We present an explanation of the dynamical in-gap spin mode in LSCO induced by an applied magnetic field H as recently observed by J. Chang et al. Our model consists of a phenomenological spin-only Hamiltonian, and the softening of the spin mode is caused by vortex pinning of dynamical stripe fluctuations which we model by a local ordering of the exchange interactions. The spin gap vanishes experimentally around H=7T which in our scenario corresponds to the field required for overlapping vortex regions.
To understand the impurity effect on Tc in FeAs superconductors, we analyze a simple two-band BCS model with repulsive interband interaction. The realized fully-gapped superconducting state with sign reversal, which is predicted by spin fluctuation theories in this compound, is suppressed by impurities due to the interband hopping of Cooper pairs, if the interband impurity scattering $I'$ is equal to the intraband one $I$. When $|I'/I| < 1$, in highly contrast, Tc is almost unchanged by strong impurity scattering since the interband scattering is almost prohibited by the multiple scattering ef…
We report crystallographic, specific heat, transport, and magnetic properties of the recently discovered noncentrosymmetric 5d-electron superconductors CaIrSi3 (Tc = 3.6 K) and CaPtSi3 (Tc = 2.3 K). The specific heat suggests that these superconductors are fully gapped. The upper critical fields are less than 1 T, consistent with limitation by conventional orbital depairing. High, non-Pauli-limited μ0 Hc2 values, often taken as a key signature of novel noncentrosymmetric physics, are not observed in these materials because the high carrier masses required to suppress orbital depairing and reve…
We investigate the superconducting gap function of topological superconductor PbTaSe$_2$. Temperature, magnetic field, and three-dimensional (3D) field-angle dependences of the specific heat prove that the superconductivity of PbTaSe$_2$ is fully-gapped, with two isotropic $s$-wave gaps. The pair-breaking effect is probed by systematically increasing non-magnetic disorders through H$^+$-irradiations. The superconducting transition temperature, $T_{\rm{c}}$, is found to be robust against disorders, which suggests that the pairing should be sign-preserved rather than sign-reversed.
To elucidate the nature of the superconducting ground state of the geometrically frustrated pyrochlore KOs2O6 (Tc=9.6K), the thermal conductivity was measured down to low temperatures (~Tc/100). We found that the quasiparticle mean free path is strikingly enhanced below a transition at Tp=7.5K, indicating enormous electron inelastic scattering in the normal state. In a magnetic field the conduction at T ->0K is nearly constant up to ~0.4Hc2, in contrast with the rapid growth expected for superconductors with an anisotropic gap. This unambiguously indicates a fully gapped superconductivity, in …
We have performed low-temperature specific heat and thermal conductivity measurements of the Ni-based superconductor BaNi$_2$As$_2$ ($T_\mathrm{c}$ = 0.7 K) in magnetic field. In zero field, thermal conductivity shows $T$-linear behavior in the normal state and exhibits a BCS-like exponential decrease below $T_\mathrm{c}$. The field dependence of the residual thermal conductivity extrapolated to zero temperature is indicative of a fully gapped superconductor. This conclusion is supported by the analysis of the specific heat data, which are well fit by the BCS temperature dependence from $T_\ma…
We have performed low-temperature specific heat $C$ and thermal conductivity $κ$ measurements on the Ni-pnictide superconductors BaNi$_2$As$_2$ ($T_\mathrm{c}$=0.7 K and SrNi$_2$P$_2$ ($T_\mathrm{c}$=1.4 K). The temperature dependences $C(T)$ and $κ(T)$ of the two compounds are similar to the results of a number of s-wave superconductors. Furthermore, the concave field responses of the residual $κ$ for BaNi$_2$As$_2$ rules out the presence of nodes on the Fermi surfaces. We postulate that fully gapped superconductivity could be universal for Ni-pnictide superconductors. Specific heat data on B…
Motivated by the fully gapped superconductivity in iron-based superconductors with uncompensated electron pockets, we propose a spin singlet, but orbital triplet analogue of the superfluid phase of He-3B. We show that orbital triplets with a nominal d-wave symmetry at the iron sites can transform as s-wave pairs under rotations about the selenium sites. Linear combinations of such d$_{xy}$ and d$_{x^{2}-y^{2}}$ triplets form a fully gapped, topological superconductor. Raman-active excitations are predicted to develop below the superconducting transition temperature.
We show that a layered superconductor, described by a two-component order parameter, has a gapped state above the ground state, topologically protected from decay, containing flow and counter flow in the absence of an applied magnetic field. This state is made of skyrmions, breaks time reversal symmetry and produces a weak local magnetic field below the present threshold of detection by $μ$SR and NMR/NQR. We estimate the density of carriers that condense into the pseudogap.
High-resolution specific-heat measurements of the organic superconductor kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br in the superconducting (B = 0) and normal (B = 14 T) state show a clearly resolvable anomaly at Tc = 11.5 K and an electronic contribution, Ces, which can be reasonably well described by strong-coupling BCS theory. Most importantly, Ces vanishes exponentially in the superconducting state which gives evidence for a fully gapped order parameter.
Superconductors derived from topological insulators and topological crystalline insulators by doping have long been considered to be candidates as topological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topological crystalline insulator with mirror symmetry protected surface states on (001), (011) and (111) oriented surfaces. The superconductor (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping in Pb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Here we report the first scanning tunneling spectroscopy measurement of the superconducting state as well a…
Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure $d$-wave superconductor only allows virtual bound states. Fully gapped $d$-wave superconducting states have however been proposed in several cuprate systems thanks to subdominant order parameters producing $d+is$- or $d+id'$-wave superconducting stat…
There are indications that some high temperature unconventional superconductors have a "complex" d-wave order parameter (with an admixture of s-wave) leading to nonzero energy gap. Since the coherence length is short and the Fermi energy is relatively small the quasiclassical approach is inapplicable and the more complicated Bogoliubov-deGennes equations should be used to investigate the excitation spectrum of such a material in a magneric field. It turns out that equations for the gapped chiral d-wave superconductor, simplify considerably and is the basis for any superconductor of that type w…
In search of the origin of superconductivity in diluted rhenium superconductors and their significantly enhanced $T_c$ compared to pure Be (0.026 K), we investigated the intermetallic ReBe$_{22}$ compound, mostly by means of muon-spin rotation/relaxation ($μ$SR). At a macroscopic level, its bulk superconductivity (with $T_c=9.4$ K) was studied via electrical resistivity, magnetization, and heat-capacity measurements. The superfluid density, as determined from transverse-field $μ$SR and electronic specific-heat measurements, suggest that ReBe$_{22}$ is a fully-gapped superconductor with some mu…
We measured the ultra-low-temperature specific heat and thermal conductivity of Au$_2$Pb single crystal, a possible three-dimensional Dirac semimetal with a superconducting transition temperature $T_c \approx$ 1.05 K. The electronic specific heat can be fitted by a two-band s-wave model, which gives the gap amplitudes $Δ_1$(0)/$k_BT_c$ = 1.38 and $Δ_2$(0)/$k_BT_c$ = 5.25. From the thermal conductivity measurements, a negligible residual linear term $κ_0/T$ in zero field and a slow field dependence of $κ_0/T$ at low field are obtained. These results suggest that Au$_2$Pb has a fully gapped supe…
The search for topological superconductors (TSCs) is one of the most urgent contemporary problems in condensed matter systems. TSCs are characterized by a full superconducting gap in the bulk and topologically protected gapless surface (or edge) states. Within each vortex core of TSCs, there exist the zero energy Majorana bound states, which are predicted to exhibit non-Abelian statistics and to form the basis of the fault-tolerant quantum computation. So far, no stoichiometric bulk material exhibits the required topological surface states (TSSs) at Fermi level combined with fully gapped bulk …
We solve the Bogoliubov-de Gennes equations self-consistently for d-wave superconductors with [110] surfaces. We find spontaneous breaking of time-reversal symmetry (TRS) caused by the spontaneous occurrence of a complex order parameter with an extended s-wave symmetry along the [110] surfaces. In the TRS-breaking phase, the d-wave order parameter itself becomes complex. We also show that vortex-antivortex pairs can appear along the [110] surfaces of nanoribbons. These pairs are detectable with surface sensitive probes.
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Neel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors.
It is now well established that at a superconductor/ferromagnet (S/F) interface an unconventional superconducting state arises in which the pairing state is odd-frequency. The hallmark signature of this superconducting state is generally understood to be an enhancement of the electronic density of states (DoS) at subgap energies close to the S/F interface. However, here we show that an odd frequency state can be present even if the DoS is fully gapped. As an example, we show that this is the case in the pioneering S/FI (where FI is a insulating ferromagnet) tunneling experiments of Meservey an…
The superconducting gap structures in the transition-metal-based kagome metal AV$_3$Sb$_5$ (A=K,Rb,Cs), the first family of quasi-two-dimensional kagome superconductors, remain elusive as there is strong experimental evidence for both nodal and nodaless gap structures. Here we show that the dichotomy can be resolved because of the coexistence of time-reversal symmetry breaking with a conventional fully gapped superconductivity. The symmetry protects the edge states which arise on the domains of the lattice symmetry breaking order to remain gapless in proximity to a conventional pairing. We dem…
We have measured the low-temperature specific heat C(T) for polycrystalline MgB_2 prepared by high pressure synthesis. C(T) below 10 K vanishes exponentially, which unambiguously indicates a fully opened superconducting energy gap. However, this gap is found to be too small to account for Tc of MgB_2. Together with the small specific heat jump DeltaC/gamma_nTc=1.13, scenarios like anisotropic s-wave or multi-component order parameter are called for. The magnetic field dependence of gamma(H) is neither linear for a fully gapped s-wave superconductor nor H^1/2 for nodal order parameter. It seems…
Spin fluctuations are considered to be one of the candidates that drive a sign-reversed s^{\pm} superconducting state in the iron pnictides. In the magnetic scenario, whether the spin fluctuation spectrum exhibits certain unique fine structures is an interesting aspect for theoretical study in order to understand experimental observations. We investigate the detailed momentum dependence of the short-range spin fluctuations using a 2-orbital model in the self-consistent fluctuation exchange approximation and find that a common feature of those fluctuations that are capable of inducing a fully g…
We investigated the superconducting gap structure of SrNi$_2$P$_{2}$ ($T_c$=1.4 K) via low-temperature magneto-thermal conductivity $κ(T,H)$ measurements. Zero field thermal conductivity $κ$ decreases exponentially $κ\propto$ exp($-aT_c/T$) with $a$=1.5, in accord with the BCS theory, and rolls over to a phonon-like $κ\propto T^3$ behavior at low temperature, similar to a number of conventional s-wave superconductors. In addition, we observed a "concave" field dependence of the residual linear term $κ_0(H)/T$. These facts strongly rule out the presence of nodes in the superconducting energy ga…
Layered, non-centrosymmetric, heavy element PbTaSe2 is found to be superconducting. We report its electronic properties accompanied by electronic structure calculations. Specific heat, electrical resistivity and magnetic susceptibility measurements indicate that PbTaSe2 is a moderately coupled, type-II BCS superconductor (Tc = 3.72 K, Ginzburg-Landau parameter Kappa = 14) with an electronphonon coupling constant of Lambda_ep = 0.74. Electronic structure calculations reveal a single bulk 3D Dirac cone at the K point of the Brillouin Zone derived exclusively from its hexagonal Pb layer; it is si…
The search for materials similar to magnesium diboride, MgB2, based on structure and electronic similarity did not produce close enough superconductors in terms of Tc. Changing the search to iso-electronic and iso-atomic number equivalents opened new doors to very many possible MgB2-like superconductors. Here we present LiBeP which meets these new conditions. We estimate its Tc to be 34.5K if two-gapped or 17.2K if single gapped.
We use resonant inelastic x-ray scattering (RIXS) to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr$_{0.9}$La$_{0.1}$CuO$_2$ (SLCO). We detect a plasmon gap of $\sim$~120 meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in SLCO are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered $t$-$J$-$V$ model calculations. A similar analysis performed on recent RIXS data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interl…
A theory of superconductivity based on the two-body Cooperon propagator is presented. This theory takes the form of a modified Gorkov equation for the Green's function and allows one to model the effect of local superconducting correlations and long range phase fluctuations on the spectral properties of high temperature superconductors, both above and below Tc. A model is proposed for the Cooperon propagator, which provides a simple physical picture of the pseudo-gap phenomenon, as well as new insights into the doping dependence of the spectral properties. Numerical calculations of the density…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well known to possess a half quantum Hall effect. Furthermore, it has been known that the surface of a weak 3D topological insulator gapped by a charge density wave exhibits a half quantum spin Hall effect. To generalize these results to all Altland-Zirnbauer symmetry classes of topological insulators and superconductors, we reproduce the classification table for th…
We study the density of states in disordered s-wave superconductors with a small gap anisotropy. Disorder comes in the form of common nonmagnetic scatterers and pairing-potential impurities, which interact with electrons via an electric potential and a local distortion of the superconducting gap. A set of equations for the quasiclassical Green functions is derived and solved. Within one spin sector, pairing-potential impurities and weak spin-polarized magnetic impurities have essentially the same effect on the density of states. We show that if the gap is isotropic, an isolated impurity with s…
The recent discovery of the topologically protected surface states in the beta-phase of PdBi2 has reignited the research interest in this class of superconductors. Here, we show results of our muon spin relaxation and rotation (muSR) measurements carried out to investigate the superconducting and magnetic properties and the topological effect in the superconducting ground state of beta-PdBi2. Zero-field muSR data reveal that no sizeable spontaneous magnetization arises with the onset of superconductivity implying that the time reversal symmetry is preserved in the superconducting state of beta…
We report a comprehensive study of the noncentrosymmetric NbReSi superconductor by means of muon-spin rotation and relaxation ($μ$SR) and nuclear magnetic resonance (NMR) techniques. NbReSi is a bulk superconductor with $T_c = 6.5$ K, characterized by a large upper critical field, which exceeds the Pauli limit. Both the superfluid density $ρ_\mathrm{sc}(T)$ (determined via transverse-field $μ$SR) and the spin-lattice relaxation rate $T_1^{-1}(T)$ (determined via NMR) suggest a nodeless superconductivity (SC) in NbReSi. We also find signatures of multigap SC, here evidenced by the field-depende…
The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered to the Fermi surface. Importantly this phenomenon is observed for compounds across several different cuprate families. In this letter we propose an exciting possibility, namely the fully gapped state is a topological superconductor.
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 mode…
Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g. superconductivity) provides a platform for exploring novel quantum phenomena and new functionalities, such as 1D chiral or helical gapless Majorana fermions, and Majorana zero modes which may find application in fault-tolerant quantum computation. Inducing superconductivity on topological surface states is a prerequisite for their experimental realization. He…
We report on the superconducting gap and pairing symmetry in layered superconductor Bi4O4S3. The measurement of temperature dependence of magnetic penetration depth was carried out using tunnel diode oscillator technique. It is observed that Bi4O4S3 is a conventional s-wave type superconductor with fully developed gap. The zero-temperature value of the superconducting energy gap Δ0 was found to be 1.54 meV, corresponding to the ratio 2Δ0/kBTc=7.2 which is much higher than the BCS value of 3.53. In the superconducting range, superfluid density is very well described by single gap s- wave model.
We investigate low-temperature electronic properties of the nondimeric organic superconductor $β^{\prime\prime}$-(BEDT-TTF)$_4$[(H$_3$O)Ga(C$_2$O$_4$)$_3$]PhNO$_2$. By examining ultrasonic properties, charge disproportionation (CD) without magnetic field dependence is detected below $T_{\rm CD}$$\sim$8~K just above the superconducting critical temperature $T_{\rm c}$$\sim$6~K. From quantum oscillations in high fields, we find variation in the Fermi surface and mass enhancement induced by the CD. Heat capacity studies elucidate that the superconducting gap function is fully gapped in the Fermi …
CsV$_3$Sb$_5$ is a newly discovered Kagome superconductor that attracts great interest due to its topological nontrivial band structure and the coexistence of superconductivity and charge-density-wave (CDW) with many exotic properties. Here, we report the detailed characterization of the CDW gap in high-quality CsV$_3$Sb$_5$ single crystals using high-resolution angle-resolved photoemission spectroscopy. We find that the CDW gap is strongly momentum dependent. While gapped around the $M$ point, the electronic states remain gapless around the $Γ$ point and along the $Γ$-$K$ direction. Such mome…
Lithium Sulfide, Li2S, is an anti-fluorite semiconductor with a band-gap of 3.865 eV. It also has exactly the same valence electron count, Ne, and atomic number, Z, as magnesium diboride, MgB2. Both have almost the same formula weight. This qualifies Li2S as a magnesium-diboride like material. Li2S passes the same computational material specific test for superconductivity as MgB2. Using our recently developed symmetry rules for searching for superconductors, we predict that Li2S, with electronegativity of 1.5, will be superconducting with a Tc of 33.8K, if double-gapped or 16.9K if single gapp…
We show that the {\it gapped} triplet superconductivity, i.e., a triplet superconductor with triplet order parameter, can be realized in strong spin-orbit-coupled quantum wells in proximity to $s$-wave superconductor. It is revealed that with the singlet order parameter induced from the superconducting proximity effect, in quantum wells, not only can the triplet pairings arise due to the spin-orbit coupling, but also the triplet order parameter can be induced due to the repulsive effective electron-electron interaction, including the electron-electron Coulomb and electron-phonon interactions. …
The nature of the pairing symmetry of the first heavy fermion superconductor CeCu$_2$Si$_2$ has recently become the subject of controversy. While CeCu$_2$Si$_2$ was generally believed to be a $d$-wave superconductor, recent low temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped $d+d$ band-mixing pairing…
We investigate the origin of Abelian and non-Abelian type magnetic instabilities induced by Fermi surface mismatch between the two pairing fermions in a non-relativistic model. The Abelian type instability occurs only in gapless state and the Meissner mass squared becomes divergent at the gapless-gapped transition point, while the non-Abelian type instability happens in both gapless and gapped states and the divergence vanishes. The non-Abelian type instability can be cured in strong coupling region.
We present tunneling data in the normal state of the electron doped cuprate superconductor Pr$_{2-x}$Ce$_x$CuO$_4$ for three different values of the doping $x$. The normal state is obtained by applying a magnetic field greater than the upper critical field, $H_{c2}$ for $T < T_c$. We observe an anomalous normal state gap near the Fermi level. From our analysis of the tunneling data we conclude that this is a feature of the normal state density of states. We discuss possible reasons for the formation of this gap and its implications for the nature of the charge carriers in the normal and the su…
We present a comprehensive study on superconducting properties of Re$_7$B$_3$ and Re$_3$B through specific heat, magnetic susceptibility, resistivity, and transverse and zero-field muon spin rotation/relaxation ($μ$SR) experiments on polycrystalline samples. Re$_7$B$_3$ (T$_C$ = 3.2~K) is a non-centrosymmetric type-II ($κ$ $\approx$ 9.27) superconductor in the weak coupling ($λ_{e-ph}$ = 0.54) regime. On the other hand, Re$_3$B (T$_C$ = 5.19~K) is a centrosymmetric type-II ($κ$ $\approx$ 34.55) superconductor in the moderate coupling ($λ_{e-ph}$ = 0.64) regime. Our transverse-field $μ$SR measu…
We study the superconducting state in newly discovered high-Tc superconductor K$_x$Fe$_2$Se$_2$ based on the ten-orbital Hubbard-Holstein model without hole-pockets. When the Coulomb interaction is large, spin-fluctuation mediated d-wave state appears due to the nesting between electron-pockets. Interestingly, the symmetry of the body-centered tetragonal structure in K$_x$Fe$_2$Se$_2$ requires the existence of nodes in the d-wave gap, although fully-gapped d-wave state is realized in the case of simple tetragonal structure. In the presence of moderate electron-phonon interaction due to Fe-ion …
We present muon spin rotation ($μ$SR) measurements on the noncentrosymmetric superconductor PbTaSe$_2$. From measurements in an applied transverse field between $H_{c1}$ and $H_{c2}$, we extract the superfluid density as a function of temperature in the vortex state. This data can be fit with a fully gapped two-band model, consistent with previous evidence from ARPES, thermal conductivity, and resistivity. Furthermore, zero field measurements show no evidence for a time reversal symmetry breaking field greater than 0.05~G in the superconducting state. This makes exotic fully gapped spin-triple…
We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupling to the superconductor is weak an energy gap is opened only in the presence of sufficiently strong attractive interactions between the edge modes, which do not commonly occur in solid state experime…
The topological invariants of gapped time reversal invariant lattice superconductors are studied by mapping the superconducting mean field Hamiltonian to a Bloch Hamiltonian. There is a single $Z_2 $ invariant in two dimensions and four such invariants in three dimensions. We briefly discuss the properties of states with non-trivial topological invariants.
