Full-gap superconductivity in spin-polarised surface states of topological semimetal β-PdBi2

Anomalous transverse resistance in the topological superconductor β-Bi2Pd

A supercurrent flowing in a superconductor meets no resistance. Yet an electric field may still be established within the superconductor in the presence of dissipative processes, such as vortex motion. Here we report the observation of a transverse voltage drop in superconducting β-Bi₂Pd thin films. Unlike the Hall effect in general or in other superconductors, the sign of the observed transverse voltage does not depend on the external magnetic field. Instead, it is dictated by the broken inversion symmetry on the film interfaces. This anomalous transverse voltage, or transverse resistance, is indicative of a chirality that likely resonates with the topological surface states reported in β-Bi₂Pd.

Centrosymmetric β-Bi₂Pd is a candidate topological superconductor. Here, the authors observe a transverse voltage in β-Bi₂Pd thin films and propose that this voltage is a result of chiral topological surface states.

Unconventional Pressure Dependence of the Superfluid Density in the Nodeless Topological Superconductor α-PdBi_{2}

We investigated the superconducting properties of the topological superconductor α-PdBi_{2} at ambient and external pressures up to 1.77 GPa using muon spin rotation experiments. The ambient pressure measurements evince a fully gapped s-wave superconducting state in the bulk of the specimen. Alternating current magnetic susceptibility and muon spin rotation measurements manifest a continuous suppression of T_{c} with increasing pressure. In parallel, we observed a significant decrease of superfluid density by ∼20% upon application of external pressure. Remarkably, the superfluid density follows a linear relation with T_{c}, which was found before in some unconventional topological superconductors and hole-doped cuprates. This finding signals a possible crossover from Bose-Einstein to Bardeen-Cooper-Schrieffer like condensation in α-PdBi_{2}.

Tomographic mapping of the hidden dimension in quasi-particle interference

Quasiparticle interference (QPI) imaging is well established to study the low-energy electronic structure in strongly correlated electron materials with unrivalled energy resolution. Yet, being a surface-sensitive technique, the interpretation of QPI only works well for anisotropic materials, where the dispersion in the direction perpendicular to the surface can be neglected and the quasiparticle interference is dominated by a quasi-2D electronic structure. Here, we explore QPI imaging of galena, a material with an electronic structure that does not exhibit pronounced anisotropy. We find that the quasiparticle interference signal is dominated by scattering vectors which are parallel to the surface plane however originate from bias-dependent cuts of the 3D electronic structure. We develop a formalism for the theoretical description of the QPI signal and demonstrate how this quasiparticle tomography can be used to obtain information about the 3D electronic structure and orbital character of the bands.

Thickness Dependence of Superconductivity in Layered Topological Superconductor β-PdBi2

We report a systematic study on the thickness-dependent superconductivity and transport properties in exfoliated layered topological superconductor β-PdBi2. The superconducting transition temperature Tc is found to decrease with the decreasing thickness. Below a critical thickness of 45 nm, the superconductivity is suppressed, but followed by an abrupt resistance jump near Tc, which is in opposite to the behavior in a superconductor. We attribute suppressed Tc to the enhanced disorder as the thickness decreases. The possible physical mechanisms were discussed for the origination of sharply increased resistance in thinner β-PdBi2 samples.

Simplified feedback control system for scanning tunneling microscopy

A Scanning Tunneling Microscope (STM) is one of the most important scanning probe tools available to study and manipulate matter at the nanoscale. In a STM, a tip is scanned on top of a surface with a separation of a few Å. Often, the tunneling current between the tip and the sample is maintained constant by modifying the distance between the tip apex and the surface through a feedback mechanism acting on a piezoelectric transducer. This produces very detailed images of the electronic properties of the surface. The feedback mechanism is nearly always made using a digital processing circuit separate from the user computer. Here, we discuss another approach using a computer and data acquisition through the universal serial bus port. We find that it allows successful ultralow noise studies of surfaces at cryogenic temperatures. We show results on different compounds including a type II Weyl semimetal (WTe₂), a quasi-two-dimensional dichalcogenide superconductor (2H-NbSe₂), a magnetic Weyl semimetal (Co₃Sn₂S₂), and an iron pnictide superconductor (FeSe).

Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors

Bound states in superconductors are expected to exhibit a spatially resolved electron-hole asymmetry which is the hallmark of their quantum nature. This asymmetry manifests as oscillations at the Fermi wavelength, which is usually tiny and thus washed out by thermal broadening or by scattering at defects. Here we demonstrate theoretically and confirm experimentally that, when coupled to magnetic impurities, bound states in a vortex core exhibit an emergent axial electron-hole asymmetry on a much longer scale, set by the coherence length. We study vortices in 2H-NbSe2 and in 2H-NbSe1.8S0.2 with magnetic impurities, characterizing these with detailed Hubbard-corrected density functional calculations. We find that the induced electron-hole imbalance depends on the band character of the superconducting material. Our results show that coupling between quantum bound states in superconductors is remarkably robust and has a strong influence in tunneling measurements.

Anisotropic Full-Gap Superconductivity in 2M-WS2 Topological Metal with Intrinsic Proximity Effect

Layered 2M-WS₂ is recently observed to show Majorana bound states in vortices, but its superconducting pairing mechanism remains unknown, hindering the understanding of its topological superconducting nature. Using the ab initio Migdal-Eliashberg theory and electron-phonon Wannier interpolation, we demonstrate that both bulk and bilayer 2M-WS₂ have a single anisotropic full-gap superconducting order of s-wave symmetry. We successfully reproduce the experimental superconducting critical temperature for the bulk and predict the bilayer 2M-WS₂, a two-dimensional (2D) Z₂ topological metal with nontrivial edge states right at the Fermi energy, to superconduct at 7 K, much higher than that in most 2D transition metal dichalcogenides (TMDs). A distinct proximity-enhanced surface superconductivity is further revealed by simulating quasiparticle density of states. This work unveils a universal electron-phonon full-gap pairing in 2M group VI TMDs and suggests a strong intrinsic surface-bulk proximity effect for 2M-WS₂, paving the way to engineering topological superconductivity in TMD-based nanoscale devices.

Multiple In-Gap States Induced by Topological Surface States in the Superconducting Topological Crystalline Insulator Heterostructure Sn_{1-x}Pb_{x}Te-Pb

Superconducting topological crystalline insulators (TCIs) have been proposed to be a new type of topological superconductor where multiple Majorana zero modes may coexist under the protection of lattice symmetries. The bulk superconductivity of TCIs has been realized, but it is quite challenging to detect the superconductivity of topological surface states inside their bulk superconducting gaps. Here, we report high-resolution scanning tunneling spectroscopy measurements on lateral Sn_{1-x}Pb_{x}Te-Pb heterostructures using superconducting tips. Both the bulk superconducting gap and the multiple in-gap states with energy differences of ∼0.3  meV can be clearly resolved on TCI Sn_{1-x}Pb_{x}Te at 0.38 K. Quasiparticle interference measurements further confirm the in-gap states are gapless. Our work demonstrates that the unique topological superconductivity of a TCI can be directly distinguished in the density of states, which helps to further investigate the multiple Dirac and Majorana fermions inside the superconducting gap.

Superconductivity of Topological Surface States and Strong Proximity Effect in Sn1- x Pbx Te-Pb Heterostructures

Superconducting topological crystalline insulators are expected to form a new type of topological superconductors to host Majorana zero modes under the protection of lattice symmetries. The bulk superconductivity of topological crystalline insulators can be induced through chemical doping and the proximity effect. However, only conventional full gaps are observed, so the existence of topological superconductivity in topological crystalline insulators is still controversial. Here, the successful fabrication of atomically flat lateral and vertical Sn_{1- x} Pb_x Te-Pb heterostructures by molecular beam epitaxy is reported. The superconductivity of the Sn_{1- x} Pb_x Te-Pb heterostructures can be directly investigated by scanning tunneling spectroscopy. Unconventional peak-dip-hump gap features and fourfold symmetric quasiparticle interference patterns taken at the zero energy in the superconducting gap support the presence of the topological superconductivity in superconducting Sn_{1- x} Pb_x Te. Strong superconducting proximity effect and easy preparation of various constructions between Sn_{1- x} Pb_x Te and Pb make the heterostructures to be a promising candidate for topological superconducting devices to detect and manipulate Majorana zero modes in the future.

Observation of half-quantum flux in the unconventional superconductor β-Bi2Pd

Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi₂Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of β-Bi₂Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.

Experimental evidence of anomalously large superconducting gap on topological surface state of β-Bi2Pd film

Connate topological superconductor (TSC) combines topological surface states with nodeless superconductivity in a single material, achieving effective p-wave pairing without interface complication. By combining angle-resolved photoemission spectroscopy and in-situ molecular beam epitaxy, we studied the momentum-resolved superconductivity in β-Bi₂Pd film. We found that the superconducting gap of topological surface state (Δ_TSS ∼ 3.8 meV) is anomalously enhanced from its bulk value (Δ_b ∼ 0.8 meV). The ratio of 2Δ_TSS/k_BT_c ∼ 16.3, is substantially larger than the BCS value. By measuring β-Bi₂Pd bulk single crystal as a comparison, we clearly observed the upward-shift of chemical potential in the film. In addition, a concomitant increasing of surface weight on the topological surface state was revealed by our first principle calculation, suggesting that the Dirac-fermion-mediated parity mixing may cause this anomalous superconducting enhancement. Our results establish β-Bi₂Pd film as a unique case of connate TSCs with a highly enhanced topological superconducting gap, which may stabilize Majorana zero modes at a higher temperature.

Possible transport evidence for three-dimensional topological superconductivity in doped β-PdBi2

Interest in topological states of matter burgeoned over a decade ago with the theoretical prediction and experimental detection of topological insulators, especially in bulk three-dimensional insulators that can be tuned out of it by doping. Their superconducting counterpart, the fully-gapped three-dimensional time-reversal-invariant topological superconductors, have evaded discovery in bulk intrinsic superconductors so far. The recently discovered topological metal β-PdBi2 is a unique candidate for tunable bulk topological superconductivity because of its intrinsic superconductivity and spin-orbit-coupling. In this work, we provide experimental transport signatures consistent with fully-gapped 3D time-reversal-invariant topological superconductivity in K-doped β-PdBi2. In particular, we find signatures of odd-parity bulk superconductivity via upper-critical field and magnetization measurements- odd-parity pairing can be argued, given the band structure of β-PdBi2, to result in 3D topological superconductivity. In addition, Andreev spectroscopy reveals surface states protected by time-reversal symmetry which might be possible evidence of Majorana surface states (Majorana cone). Moreover, we find that the undoped bulk system is a trivial superconductor. Thus, we discover β-PdBi2 as a unique bulk material that, on doping, can potentially undergo an unprecedented topological quantum phase transition in the superconducting state.

Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)

Majorana quasiparticles in condensed matter are important for topological quantum computing^1-3, but remain elusive. Vortex cores of topological superconductors may accommodate Majorana quasiparticles that appear as the Majorana bound state (MBS) at zero energy^4,5. The iron-based superconductor Fe(Se,Te) possesses a superconducting topological surface state^6-9 that was investigated by scanning tunnelling microscopy (STM) studies, which suggest such a zero-energy vortex bound state (ZVBS)^10,11. Here we present ultrahigh energy-resolution spectroscopic imaging (SI)-STM to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 ± 20 μeV, which constrained its MBS origin, and showed that some vortices host the ZVBS but others do not. We show that the fraction of vortices hosting the ZVBS decreases with increasing magnetic field and that local quenched disorders are not related to the ZVBS. Our observations elucidate the necessary conditions to realize the ZVBS, which paves the way towards controllable Majorana quasiparticles.

Nodal-chain network, intersecting nodal rings and triple points coexisting in nonsymmorphic Ba3Si4

Coexistence of topological elements in topological metals/semimetals (TMs) has gradually attracted attention. However, non-topological factors always interfere with the Fermi surface and cover interesting topological properties. Here, we find that Ba3Si4 is a "clean" TM which contains coexisting nodal-chain networks, intersecting nodal rings (INRs) and triple points, in the absence of spin-orbit coupling (SOC). Moreover, the nodal rings in the topological phase exhibit diverse types: from type-I and type-II to type-III rings according to band dispersions. All of the topological elements are generated by crossings of three energy bands, and thus they are correlated rather than mutually independent. When some structural symmetries are eliminated by an external strain, the topological phase evolves into another phase including a Hopf link, a one-dimensional nodal chain and new INRs.

Influence of Magnetic Ordering between Cr Adatoms on the Yu-Shiba-Rusinov States of the β-Bi_{2}Pd Superconductor

We show that the magnetic ordering of coupled atomic dimers on a superconductor is revealed by their intragap spectral features. Chromium atoms on the superconductor β-Bi_{2}Pd surface display Yu-Shiba-Rusinov bound states, detected as pairs of intragap excitations in tunneling spectra. By means of atomic manipulation with a scanning tunneling microscope's tip, we form Cr dimers with different arrangements and find that their intragap features appear either shifted or split with respect to single atoms. These spectral variations are associated with the magnetic coupling, ferromagnetic or antiferromagnetic, of the dimer, as confirmed by density functional theory simulations. The striking qualitative differences between the observed tunneling spectra prove that intragap Shiba states are extremely sensitive to the magnetic ordering on the atomic scale.