Most superconducting materials are well-understood and conventional in the sense that the pairs of electrons that cause the superconductivity by their condensation have the highest possible symmetry. Famous exceptions are the enigmatic high-$T_c$ cuprate superconductors. Nodes in their superconducting gap are the fingerprint of their unconventional character and imply superconducting pairing of $d$-wave symmetry. Here, using angle-resolved photoemission spectroscopy, we observe that the Weyl semimetal PtBi$_2$ harbors nodes in its superconducting gap, implying unconventional $i$-wave pairing symmetry. At temperatures below $10\,\mathrm{K}$, the superconductivity in PtBi$_2$ gaps out its topological surface states, the Fermi arcs, while its bulk states remain normal. The nodes in the superconducting gap that we observe are located exactly at the center of the Fermi arcs, and imply the presence of topologically protected Majorana cones around this locus in momentum space. From this, we infer theoretically that robust zero-energy Majorana flat bands emerge at surface step edges. This not only establishes PtBi$_2$ surfaces as unconventional, topological $i$-wave superconductors but also as a promising material platform in the ongoing effort to generate and manipulate Majorana bound states.
Mechanism for Nodal Topological Superconductivity on PtBi$_2$ Surface
Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）
Probing bulk superconductivity in centrosymmetric Te-doped PtBi$_2$ single crystals
Leibniz Institute for Solid State and Materials Research（莱布尼茨固体和材料研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Centro Atómico Bariloche, CNEA-CONICET（巴里洛切原子中心，CNEA-CONICET）；B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine（乌克兰国家科学院B.维尔金低温物理与工程研究所）；Kyiv Academic University（基辅学术大学）
Fermiology and spin polarization of topological surface states in PtBi$_2$
Norwegian University of Science and Technology（挪威科技大学）；University of Würzburg（维尔茨堡大学）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）；University of Amsterdam（阿姆斯特丹大学）；Univ. Nacional de Cuyo（门多萨国立大学）；Lund University（隆德大学）
Surface-extended Andreev bound states emerging from intrinsic surface superconductivity of PtBi$_2$
Universität Würzburg（维尔茨堡大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Bergische Universität Wuppertal（伍珀塔尔大学）；Leibniz-Institute for Solid State and Materials Research (IFW-Dresden)（德累斯顿固体与材料研究所）；Indian Institute of Science Education and Research（印度科学与教育研究所）；Technische Universität Dresden（德累斯顿工业大学）
Tunable Chern superconductivity of PtBi$_2$ in slab geometry
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿莱布尼茨固体与材料研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）；Institute for Theoretical Physics, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
A minimal model for the Weyl nodes and Fermi arcs of PtBi$_2$
Centro Atómico Bariloche（巴里洛切原子中心）；Instituto Balseiro, CNEA（巴尔塞罗研究所，CNEA）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（国家科学研究委员会）；Instituto de Nanociencia y Nanotecnología CNEA-CONICET（CNEA-CONICET纳米科学与技术研究所）
Owing to the specific topological states in nodal-line semimetals, novel topological superconductivity is expected to emerge in these systems. In this letter, by combination of the first-principles calculations and resistivity, susceptibility and specific heat measurements, we demonstrate that La$_3$Pt$_3$Bi$_4$ is a topologically nontrivial nodal-ring semimetal protected by the gliding-mirror symmetry even in the presence of spin-orbit coupling. Meanwhile, we discover bulk superconductivity with a transition temperature of $\sim$1.1 K, and an upper critical field of $\sim$0.41 T. These findin…
The combination with superconductivity and topological nontrivial band structure provides a promising route towards novel quantum states such as topological superconductivity. Here, we report the first observation of superconductivity (4.1 K) in Ba5In4Bi5 single crystal, a noncentrosymmetric topological semimetal featuring nodal chain loops at the high-symmetry points R and X. The magnetization, resistivity, and specific heat capacity measurements reveal that Ba5In4Bi5 is a moderately coupled type-II Bardeen-Cooper-Schrieffer superconductor. Bulk superconductivity is suggested from the magneti…
We found superconductivity in CaSb$_2$ with the transition temperature of 1.7 K by means of electrical-resistivity, magnetic-susceptibility, and specific-heat measurements. This material crystallizes in a nonsymmorphic structure and is predicted to have multiple Dirac nodal lines in the bulk electronic band structure protected by symmetry even in the presence of spin-orbit coupling. We discuss a possible topological superconductivity for the quasi-2-dimensional band originating mainly from one of the antimony sites.
We suggest theoretical explanation of the high upper critical magnetic field, perpendicular to conducting chains, Hc2, experimentally observed in the superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In particular, we compare the results of d-wave-like nodal, d-wave-like node-less, and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal scenario, superconductivity can naturally exceed both the orbital upper critical magnetic field and Clogston-Shandrasekhar paramagnetic limit as well as reach experimental value, Hc2 = 6T, in contrast to d-wave-like…
Finding of unconventional superconductivity (USC) in FeSe in an electronic "normal" state with broken $C_{4v}$ rotational symmetry testifies to the diversity of pairing states in Fe-based superconductors. Moreover, such USC emerges as a direct instability of a normal state without Landau Fermi liquid quasiparticles, increasingly dubbed a `strange' metal. Here, we combine inputs from a first-principles correlated electronic structure method (LDA+DMFT) and symmetry analyses to propose a novel mechanism for unconventional nodal superconductivity as a direct instability of an incoherent bad-metal …
We report a detailed study of superconductivity in polycrystalline SnTaS$_2$ using electrical transport, magnetization and heat capacity measurements. SnTaS$_2$ crystallizes in centrosymmetric hexagonal structure with space group $P6_3/mmc$. Electrical resistivity, magnetization and specific heat data suggest SnTaS$_2$ to be a weakly coupled, type-II superconductor with $T_c \approx$ 2.8 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 inclus…
We demonstrate that checkerboard magnet-superconductor hybrid systems possess a rich phase diagram exhibiting both strong topological superconducting (STSC) and topological nodal point superconducting (TNPSC) phases. We show that TNPSC phases exist both for ferromagnetic and antiferromagnetic systems, yielding a plethora of qualitatively different edge mode structures. Checkerboard MSH systems also facilitate the emergence of STSC phases which can be induced even in the limit of vanishing magnetization. Our results provide a new path for the quantum engineering of topological superconducting p…
We report the observation of two gaps in the superconductor SmFeAsO$_{0.9}$F$_{0.1}$ (F-SmFeAsO) with $T_c=51.5K$ as measured by point-contact spectroscopy. Both gaps decrease with temperature and vanish at $T_c$ and the temperature dependence of the gaps are described by the theoretical prediction of the Bardeen-Cooper-Schrieffer (BCS) theory. A zero-bias conductance peak (ZBCP) was observed, indicating the presence of Andreev bound states at the surface of F-SmFeAsO. Our results strongly suggest an unconventional nodal superconductivity with multiple gaps in F-SmFeAsO.
Weyl nodal loop semimetals (WNLs) host a closed nodal line loop Fermi surface in the bulk, protected zero-energy flat band, or drumhead, surface states, and strong spin-polarization. The large density of states of the drumhead states makes WNL semimetals exceedingly prone to electronic ordering. At the same time, the spin-polarization naively prevents conventional superconductivity due to its spin-singlet nature. Here we show the complete opposite: WNLs are extremely promising materials for superconducting Josephson junctions, entirely due to odd-frequency superconductivity. By sandwiching a W…
Infinite-layer nickelates present a new family of potential unconventional superconductors. A key open question is the superconducting pairing symmetry. We present low-temperature measurements of the London penetration depth in optimally doped La_{0.8}Sr_{0.2}NiO_{2}, Pr_{0.8}Sr_{0.2}NiO_{2}, and Nd_{0.8}Sr_{0.2}NiO_{2}. For La and Pr-nickelates, the superfluid density shows a quadratic temperature dependence, indicating nodal superconductivity in the presence of disorder. Nd-nickelate exhibits complex low-temperature behavior, which we attribute to magnetic impurities. These results are consi…
We performed 121/123Sb-nuclear quadrupole resonance (NQR) measurements on the superconducting (SC) line-nodal material CaSb2 in order to investigate electronic properties in the normal and SC states from a microscopic point of view. In the normal state, the nuclear spin-lattice relaxation rate 1/T1 for the Sb(1) site, which is responsible for the line-nodal parts, is approximately proportional to temperature, indicating the conventional Fermi liquid state. From comparison with band structure calculations, it is considered that the NQR properties related to the line-nodal character are hidden b…
We performed point-contact Andreev reflection spectroscopy measurements in Ca(Fe_{1-x}Co_x)2As2 single crystals with effective x=0.060 +- 0.005. The spectra of ab-plane contacts show a zero-bias maximum and broad shoulders at about 5-6 meV. Their fit with the three-dimensional Blonder-Tinkham-Klapwijk model (making use of a analytical expression for the Fermi surface that mimics the one calculated from first principles) shows that this compound presents a large isotropic gap on the quasi-2D electronlike Fermi surface sheets and a smaller anisotropic (possibly nodal) gap on the 3D holelike Ferm…
CaSb2 is a topological nodal-line semimetal that becomes superconducting below 1.6 K, providing an ideal platform to investigate the interplay between topologically nontrivial electronic bands and superconductivity. In this work, we investigated the superconducting order parameter of CaSb2 by measuring its magnetic penetration depth change Δλ(T) down to 0.07 K, using a tunneling diode oscillator (TDO) based technique. Well inside the superconducting state, Δλ(T) shows an exponential activated behavior, and provides direct evidence for a nodeless superconducting gap. By analyzing the temperatur…
We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi poin…
We report an investigation of the London penetration depth $Δλ(T)$ on single crystals of the layered superconductor Ta$_4$Pd$_3$Te$_{16}$, where the crystal structure has quasi-one-dimensional characteristics. A linear temperature dependence of $Δλ(T)$ is observed for $T\ll T_c$, in contrast to the exponential decay of fully gapped superconductors. This indicates the existence of line nodes in the superconducting energy gap. A detailed analysis shows that the normalized superfluid density $ρ_s(T)$, which is converted from $Δλ(T)$, can be well described by a multigap scenario, with nodes in one…
The temperature dependent evolution of the renormalization effect in optimally-doped Bi2212 along the nodal direction has been studied via angle-resolved photoemission spectroscopy. Fine structure is observed in the real part of the self-energy (Re$Σ$), including a subkink and maximum, suggesting that electrons couple to a spectrum of bosonic modes, instead of just one mode. Upon cooling through the superconducting phase transition, the fine structures of the extracted Re$Σ$ exhibit a two-processes evolution demonstrating an interplay between kink renormalization and superconductivity. We show…
Previous works on nodal d-wave superconductors have shown that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like modulated superconducting (SC) state can be realized with no magnetic field when quasiparticles acquire an additional linear term in the wavevector in their dispersion. In the present work, stability of such a novel modulated SC state in an artificial film against an applied magnetic field is studied. As a reflection of the presence of the two different FFLO states, one close to zero field and the other at the high field end, in a single field v.s. temperature phase diagram of thin fil…
NaAlSi is an sp electron superconductor crystallizing in a layered structure of the anti-PbFCl type with a relatively high transition temperature Tc of ~7 K. Recent electronic state calculations revealed the presence of topological nodal lines in the semimetallic band structure, which attracted much attention owing to the superconductivity. However, experimental investigation remained limited because of the lack of single crystals. Here, we successfully prepared single crystals of NaAlSi by a Na-Ga flux method and characterized their superconducting and normal-state properties through electric…
Phonon-driven nodal surface superconductivity of Fermi arcs
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿亥姆霍兹固体与材料研究所）；Department of Mathematics, City St George’s, University of London（伦敦大学城市圣乔治学院数学系）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）
Three-component fermion beyond the conventional Dirac Weyl Majorana classification attracts extensive attentions recently and many efforts have been paid to explore their superconductivity. Based on first-principles calculations, we systematically investigate the electron-phonon coupling (EPC) in the three-component fermion materials WN, WC and TaN. The EPC in pristine and pressured WC and TaN are to small to induce superconductivity. Electron doping can efficiently enhance the EPC strength and the predicted Tcs reach the value of experiments. Upon 0.6 electron/unitcell doping, the EPC strengt…
Distinguishing nodal and nonunitary superconductivity in quasiparticle interference of an Ising superconductor with Rashba spin-orbit coupling: an example of NbSe$_2$
Coexistence of topological bands and charge density wave (CDW) in topological materials has attracted immense attentions because of their fantastic properties, such as axionic-CDW, three-dimensional quantum Hall effect, etc. In this work, a nodal-line semimetal InxTaS2 characterized by CDW and superconductivity is successfully synthesized, whose structure and topological bands (two separated Wely rings) are similar to In0.58TaSe2. A 2 x 2 commensurate CDW is observed at low temperature in InxTaS2, identified by transport properties and STM measurements. Moreover, superconductivity emerges belo…
Point contact Andreev reflection spectra have been taken as a function of temperature and magnetic field on the polycrystalline form of the newly discovered iron-based superconductor Sr2ScFePO3. A zero bias conductance peak which disappears at the superconducting transition temperature, dominates all of the spectra. Data taken in high magnetic fields show that this feature survives until 7T at 2K and a flattening of the feature is observed in some contacts. Here we inspect whether these observations can be interpreted within a d-wave, or nodal order parameter framework which would be consisten…
We measure changes in the penetration depth $λ$ of the $T_c \approx 6$ K superconductor LaFePO. In the process scanning SQUID susceptometry is demonstrated as a technique for accurately measuring {\it local} temperature-dependent changes in $λ$, making it ideal for studying early or difficult-to-grow materials. $λ$ of LaFePO is found to vary linearly with temperature from 0.36 to $\sim$2 K, with a slope of 143$\pm$15 Å/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to $\sim T_c/3$ is similar to the cuprate superconductors, indicating well-developed no…
In the last few years the gap symmetries of many new superconductors,including Sr$_2$RuO$_4$, CeCoIn$_5$, $κ$-(ET)$_{2}$Cu(NCS)$_{2}$, YNi$_{2}$B$_{2}$C and PrOs$_{4}$Sb$_{12}$, have been identified via angle-dependent magnetothermal conductivity measurements. However, a controversy still persists as to the nature of the superconductivity in Sr$_2$RuO$_4$. For PrOs$_{4}$Sb$_{12}$, spin-triplet superconductivity has recently been proposed. Here, we also propose g-wave superconductivity for UPd$_2$Al$_3$ (i.e., $Δ({\bf k})=Δ\cos(2χ), χ= ck_{z}$) based on recent thermal conductivity data.
We report muon spin relaxation and rotation ($μ$SR) measurements on hydrothermally-grown single crystals of the tetragonal superconductor~FeS, which help to clarify the controversial magnetic state and superconducting gap symmetry of this compound. $μ$SR time spectra were obtained from 280~K down to 0.025~K in zero field (ZF) and applied fields up to 20 mT. In ZF the observed loss of initial asymmetry (signal amplitude) and increase of depolarization rate~$Λ_\mathrm{ZF}$ below 10~K indicate the onset of static magnetism, which coexists with superconductivity below $T_c$. Transverse-field $μ$SR…
We investigate the effect of a spin-density wave (SDW) on $s_{\pm}$ superconductivity in Fe-based superconductors. We show that, contrary to the common wisdom, no nodes open at the new, reconnected Fermi surfaces when the hole and electron pockets fold down in the SDW state, despite the fact that the $s_{\pm}$ gap changes sign between the two pockets. Instead, the order parameter preserves its sign along the newly formed Fermi surfaces. The familiar experimental signatures of an $s_{\pm}$ symmetry are still preserved, although they appear in a mathematically different way. For a regular $s$ ca…
We report $^{31}$P- and $^{75}$As-NMR studies on (Ca$_4$Al$_2$O$_{6}$)Fe$_2$(As$_{1-x}$P$_x$)$_2$ with an isovalent substitution of P for As. We present the novel evolution of emergent phases that the nodeless superconductivity (SC) in 0$\le x \le$0.4 and the nodal one around $x$=1 are intimately separated by the onset of a commensurate stripe-type antiferromagnetic (AFM) order in 0.5$\le x \le$ 0.95, as an isovalent substitution of P for As decreases a pnictogen height $h_{Pn}$ measured from the Fe plane. It is demonstrated that the AFM order takes place under a condition of 1.32Å$\le h_{Pn} …
We consider the problem of the orbital upper critical magnetic field, parallel to the most conducting axis of a quasi-one-dimensional layered superconductor. It is shown that superconductivity can be destroyed through orbital effects at fields much higher than the so-called Clogston-Chandrasekhar paramagnetic limiting field, $H_p$, provided that superconducting pairing of electrons are of a triplet nature. We demonstrate that the superconducting state of the quasi-one-dimensional layered conductor, $\mathrm{Li_{0.9}Mo_6O_{17}}$, is well described by the suggested theory. To this end, we consid…
NaAlSi is a quasi-two-dimensional semimetal with superconductivity below Tc = 6.8 K and a band structure characterized by nodal lines near the Fermi level and potential topological surface states. Electrical resistivity measurements on its superconducting transitions in magnetic fields were made using plate-like single crystals. In the magnetic field-temperature phase diagram, we observed a substantial reduction in resistivity in a pre-transitional zone above the bulk superconducting regime only when the magnetic fields were perpendicular to the plane, rather than parallel to it. Significant s…
ZrSiS was recently shown to be a new material with topologically non-trivial band structure which exhibits multiple Dirac nodes and a robust linear band dispersion up to an unusually high energy of 2\,eV. Such a robust linear dispersion makes the topological properties of ZrSiS insensitive to perturbations like carrier doping or lattice distortion. Here we show that a novel superconducting phase with a remarkably high $T_c$ of 7.5\,K can be induced in single crystals of ZrSiS by a non-superconducting metallic tip of Ag. From first-principles calculations we show that the observed superconducti…
The physical properties of the Zr$_5$Pt$_3$ compound with interstitial carbon in hexagonal D8$_8$-structure was investigated. A set of macroscopic measurements reveal a bulk superconducting at approximately 7 K for Zr$_5$Pt$_3$C$_{0.3}$ close to Zr$_5$Pt$_3$, also with a correlate anomalous resistivity behavior. However, both the signatures of strong electron-electron interaction, and the electronic contribution to specific heat, increase dramatically with the C doping. For the first time the x-ray photoelectron spectra compared with DFT/PWLO calculations of electronic structure show a complex…
