source of valley entanglement. We further predict large oscillations of cross conductance as a function of the doping of the superconductor, the junction length, and the bias voltage. Our results may provide a tool for realizing fast nonlocal switching of the valley-entanglement state.

Berezinskii–Kosterlitz–Thouless transition in an Al superconducting nanofilm grown on GaAs by molecular beam epitaxy

We have performed extensive transport experiments on a 4 nm thick aluminum (Al) superconducting film grown on a GaAs substrate by molecular beam epitaxy (MBE). Nonlinear current–voltage (I–V) measurements on such a MBE-grown superconducting nanofilm show that V ∼ I3, which is evidence for the Berezinskii–Kosterlitz–Thouless (BKT) transition, both in the low-voltage (TBKT ≈ 1.97 K) and high-voltage regions (TBKT ≈ 2.17 K). In order to further study the two regions where the I–V curves are BKT-like, our experimental data are fitted to the temperature-induced vortices/antivortices unbinding model as well as the dynamical scaling theory. It is found that the transition temperature obtained in the high-voltage region is the correct TBKT as confirmed by fitting the data to the aforementioned models. Our experimental results unequivocally show that I–V measurements alone may not allow one to determine TBKT for superconducting transition. Therefore, one should try to fit one’s results to the temperature-induced vortices/antivortices unbinding model and the dynamical scaling theory to accurately determine TBKT in a two-dimensional superconductor.

Majorana corner flat bands in two-dimensional second-order topological superconductors

In this paper we find that confining a second-order topological superconductor with a harmonic potential leads to a proliferation of Majorana corner modes. As a consequence, this results in the formation of Majorana corner flat bands which have a fundamentally different origin from that of the conventional mechanism. This is due to the fact that they arise solely from the one-dimensional gapped boundary states of the hybrid system that become gapless without the bulk gap closing under the increase of the trapping potential magnitude. The Majorana corner states are found to be robust against the strength of the harmonic trap and the transition from Majorana corner states to Majorana flat bands is merely a smooth crossover. As a harmonic trap can potentially be realized in heterostructures, this proposal paves a way to observe these Majorana corner flat bands in an experimental context.