We report on tunneling spectroscopy measurements using a Scanning Tunneling Microscope (STM) on the spin triplet superconductor Sr2RuO4. We find a negligible density of states close to the Fermi level and a fully opened gap with a value of $Δ$=0.28 meV, which disappears at T$_c$ = 1.5 K. $Δ$ is close to the result expected from weak coupling BCS theory ($Δ_0$=1.76kBT$_c$ = 0.229 meV). Odd parity superconductivity is associated with a fully isotropic gap without nodes over a significant part of the Fermi surface.
In this work zero-temperature phase diagrams of cuprates with Ba$_2$CuO$_3$-type CuO chain structure is investigated. The projective symmetry group analysis is employed in the strong coupling limit, and renormalization group with bosonization analysis is employed in the weak coupling limit. We find that in both of these two limits, large areas of the phase diagrams are filled with nodeless $s$-wave superconducting phases (with weak $d$-wave components), instead of pure $d$-wave phase mostly found in cuprates. This implies that nodeless $s$-wave phase is the dominant superconducting phase in cu…
Spin-Polarized Josephson Supercurrent in Nodeless Altermagnets
Zhejiang University（浙江大学）；Hefei National Laboratory（合肥国家实验室）；University of Science and Technology of China（中国科学技术大学）；University of Chinese Academy of Sciences（中国科学院大学）
Thermal conductivity of overdoped BaFe$_{1.73}$Co$_{0.27}$As$_2$ single crystal: Evidence for nodeless multiple superconducting gaps and interband interactions
测量了过掺杂的FeAs基超导体BaFe $_{1.73}$ Co $_{0.27}$ As $_2$（$T_c$ = 8.1 K）单晶的面内热导率$κ$，其热导率低至80 mK。在零磁场下，剩余的线性项$κ_0/T$可以忽略不计，表明在$ab$平面上存在无结超导能隙.在磁场中，$κ_0/T$迅速增加，与传统的s波超导体有很大不同。这种反常的$κ_0/T(H)$可能揭示了在过掺杂BaFe $_{1.73}$ Co $_{0.27}$ As $_2$中的一种奇异的超导能隙结构：消失空穴（$β$）的能隙比包含大部分载流子的电子（$γ$和$δ$）的能隙大得多。这种奇异的带隙结构是由带间相互作用诱导的超导态的证据，其中具有{ \it较小}态密度的带具有{ \it较大}带隙。
Motivated by the recently discovered time-reversal symmetry-breaking superconductivity in epitaxial Bi/Ni bilayer system with transition temperature $T_c\approx 4.2$K and the observation of zero-bias anomaly in tunneling measurements, we show that gap-filling states can appear in the fully gapped $d_{xy}\pm id_{x^2-y^2}$ superconducting states. We consider a model of helical electron states with d-wave pairing. In particular, we show that both magnetic and non-magnetic impurities can create states within the superconducting gap. Alternatively, we also show that the coupling of the electron spi…
The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a …
Multiple nodeless superconducting gaps in optimally-doped SrTi$_{1-x}$Nb$_{x}$O$_{3}$
我们首次研究了超导SrTi $_{1-x}$ Nb $_{x}$ O $_{3}$的热导率，充分掺杂到接近其最大临界温度。由比热跃变确定的体临界温度发生在比电阻T $_{c}$低得多的温度。热导率，占主导地位的电子的贡献，偏离其正常状态的幅度在散装T $_{c}$，以下的Bardeen-Rickayzen-Tewordt（BRT）的行为，预计由Bogoliubov激发的热传输。在非常低的温度下T-线性项的缺乏排除了节准粒子的存在。另一方面，热传导率的场依赖性指向至少两个不同的超导间隙的存在。最佳掺杂的钛酸锶是一种多能隙无结超导体。
The ThIrSi superconductor, with $T_c = 6.5$ K, is expected to show unusual features in view of its noncentrosymmetric structure and the presence of heavy elements featuring a sizable spin-orbit coupling. Here, we report a comprehensive study of its electronic properties by means of local-probe techniques: muon-spin rotation and relaxation ({\textmu}SR) and nuclear magnetic resonance (NMR). Both the superfluid density $ρ_\mathrm{sc}(T)$ (determined via transverse-field {\textmu}SR) and the spin-lattice relaxation rate $T_1^{-1}(T)$ (determined via NMR) suggest a nodeless superconductivity. Furt…
Recently it was found that selenium doping can suppress the charge-density-wave (CDW) order and induce bulk superconductivity in ZrTe$_3$. The observed superconducting dome suggests the existence of a CDW quantum critical point (QCP) in ZrTe$_{3-x}$Se$_x$ near $x \approx$ 0.04. To elucidate its superconducting state near the CDW QCP, we measure the thermal conductivity of two ZrTe$_{3-x}$Se$_x$ single crystals ($x$ = 0.044 and 0.051) down to 80 mK. For both samples, the residual linear term $κ_0/T$ at zero field is negligible, which is a clear evidence for nodeless superconducting gap. Further…
Intrinsic Electronic Structure and Nodeless Superconducting Gap of $\mathrm{YBa_{2} Cu_{3} O_{7-δ} }$ Observed by Spatially-Resolved Laser-Based Angle Resolved Photoemission Spectroscopy
We present a theoretical model to show that the transition from an antiferromagnetic (AFM) phase to the $d_{x^2-y^2}$-wave superconductivity occurs through a robust companion of a finite momentum pairing between $({\bf k},\uparrow)$ and $(-{\bf k}-{\bf Q},\downarrow)$ electrons, namely pair-density wave (PDW) state, where ${\bf Q}=(π,π)$ is the AFM wavevector. Interestingly, the spatial structure of the PDW is constrained to be a $p+ip$-wave symmetry, which follows $p_{\bf k}=p_{-{\bf k}-{\bf Q}}$ under fermions exchange in cuprates, dictating a spin-singlet pairing. Furthermore, the PDW state…
High-pressure synthesis techniques have allowed for the growth of Sn$_{1-x}$In$_x$Te samples beyond the ambient In-saturation limit of $x$ = 0.5 (T$_c \sim$ 4.5 K). In this study, we present measurements of the temperature dependence of the London penetration depth $Δλ(T)$ in this superconducting doped topological insulator for $x$ = 0.7, where T$_{c,onset}\approx 5$ K. The results indicate fully gapped BCS-like behavior, ruling out odd-parity $A_{2u}$ pairing; however, odd-parity $A_{1u}$ pairing is still possible. Critical field values measured below 1 K and other superconducting parameters …
A nodeless $d$-wave state is likely in superconducting monolayer FeSe on SrTiO$_3$. The lack of nodes is surprising but has been shown to be a natural consequence of the observed small interband spin-orbit coupling. Here we examine the evolution from a nodeless state to the nodal state as this spin-orbit coupling is increased from a topological perspective. We show that this evolution depends strongly on the orbital content of the superconducting degrees of freedom. In particular, there are two $d$-wave solutions, which we call orbitally trivial and orbitally nontrivial. In both cases, the nod…
Common Fermi Surface Topology and Nodeless Superconducting Gap in K0.68Fe1.79Se2 and (Tl0.45K0.34)Fe1.84Se2 Superconductors Revealed from Angle-Resolved Photoemission Spectroscopy
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…
Similar to chemical doping, pressure produces and stabilizes new phases of known materials, whose properties may differ greatly from those of their standard counterparts. Here, by considering a series of LaFeAs$_{1-x}$P$_x$O iron-pnictides synthesized under high-pressure high-temperature conditions, we investigate the simultaneous effects of pressure and isoelectronic doping in the 1111 family. Results of numerous macro- and microscopic technique measurements, unambiguously show a radically different phase diagram for the pressure-grown materials, characterized by the lack of magnetic order an…
Direct observation of a nodeless superconducting energy gap in the optical conductivity of iron-pnictides
测量了外延生长的Ba（Fe $_{0.9}$ Co $_{0.1}$）$_2$ As $_2$薄膜随温度变化的光学反射率和复透射率，并在宽频率范围内测量了其光学电导率和介电常数。超导能隙$2Δ_0 = 3.7$在低于$T_c\approx 20$ K时的打开是通过完全消失的光学电导率{ \em直接}观察到的。Ba（Fe $_{0.9}$ Co $_{0.1}$）$_2$ As $_2$超导态的电动力学性质与温度和频率相关，与序参量中无节点的BCS预言一致.冷凝物$1.94\times 10^7 {\rm cm}^{-2}$的光谱权重对应于伦敦穿透深度$λ_L=3600$ λ。
Pairing in the cuprate high-temperature superconductors and its origin remain among the most enduring mysteries in condensed matter physics. With cross-sectional scanning tunneling microscopy/ spectroscopy, we clearly reveal the spatial-dependence or inhomogeneity of the superconducting gap structure of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) and YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) along their $c$-axes on a scale shorter than the interlayer spacing. By tunneling into the (100) plane of a Bi2212 single crystal and a YBCO film, we observe both U-shaped tunneling spectra with extended flat zero-conducta…
Motivated by the recent observations of nodeless superconductivity in the monolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional $t$-$J$ model in proximity to an antiferromagnetic (AF) insulator. We found that (i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity induced AF field. (ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodel…
Nodeless superconductivity in the presence of spin-density wave in pnictide superconductors: The case of BaFe$_{2-x}$Ni$_{x}$As$_{2}$
铁基超导体的特点表现在其电子、磁性和库珀对的配对对称性上，但后者仍有待探索。通常在这些材料中，超导性与磁序共存并竞争，从而产生非常规的配对机制。本文报道了BaFe $_{2-x}$ Ni $_{x}$ As $_{2}$单晶体在超导状态下的体磁化强度和低温比热的测量结果。{电子}比热在超导转变温度处显示出明显的异常，并且{在超导状态的低温下}显示出小的剩余部分。当$x$ = 0.092、0.096和0.10时，正常态索末菲系数随Ni掺杂而增加，这说明磁性和超导性之间存在竞争。我们的超导态比热和伦敦穿透深度的温度依赖性的分析提供了强有力的证据，一个两带$s$波序参数。此外，从低临界场计算的伦敦穿透深度的数据遵循指数温度依赖性，完全带隙超导体的特征。这些观察清楚地表明，在接近最佳掺杂的化合物中的超导能隙是无节点的。
The thermal conductivity of the iron-based superconductor FeSe was measured at temperatures down to 50 mK in magnetic fields up to 17 T. In zero magnetic field, the electronic residual linear term in the T = 0 limit, κ_0/T, is vanishingly small. Application of a magnetic field H causes no increase in κ_0/T initially. Those two observations show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of κ_0/T has the classic shape of a two-band superconductor, such as MgB2: it rises exponentially at very l…
The issue of whether the quantum critical point (QCP) is hidden inside unconventional superconductors is a matter of hot debate. Although a prominent experiment on London penetration depth has demonstrated the existence of the QCP in the isovalent-doped iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$, with the observation of a sharp peak in the penetration depth in the vicinity of the disappearance of magnetic order at zero temperature, the nature of such an emerging QCP remains unclear. Here, we provide a unique picture to understand well the phenomena of the QCP based on the framewor…
Monolayer FeSe exhibits the highest transition temperature among the iron based superconductors and appears to be fully gapped, seemingly consistent with $s$-wave superconductivity. Here, we develop a theory for the superconductivity based on coupling to fluctuations of checkerboard magnetic order (which has the same translation symmetry as the lattice). The electronic states are described by a symmetry based ${\bf k}\cdot {\bf p}$-like theory and naturally account for the states observed by angle resolved photoemission spectroscopy. We show that a prediction of this theory is that the resulta…
Multi-gap nodeless superconductivity in nickel chalcogenide TlNi2Se2
对TlNi $_2$ Se $_2$单晶进行了低温热导率的测量，$T_c$ $\simeq$为3.7 K.在零场下，$T$ $\rightarrow$ 0 K（$κ_0/T$）的剩余电子贡献与总热导率很好地分离，总热导率小于其正常状态值的0.45%.如此微小的残留$κ_0/T$不太可能是由节状准粒子贡献的。无节点间隙结构得到了低磁场中$κ_0(H)/T$非常弱的场依赖性的支持。在整个场范围内，$κ_0(H)/T$呈现“$S$“形曲线，如在镍磷属元素化物BaNi $_2$ As $_2$和SrNi $_2$ P $_2$的情况。镍基超导体的这一共同特征可以用多个无结超导带隙来解释。
Superconducting gap structure was probed in type-II Dirac semimetal PdTe$_2$ by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding $λ(T=0)=230$~nm as the only fit parameter at a fixed $Δ(0)/T_c\approx 1.76$, and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-indep…
Recent discovery of superconductivity in the twisted bilayer graphene has stimulated numerous theoretical proposals concerning its exact gap symmetry. Among them, $d+id$ or $p+ip$-wave were believed to be the most plausible solutions. Here considering the superconductivity emerges near a correlated insulating state and may be induced by antiferromagnetic spin fluctuations, we apply the strong-coupling Eliashberg theory with both inter- and intraband quantum critical pairing interactions and discuss the possible gap symmetry in an effective low-energy four-orbital model. Our calculations reveal…
The pairing mechanism of high-temperature superconductivity in cuprates remains the biggest unresolved mystery in condensed matter physics. To solve the problem, one of the most effective approaches is to investigate directly the superconducting CuO2 layers. Here, by growing CuO2 monolayer films on Bi2Sr2CaCu2O8+δ substrates, we identify two distinct and spatially separated energy gaps centered at the Fermi energy, a smaller U-like gap and a larger V-like gap on the films, and study their interactions with alien atoms by low-temperature scanning tunneling microscopy. The newly discovered U-lik…
The noncentrosymmetric superconductor Mo$_3$Rh$_2$N, with $T_c = 4.6$ K, adopts a $β$-Mn-type structure (space group $P$4$_1$32), similar to that of Mo$_3$Al$_2$C. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation ($μ$SR). The low-temperature superfluid density, measured via transverse-field (TF)-$μ$SR, evidences a fully-gapped superconducting state with $Δ_0 = 1.73 k_\mathrm{B}T_c$, very close to 1.76 $k_\mathrm{B}T_c$ - the BCS gap value for …
Recently, a new family of iron-based superconductors called 12442 was discovered and the muon spin relaxation ($μ$SR) measurements on KCa$_2$Fe$_4$As$_4$F$_2$ and CsCa$_2$Fe$_4$As$_4$F$_2$ polycrystals, two members of the family, indicated that both have a nodal superconducting gap structure with $s+d$ pairing symmetry. Here we report the ultralow-temperature thermal conductivity measurements on CsCa$_2$Fe$_4$As$_4$F$_2$ single crystals ($T_c$ = 29.3 K). A negligible residual linear term $κ_0/T$ in zero field and the field dependence of $κ_0/T$ suggest multiple nodeless superconducting gaps in…
Magnetic Penetration Depth Measurements of Pr$_{2-x}$Ce$_x$CuO$_{4-δ}$ Films on Buffered Substrates: Evidence for a Nodeless Gap
测量了在SrTiO $_3$（001）衬底上生长的Pr $_{2-x}$ Ce $_{x}$ CuO $_{4-δ}$（$0.115 \leq x \leq 0.152$）超导薄膜的磁穿透深度的平方倒数。这些薄膜的$λ^{-2}(0)$、$T_c$和正常状态的结晶率表明它们是干净和均匀的。在宽范围的Ce掺杂，$0.124\leq x \leq 0.144$，$λ^{-2}(T)$在低$T$是平坦的：它的变化小于0.15%，超过3倍的$T$的变化，表明在超导态密度的差距。拟合到$λ^{-2}(T)$的第一个5%减小产生在$0.29\leqΔ_{\rm min}/k_BT_c\leq1.01$范围内的最小超导能隙值。
