Simultaneous Nodal Superconductivity and Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor CaPtAs
T. Shang, M. Smidman, A. Wang, L. -J. Chang, C. Baines, M. K. Lee, Z. Y. Nie, G. M. Pang, W. Xie, W. B. Jiang, M. Shi, M. Medarde, T. Shiroka, H. Q. Yuan
By employing a series of experimental techniques, we provide clear evidence that CaPtAs represents a rare example of a noncentrosymmetric superconductor which simultaneously exhibits nodes in the superconducting gap and broken time-reversal symmetry (TRS) in its superconducting state (below $T_c$ $\approx$ 1.5 K). Unlike in fully-gapped superconductors, the magnetic penetration depth $λ(T)$ does not saturate at low temperatures, but instead it shows a $T^2$-dependence, characteristic of gap nodes. Both the superfluid density and the electronic specific heat are best described by a two-gap model comprising of a nodeless gap and a gap with nodes, rather than by single-band models. At the same time, zero-field muon-spin spectra exhibit increased relaxation rates below the onset of superconductivity, implying that TRS is broken in the superconducting state of CaPtAs, hence indicating its unconventional nature. Our observations suggest CaPtAs to be a new remarkable material which links two apparently disparate classes, that of TRS-breaking correlated magnetic superconductors with nodal gaps and the weakly-correlated noncentrosymmetric superconductors with broken TRS, normally exhibiting only a fully-gapped behavior.
We present synthesis and $^{75}$As-nuclear quadrupole resonance (NQR) measurements for the noncentrosymmetric superconductor CaPtAs with a superconducting transition temperature $T_c$ of $\sim 1.5$ K. We discovered two different forms of CaPtAs during synthesis; one is a high-temperature tetragonal form that was previously reported, and the other is a low-temperature form consistent with the orthorhombic structure of CaPtP. According to the $^{75}$As-NQR measurement for superconducting tetragonal CaPtAs, the nuclear spin-lattice relaxation rate $1/T_1$ has an obvious coherence peak below $T_c$…
We report the discovery of a new noncentrosymmetric superconductor CaPtAs. It crystallizes in a tetragonal structure (space group $I4_1md$, No.109), featuring three dimensional honeycomb networks of Pt-As and a much elongated $c$-axis ($a = b = 4.18 $ Å, and $c = 43.70 $ Å). The superconductivity of CaPtAs with $T_c$ = 1.47 K was characterized by means of electrical resistivity, specific heat, and ac magnetic susceptibility. The electronic specific heat $C_\mathrm{e}(T)/T$ shows evidence for a deviation from the behavior of a conventional BCS superconductor, and can be reasonably fitted by a $…
Low-temperature thermal conductivity measurements were performed on single crystal of PbTaSe$_2$, a noncentrosymmetric superconductor with topological bulk nodal lines in the electronic band structure. It is found that the residual linear term $κ_0/T$ is negligible in zero magnetic field. Furthermore, the field dependence of $κ_0/T$ exhibits a clear "$S$"-shape curve. These results suggest that PbTaSe$_2$ has multiple nodeless superconducting gaps. Therefore, the spin-triplet state with gap nodes does not play an important role in this noncentrosymmetric superconductor with strong spin-orbital…
We study the stability of topologically protected zero-energy flat bands at the surface of nodal noncentrosymmetric superconductors, accounting for the alteration of the gap near the surface. Within a selfconsistent mean-field theory, we show that the flat bands survive in a broad temperature range below the bulk transition temperature. There is a second transition at a lower temperature, however, below which the system spontaneously breaks time-reversal symmetry. The surface bands are shifted away from zero energy and become weakly dispersive. Simultaneously, a spin polarization and an equili…
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…
The newly discovered noncentrosymmetric superconductor ThCoC$_{2}$ exhibits numerous unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC$_{2}$ by muon spin rotation/relaxation $(μ$SR) measurements. Temperature dependence of the magnetic penetration depth measured using the transverse field $μ$SR measurement reveal the evidence of nodal pairing symmetry. To understand these findings, we carry out the calculations of superconducting pairing eigenvalue and eigenfunction symmetry due to the spin-fluctuation mechanism…
Surfaces of nodal noncentrosymmetric superconductors can host flat bands of Majorana modes, which provide a promising platform for quantum computation if one can find methods for manipulating localized Majorana wave packets. We study the fate of such flat bands when part of the surface is subjected to an exchange field induced by a ferromagnetic insulator. We use exact diagonalization to find the eigenstates and eigenenergies of the Bogoliubov-de Gennes Hamiltonian of a model system, for which an exchange field is applied along a strip on the surface of a slab. We consider different orientatio…
We study two-dimensional noncentrosymmetric nodal superconductors under Zeeman field and clarify the field angle dependence of topological properties. It has been shown that the nodal excitation acquires an excitation gap due to the Zeeman field perpendicular to anti-symmetric spin-orbit coupling, and then gapful topological superconductivity is realized. We show that the system undergoes gapful-gapless transition against tilting of the field. The gapless phase remains to show a finite band gap and unusual Majorana edge states in between the bulk bands. The Majorana edge states naturally propa…
Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians.…
For a noncentrosymmetric superconductor such as Y$_2$C$_3$, we consider a parity-mixing model composed of spin-singlet s-wave and spin-triplet f-wave pairing components. The $d$-vector in f-wave state is chosen to be parallel to the Dresselhaus asymmetric spin-orbit coupling vector. It is found that, the quasiparticle excitation spectrum exhibits distinct nodal structure as a consequence of parity-mixing. Our calculation predict anomalous noninteger power laws for low-temperature nuclear spin-lattice relaxation rate $T_{1}^{-1}$. We demonstrate particularly that such a model can qualitatively …
A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. An augmented cluster magnetic multipole order in a crystal lacking local space inversion parity may break global inversion symmetry, and then, it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by Sr$_2$IrO$_4$. We find that even-parity superconductivity is more significantly suppressed by a spin-orbit coupl…
Three-dimensional line-nodal superconductors exhibit nontrivial topology, which is protected by the time-reversal symmetry. Here we investigate four types of short-range interaction between the gapless line-nodal fermionic quasiparticles by carrying renormalization group analysis. We find that such interactions can induce the dynamical breaking of time-reversal symmetry, which alters the topology and might lead to six possible distinct superconducting states, distinguished by the group representations. After computing the susceptibilities for all the possible phase-transition instabilities, we…
We report the electronic properties of superconductivity in the topological nodal-line semimetal PbTaSe$_2$. Angle-resolved photoemission measurements accompanied by band calculations confirmed the nodal-line band structure in the normal state of single crystalline PbTaSe$_2$. Resistivity, magnetic-susceptibility and specific heat measurements have also been performed on high-quality single crystals. We observed upward features and large anisotropy in upper critical field ($H_{c2}$) measured in-plane (H//\textbf{ab}) and out-plane (H//\textbf{c}), respectively. Especially, $H_{c2}$ measured in…
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topol…
We report the finding of a novel pairing state in a newly discovered superconductor Na$_2$Cr$_3$As$_3$. This material has a noncentrosymmetric quasi-one-dimensional crystal structure and is superconducting at $T_{\mathrm{C}}\sim$ 8.0 K. We find that the magnetic penetration depth data suggests the presence of a nodal line $p_z$-wave pairing state with zero magnetic moment using transverse-field muon-spin rotation (TF-$μ$SR) measurements. The nodal gap observed in Na$_2$Cr$_3$As$_3$ compound is consistent with that observed in isostructural (K,Cs)$_2$Cr$_3$As$_3$ compounds using TF-$μ$SR measur…
We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in the absence of external magnetic fields or Zeeman fields. Spin-singlet ($Δ_s$) and spin-triplet ($Δ_t$) pairings can coexist in superconductors whose crystal structure lacks inversion symmetry. The TRS can be spontaneously broken once a relative phase of $\pmπ/2$ is developed, forming a TRS-breaking unitary pairing state ($Δ_s\pm iΔ_t$). We demonstrate that such unitary pairing could give rise to spontaneous spin-polarization w…
We report superconductivity in Sn$_{x}$NbSe$_{2-δ}$, a topological nodal-line semimetal candidate with a noncentrosymmetric crystal structure. The superconducting transition temperature $T_{c}$ of this compound is extremely sensitive to Sn concentration $x$ and Se deficiency $δ$, 5.0 K for Sn$_{0.13}$NbSe$_{1.70}$ and 8.6 K for Sn$_{0.14}$NbSe$_{1.71}$ and Sn$_{0.15}$NbSe$_{1.69}$. In all samples, the temperature dependence of the upper critical field $H_{c2}(T)$ differs from the prediction of the Werthamer-Helfand-Hohenberg theory. While the zero-temperature value of the in-plane upper critic…
Superconductors without inversion symmetry in their crystal structure are known to exhibit unconventional properties. Recently, based on the measured temperature dependence of the magnetic field penetration depth, superconductivity in noncentrosymmetric $\mathrm{ThCoC_2}$ was proposed to be a nodal $d$-wave and mediated by the spin fluctuations. Moreover, a non-BCS behavior of the temperature dependence of the electronic specific heat and the magnetic upper critical field were reported. In this work, the electronic structure, phonons and electron-phonon coupling are studied in $\mathrm{ThCoC_2…
Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned goal, the existence of superconducting nodes, one of the few important experimental signatures of unconventional superconductivity, plays a vital role in exploring the possibility of unconventional superconductivity. The interplay between superconducting nodes and topology has been actively investigated, and intensive research in the past decade has revealed va…
Spin-Orbital Intertwined Topological Superconductivity in a Class of Correlated Noncentrosymmetric Materials
Anhui Provincial Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心安徽省低能量子材料与器件重点实验室）；University of Science and Technology of China（中国科学技术大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Based on first-principles calculations and effective model analysis, we propose that the noncentrosymmetric superconductor YCoC$_2$ in normal state is a topological semimetal. In the absence of spin-orbit coupling (SOC), it can host two intersecting nodal rings protected by two mirror planes, respectively. One ring is composed of type-I nodes, where the two crossing bands have opposite slop sign in their dispersions. The other ring consists of both type-I and type-II nodes (the slop signs of the two bands are the same in certain direction). In the presence of SOC, the former nodal ring is gapp…
We show that Weyl superconductivity can be induced by finite supercurrent in noncentrosymmetric spin-orbit-coupled superconductors with line nodes. We introduce a three-dimensional tight-binding model of a tetragonal superconductor in a $D+p$-wave pairing state with a finite center-of-mass momentum, and elucidate that a line-nodal to point-nodal spectral transition occurs by applying an infinitesimal supercurrent. We also clarify that the higher-order effect in spin-orbit coupling is particularly important for this phenomenon. The point nodes are protected by topologically nontrivial Weyl char…
We propose a generic scenario for realizing gapful topological superconductors (TSCs) from gapless spin-singlet superconductors (SCs). Noncentrosymmetric nodal SCs in two dimension are shown to be gapful under a Zeeman field, as a result of the cooperation of inversion-symmetry breaking and time-reversal-symmetry breaking. In particular, non-s-wave SCs acquire a large excitation gap. Such paramagnetically-induced gapful SCs may be classified into TSCs in the symmetry class D specified by the Chern number. We show nontrivial Chern numbers over a wide parameter range for spin-singlet SCs. A vari…
We study three-dimensional time-reversal-invariant topological superconductivity in noncentrosymmetric materials such as RhSi, CoSi, and AlPt which host coupled multifold nodes energetically split by the spin-orbit coupling at the same time-reversal-invariant momentum (TRIM). The topological superconductivity arises from the $s_{+} \oplus s_{-}$ gap function, which is $\boldsymbol{k}$ independent, but with opposite signs for the two nodes split at the same TRIM. We consider various electron-electron interactions in the tight-binding model for RhSi and find that the topological superconducting …
Recently, multifold fermions characterized by band crossings with multifold degeneracy and Fermi surfaces with nontrivial Chern numbers have been discovered experimentally in AlPt[arXiv:1812.03310] and XSi(X=Rh,Co)[arXiv:1812.04466][arXiv:1901.03358][arXiv:1809.01312]. In this work, we largely expand the family of multifold fermion materials by pointing out that several well-studied noncentrosymmetric superconductors are indeed multifold fermion metals. Importantly, their normal state topological properties, which have been ignored in previous studies, play an important role in the superconduc…
Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair pote…
