2D Superconductors Research Articles

SuperScreen: An open-source package for simulating the magnetic response of two-dimensional superconducting devices

Quantitative understanding of the spatial distribution of magnetic fields and Meissner screening currents in two-dimensional (2D) superconductors and mesoscopic thin film superconducting devices is critical to interpreting the results of magnetic measurements of such systems. Here, we introduce SuperScreen, an open-source Python package for simulating the response of 2D superconductors to trapped flux and applied time-independent or quasi-DC magnetic fields for any value of the effective magnetic penetration depth, Λ. Given an applied magnetic field, SuperScreen solves the 2D London equation using an efficient matrix inversion method [1,2] to obtain the Meissner currents and magnetic fields in and around structures composed of one or more superconducting thin films of arbitrary geometry. SuperScreen can be used to model screening effects and calculate self- and mutual-inductance in thin film superconducting devices. Program summaryProgram title: SuperScreenCPC Library link to program files:https://doi.org/10.17632/bds57s4c83.1Developer's repository link:http://www.github.com/loganbvh/superscreenCode Ocean capsule:https://codeocean.com/capsule/5305996Licensing provisions: MIT licenseProgramming language: PythonNature of problem:SuperScreen solves for Meissner screening currents in structures composed of 2D or thin film superconductors in the presence of an applied magnetic field, pinned vortices, and trapped flux.Solution method: This package solves the 2D London equation for superconducting thin films using a matrix inversion method [1,2].

Hot-lines topology and the fate of the spin resonance mode in three-dimensional unconventional superconductors

In the quasi-two-dimensional (quasi-2D) copper- and iron-based superconductors, the onset of superconductivity is accompanied by a prominent peak in the magnetic spectrum at momenta close to the wave-vector of the nearby antiferromagnetic state. Such a peak is well described in terms of a spin resonance mode, i.e., a spin-1 exciton theoretically predicted for quasi-2D superconductors with a sign-changing gap. The same theories, however, indicate that such a resonance mode should be absent in a three-dimensional (3D) system with a spherical Fermi surface. This raises the question of the fate of the spin resonance mode in layered unconventional superconductors that are not strongly anisotropic, such as certain heavy-fermion compounds and potentially the newly discovered nickelate superconductor NdNiO$_2$. Here, we use the random-phase-approximation to calculate the dynamical spin susceptibility of 3D superconductors with a $d_{x^2-y^2}$-wave gap symmetry and corrugated cylindrical-like Fermi surfaces. By varying the out-of-plane hopping anisotropy $t_z/t$, we demonstrate that the appearance of a spin resonance mode is determined by the topology of the hot lines -- i.e. lines on the Fermi surface that are connected by the magnetic wave-vector. For an in-plane antiferromagnetic wave-vector, the hot lines undergo a topological transition from open lines to closed loops at a critical $t_z/t$ value. The closed hot lines cross the nodal superconducting lines, making the spin resonance mode overdamped and incoherent. In contrast, for an out-of-plane antiferromagnetic wave-vector, the hot lines remain open and the spin resonance mode remains sharp. We discuss the experimental implications of our results for the out-of-plane dispersion of the spin resonance mode and, more generally, for inelastic neutron scattering experiments on unconventional superconductors.

(Invited) Unusual Superconducting Behavior in an Ultrathin Weyl Semimetal

Two dimensional materials are layered materials that may be readily exfoliated down to a single atomic layer, presenting an opportunity to noninvasively, and efficiently, control electrical and magnetic ordering, as well as topology. In this talk, I discuss how topology emerges from the bulk, down to the monolayer and how the influence of an electrostatic gate allows us to identify a unique superconducting state in few-layer Td-MoTe2. In the bulk, MoTe2 is a type II Weyl semimetal with a superconducting transition temperature of 120 mK. First, I will discuss how in the clean limit the superconducting transition temperature is enhanced by a factor of 60x, as compared to bulk, in monolayer Td-MoTe2, while still retaining a low carrier density (~1013/cm2), and a density of states that is comparable to the bulk. I will show how the crystal structure factors into the behavior of the superconducting state under external in-plane magnetic fields and how this can be used to quantify of the spin-orbit coupling, an important factor for determining topology and realizing topological superconducting states. After discussion of the monolayer, I will show that this enhancement remains in bilayer MoTe2, despite the change in symmetry. Strangely, our results indicate that superconductivity in bilayer MoTe2 is much more tunable by an electrostatic gate than that of monolayer MoTe2. In addition, for monolayer the response to high in-plane magnetic fields is distinct from that of other 2D superconductors and reflects the canted spin texture of the electron pockets. In bilayer, there is a strong deviation from this behavior, and instead an anomalous anisotropic behavior is observed with in-plane magnetic fields. These findings have profound implications on 2D superconductivity, where previously strong spin-orbit effects were only considered in the case of out-of-plane spin textures and offer an avenue for future exploration in similarly structured materials.

Momentum microscopy of Pb-intercalated graphene on SiC: Charge neutrality and electronic structure of interfacial Pb

Intercalation is an established technique for tailoring the electronic structure of epitaxial graphene. Moreover, it enables the synthesis of otherwise unstable two-dimensional (2D) layers of elements with unique physical properties compared to their bulk versions due to interfacial quantum confinement. In this work, we present uniformly Pb-intercalated quasi-freestanding monolayer graphene on SiC, which turns out to be essentially charge neutral with an unprecedented $p$-type carrier density of only $(5.5\pm2.5)\times10^9$ cm$^{-2}$. Probing the low-energy electronic structure throughout the entire first surface Brillouin zone by means of momentum microscopy, we clearly discern additional bands related to metallic 2D-Pb at the interface. Low-energy electron diffraction further reveals a $10\times10$ Moir\'e superperiodicity relative to graphene, counterparts of which cannot be directly identified in the available band structure data. Our experiments demonstrate 2D interlayer confinement and associated band structure formation of a heavy-element superconductor, paving the way towards strong spin-orbit coupling effects or even 2D superconductivity at the graphene/SiC interface.

Emergence of superconductivity in an InSe monolayer: Roles of deposited metal and biaxial strain

Two-dimensional (2D) superconductors are important for both fundamental superconducting physics and potential nanoscale applications. Here, using first-principles calculations, we unravel that an Na-deposited InSe monolayer (NaIn2Se2) is dynamically stable and may constitute a novel 2D superconductor with a transition temperature (Tc) of 4.42 K due to the combined effect of strong Fermi nesting and strong electron-phonon coupling (EPC) from in-plane phonons. In contrast, Li- and Mg-deposited InSe monolayers are dynamically unstable. Furthermore, a 3% biaxial tensile strain increases the EPC strength of NaIn2Se2 and Tc is increased to 4.88 K. However, a 3% compressive strain slightly lowers Tc to 4.12 K. Our work demonstrates that Na-deposited InSe monolayer may be a novel 2D superconductor and that strain is important to maximize its Tc.

Theoretical prediction of superconductivity in monolayer B3N

Using first-principles calculations, we predict the two-dimensional (2D) monolayer boron-nitrogen compound ${\mathrm{B}}_{3}\mathrm{N}$, which shows a honeycomb lattice similar to graphene. Its stability is proved by phonon spectra and ab initio molecular dynamics simulations. Since pristine ${\mathrm{B}}_{3}\mathrm{N}$ is a metal by band structure calculation, we investigate the electron-phonon coupling and possible phonon-mediated superconductivity. Based on the Eliashberg equation, the calculated electron-phonon coupling strength is about 0.66, and the superconducting transition temperature ${T}_{c}$ is 14.1 K, which is comparable to that of borophene. Furthermore, when 0.04 electron/cell doping and 10% biaxial tensile strain are applied, ${T}_{c}$ can be increased to 17.4 K. Thus, the predicted ${\mathrm{B}}_{3}\mathrm{N}$ provides a platform for 2D superconductivity.

On the Localization of Persistent Currents Due to Trapped Magnetic Flux at the Stacking Faults of Graphite at Room Temperature

Granular superconductivity at high temperatures in graphite can emerge at certain two-dimensional (2D) stacking faults (SFs) between regions with twisted (around the c-axis) or untwisted crystalline regions with Bernal (ABA…) and/or rhombohedral (ABCABCA…) stacking order. One way to observe experimentally such 2D superconductivity is to measure the frozen magnetic flux produced by a permanent current loop that remains after removing an external magnetic field applied normal to the SFs. Magnetic force microscopy was used to localize and characterize such a permanent current path found in one natural graphite sample out of ∼50 measured graphite samples of different origins. The position of the current path drifts with time and roughly follows a logarithmic time dependence similar to the one for flux creep in type II superconductors. We demonstrate that a ≃10 nm deep scratch on the sample surface at the position of the current path causes a change in its location. A further scratch was enough to irreversibly destroy the remanent state of the sample at room temperature. Our studies clarify some of the reasons for the difficulties of finding a trapped flux in a remanent state at room temperature in graphite samples with SFs.

Circular Photogalvanic Effect in Oxide Two-Dimensional Electron Gases.

Two-dimensional electron gases (2DEGs) at the LaAlO_{3}/SrTiO_{3} interface have attracted wide interest, and some exotic phenomena are observed, including 2D superconductivity, 2D magnetism, and diverse effects associated with Rashba spin-orbit coupling. Despite the intensive investigations, however, there are still hidden aspects that remain unexplored. For the first time, here we report on the circular photogalvanic effect (CPGE) for the oxide 2DEG. Spin polarized electrons are selectively excited by circular polarized light from the in-gap states of SrTiO_{3} to 2DEG and are converted into electric current via the mechanism of spin-momentum locking arising from Rashba spin-orbit coupling. Moreover, the CPGE can be effectively modified by the density and distribution of oxygen vacancies. This Letter presents an effective approach to generate and manipulate the spin polarized current, paving the way toward oxide spintronics.

Hydrogenation-induced high-temperature superconductivity in two-dimensional molybdenum carbide Mo2C3

Two-dimensional (2D) superconductors have important potential applications in constructing nano superconducting devices, thus, 2D superconductors with high critical temperature (T c ) are highly desired. Till now, the T c of 2D superconductors are still relatively low. Based on density functional first-principles calculations, we predicted a new stable 2D transition metal molybdenum carbide 2H-Mo2C3. Based on the Eliashberg theory, we predict that it is not a superconductor. However, after hydrogenation, the hydrogen atoms increase the electronic density of states at the Fermi level, and strengthen the electron-phonon coupling. Accordingly, the hydrogenated 2H-Mo2C3, i.e., 2H-Mo2C3H2, is a 2D superconductor with T c of 53 K, exceeding the McMillan limit. Thus, hydrogenation is an important strategy for obtaining 2D high-temperature superconductors at atmosphere pressure. In view of the high superconducting T c of 2H-Mo2C3H2, it is highly expected to be synthesized in future experiments.

Two-dimensional superconductivity in a bulk superlattice van der Waals material Ba6Nb11Se28

The observation of clean 2D superconductivity and bosonic Landau levels below 0.85 K in superlattice van der Waals material ${\mathrm{Ba}}_{6}{\mathrm{Nb}}_{11}{\mathrm{S}}_{28}$ have received much interest. Here we report the crystal structure, Hall resistivity, and 2D superconductivity of its sister compound, ${\mathrm{Ba}}_{6}{\mathrm{Nb}}_{11}{\mathrm{Se}}_{28}$. The atomic-resolution transmission electron microscopy images reveal an alternate stacking of $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ with a 3 \ifmmode\times\else\texttimes\fi{} 3 commensurate block layer, which is isostructural to ${\mathrm{Ba}}_{6}{\mathrm{Nb}}_{11}{\mathrm{S}}_{28}$ and with a larger $\mathrm{Nb}{X}_{2}$ ($X=\mathrm{S}$, Se) interlayer distance (12.8 \AA{}). Transport property measurements demonstrate a twofold enhancement in superconducting temperature $({{T}_{\mathrm{c}}}^{0}=2.2\phantom{\rule{0.16em}{0ex}}\mathrm{K})$, meanwhile the anisotropy in resistivity and carrier mobility in ${\mathrm{Ba}}_{6}{\mathrm{Nb}}_{11}{\mathrm{Se}}_{28}$ decrease drastically compared to its sulfur counterpart, driving the superconductor towards the dirty limit. Further measurements of angular-dependent upper critical field suggest the superconductivity in ${\mathrm{Ba}}_{6}{\mathrm{Nb}}_{11}{\mathrm{Se}}_{28}$ be Pauli-limit breaking (2 times the ${\ensuremath{\mu}}_{0}{H}_{P}$), and can be well described by the 2D Tinkham form. Our findings offer a valuable platform to investigate 2D superconductivity in bulk superlattice materials based on the transition-metal dichalcogenides.

Disorder-induced 2D superconductivity in a NbTiN film grown on Si by ultrahigh-vacuum magneton sputtering

We report on the growth and characterization of a niobium titanium nitride (NbTiN) film on a Si substrate prepared by ultrahigh vacuum sputtering. We show that the superconducting transition temperature is lower than those of high-quality NbTiN films. Interestingly, even though the zero-temperature Ginzburg-Landau coherence length (=9.77 nm) is significantly shorter than the film thickness (=86 nm), we are still able to observe the Berezinskii-Kosterlitz-Thouless-like transition, indicating the two-dimensional (2D) signature of our three-dimensional (3D) sample. We propose that the mechanism of hidden 2D superconducting property is similar to the recently reported results of the disordered induced 3D to 2D superconductor transition. We suggest further theoretical work is required for studying our new experimental results.

Experimental and first-principles studies of superconductivity in topological nodal line semimetal SnTaS2

We report a detailed study of superconductivity in polycrystalline SnTaS2 using electrical transport, magnetization and heat capacity measurements. SnTaS2 crystallizes in centrosymmetric hexagonal structure with space group . Electrical resistivity, magnetization and specific heat data suggest SnTaS2 to be a weakly coupled, type-II superconductor with K. First-principles calculations show signature for nodal line topology in the electronic band structure, protected by the spatial-inversion and time-reversal symmetries, that strongly gapped out by the inclusion of spin–orbit coupling. Superconductivity in layered SnTaS2 with nodal line topological state makes it a strong candidate to be considered for a 3D topological superconductor.

First-Principles Prediction of Superconductivity in High-Buckled Two-Dimensional Tin

Two-dimensional (2D) superconductors exhibit a variety of fascinating phenomena such as the Kosterlitz–Thouless–Berezinskii transition, electron quantum confinement effect, charge density wave, and topologically non-trivial band. Until now, the superconductivity of a classical elemental 2D system of tin has not yet been confirmed. Herein, using the microscopic theory of Bardeen, Cooper, and Schrieffer (BCS) and density functional theory calculations, we meticulously study the electron–phonon coupling, electronic structures, and phase transition of low-buckled (LB) stanene and high-buckled (HB) 2D tin. We demonstrate that the HB 2D tin exhibits remarkable multi-gap electron–phonon coupling superconductivity with critical temperatures approximating those of the conventional bulk tin and few-layer LB stanene. Our results clearly show the strain-induced transitions of the orbital occupation, band structure, and superconductivity from LB to HB structures. Our discovery of HB 2D tin as an excellent 2D superconductor should stimulate the experimental synthesis and characterization of its superconducting properties.

Enhanced critical field and anomalous metallic state in two-dimensional centrosymmetric 1T′−WS2

Layered transition-metal chalcogenide material (TMD) offers a platform to investigate two-dimensional (2D) superconductivity. Here, we report an electrical transport study of 2D centrosymmetric superconductor $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{S}}_{2}$. For a typical five-layer sample, the 2D superconductivity is revealed in Berezinskii-Kosterlitz-Thouless (BKT) transition with the characteristic temperature ${T}_{BKT}\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The superconductivity is observed with a strong resist against the in-plane magnetic field. We find that the critical in-plane magnetic field is \ensuremath{\sim}3 times the Pauli paramagnetic limit ${B}_{p}$, with effective Zeeman-type spin-orbital coupling $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{{\ensuremath{\beta}}_{\mathrm{SO}}}\ensuremath{\sim}2.8\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. In addition, we find the magnetoresistance trend to saturate at low temperature, suggesting anomalous quantum metallic states. These findings might stimulate further investigations on the correlation between superconductivity and symmetry of 2D superconductors, as well as the quantum metallic states at low temperature with finite magnetic field.

Superconductivity 2022

Superconductivity in metals and alloys, i.e., conventional superconductivity, has seen many new developments in recent years, leading to a renewed interest in the principles of superconductivity and the search for new materials. The most striking discoveries include the near-room-temperature superconductivity in metal hydrides (LaH10) under pressure, the extreme stability of superconductivity in NbTi up to 261 GPa pressure, the discovery of high-entropy alloy (HEA) superconductor materials, and the machine learning prediction of new superconducting materials. Other interesting research concerns the properties of 2D superconductors, topological superconductors, e.g., in hybrid systems, and the use of nanotechnology to create nanowires and nanostructures with new properties. Furthermore, and most importantly, the drive from new accelerator and fusion reactors for stronger superconducting magnets has lead to improved cable materials, showing the highest critical current densities ever. Thus, this Special Issue aims to bring together a collection of papers reflecting the present activity in this field.

Orbital-selective two-dimensional superconductivity in 2H−NbS2

Orbital-selective superconductivity is crucial for understanding the pairing mechanism for multiband superconductors. Atomic $d$ orbitals with anisotropic spatial extension can directly determine the energy dispersion of subbands with two-dimensional (2D) or three-dimensional (3D) nature in band structure. Theoretically, owing to the coexistence of these 2D and 3D subbands, the orbital-selective superconductivity can exhibit band-dependent dimensionality in multiband superconductors. However, to experimentally confirm this orbital-selective 2D superconductivity remains challenging and elusive. Herein, based on angle-dependent upper critical magnetic field on $2\mathrm{H}\text{\ensuremath{-}}{\mathrm{NbS}}_{2}$ flakes, we observe a cusp peak associated with a 2D superconducting subband from the ${d}_{xy}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals of Nb atoms, and a round peak related to a 3D subband, directly confirming the existence of intrinsic 2D superconductivity in $2\mathrm{H}\text{\ensuremath{-}}{\mathrm{NbS}}_{2}$ thick flake and its orbital-selective superconducting nature. The 2D superconductivity remains robust under large electric current or high pressure. Such observations shed light on the orbital-selective pairing mechanism and resulting band-dependent dimensionality for multiband superconductors.

Two-dimensional superconductivity in single-band correlated 2H -type NbO2 layers

The oxide superconductor ${\mathrm{Li}}_{1\text{\ensuremath{-}}x}\mathrm{Nb}{\mathrm{O}}_{2}$ has two-dimensional (2D) $\mathrm{Nb}{\mathrm{O}}_{2}$ layers consisting of edge-shared triangular prisms. This structure is a unique oxide analog to $2H$-type transition-metal dichalcogenides (TMDs), yet its electronic properties have not received any significant attention. Using ${\mathrm{Li}}_{1\text{\ensuremath{-}}x}\mathrm{Nb}{\mathrm{O}}_{2}$ epitaxial films, we find the 2D superconductivity associated with the Berezinskii-Kosterlitz-Thouless transition and a large anisotropy of the upper critical field. The temperature-independent anisotropy strongly suggests single-band superconductivity, in contrast to TMDs. Correspondingly, the largely isolated single ${d}_{z2}$ state revealed by synchrotron-radiation photoelectron spectroscopy and density functional theory is explained in terms of strong ligand field splitting. These results indicate that superconductivity in ${\mathrm{Li}}_{1\text{\ensuremath{-}}x}\mathrm{Nb}{\mathrm{O}}_{2}$ occurs in 2D $\mathrm{Nb}{\mathrm{O}}_{2}$ layers with a narrow and correlated single band, reminiscent of superconductivity in cuprates. Our study provides insight into the unconventional correlation in the Hubbard system with a 2D triangular lattice.

Enhancing the hybridization of plasmons in graphene with 2D superconductor collective modes

We explore ways in which the close proximity between graphene sheets and monolayers of 2D superconductors can lead to hybridization between their collective excitations. We consider heterostructures formed by combinations of graphene sheets and 2D superconductor monolayers. The broad range of energies in which the graphene plasmon can exist, together with its tunability, makes such heterostructures promising platforms for probing the many-body physics of superconductors. We show that the hybridization between the graphene plasmon and the Bardasis–Schrieffer mode of a 2D superconductor results in clear signatures on the near-field reflection coefficient of the heterostructure, which in principle can be observed in scanning near-field microscopy experiments.

Universal Dynamics of Magnetic Monopoles in Two-Dimensional Kagomé Ice

A magnetic monopole in spin ice is a novel quasiparticle excitation in condensed matter physics, and we found that the ac frequency dependent magnetic susceptibility $\chi(\omega)$ in the two-dimensional (2D) spin ice (so-called kagom\'{e} ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG) systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge correlation length $\xi (\propto1/\sqrt{\omega_1})$, where $\omega_{1}$ is a characteristic frequency proportional to the peak position of the imaginary part of $\chi(\omega)$. It is a generic behavior among a wide variety of models such as the vortex dynamics of 2D superconductors, 2D superfluids, classical XY magnets, and dynamics of melting of Wigner crystals.

Proximity Effects on the Charge Density Wave Order and Superconductivity in Single-Layer NbSe2.

Collective electronic states such as the charge density wave (CDW) order and superconductivity (SC) respond sensitively to external perturbations. Such sensitivity is dramatically enhanced in two dimensions (2D), where 2D materials hosting such electronic states are largely exposed to the environment. In this regard, the ineludible presence of supporting substrates triggers various proximity effects on 2D materials that may ultimately compromise the stability and properties of the electronic ground state. In this work, we investigate the impact of proximity effects on the CDW and superconducting states in single-layer (SL) NbSe2 on four substrates of diverse nature, namely, bilayer graphene (BLG), SL-boron nitride (h-BN), Au(111), and bulk WSe2. By combining low-temperature (340 mK) scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we compare the electronic structure of this prototypical 2D superconductor on each substrate. We find that, even when the electronic band structure of SL-NbSe2 remains largely unaffected by the substrate except when placed on Au(111), where a charge transfer occurs, both the CDW and SC show disparate behaviors. On the insulating h-BN/Ir(111) substrate and the metallic BLG/SiC(0001) substrate, both the 3 × 3 CDW and superconducting phases persist in SL-NbSe2 with very similar properties, which reveals the negligible impact of graphene on these electronic phases. In contrast, these collective electronic phases are severely weakened and even absent on the bulk insulating WSe2 substrate and the metallic single-crystal Au(111) substrate. Our results provide valuable insights into the fragile stability of such electronic ground states in 2D materials.