We report a fluctuation-driven state of matter that develops near an accidental degeneracy point of two symmetry-distinct primary phases. Due to symmetry mixing, this bound-state order exhibits unique signatures, incompatible with either parent phase. Within a field-theoretical formalism, we derive the generic phase diagram for system with bound-state order, study its response to strain, and evaluate analytic expressions for a specific model. Our results support the $(d + ig)$-superconducting state as a candidate for $\mathrm{Sr}_{2}\mathrm{Ru}\mathrm{O}_{4}$: Most noticeably, the derived strain-dependence is in excellent agreement with recent experiments [Hicks \textit{et al.} Science (2014) and Grinenko \textit{et al.} arXiv (2020)]. The evolution above a non-vanishing strain from a joint onset of superconductivity and time-reversal symmetry-breaking to two split phase transitions provides a testable prediction for this scenario.
In contrast to conventional superconducting (SC) materials, superconductivity in high-temperature superconductors (HTCs) usually emerges in the presence of other fluctuating orders with similar or higher energy scales, thus instigating debates over their relevance for the SC pairing mechanism. In iron-based superconductors (IBSCs), local orbital fluctuations have been proposed to be directly responsible for the structural phase transition and closely related to the observed giant magnetic anisotropy and electronic nematicity. However, whether superconductivity can emerge from, or even coexist …
We report local probe ($μ$SR) measurements on the recently discovered tetragonal FeS superconductor which has been predicted to be electronically very similar to superconducting FeSe. Most remarkably, we find that low moment ($10^{-2}-10^{-3}μ_\mathrm{B})$ disordered magnetism with a transition temperature of $T_\mathrm{N}\approx 20$ K microscopically coexists with bulk superconductivity below $T_\mathrm{c}=4.3(1)$ K. From transverse field $μ$SR we obtain an in-plane penetration depth $λ_\mathrm{ab}(0)=223(2)$ nm for FeS. The temperature dependence of the corresponding superfluid density $λ_\m…
We report the full complex dielectric function of high-purity $\textrm{Ba}_{0.68}\textrm{K}_{0.32}\textrm{Fe}_2\textrm{As}_2$ single crystals with $T_{\mathrm{c}}=38.5\ \textrm{K}$ determined by wide-band spectroscopic ellipsometry at temperatures $10\leq T\leq300\ \textrm{K}$. We discuss the microscopic origin of superconductivity-induced infrared optical anomalies in the framework of a multiband Eliashberg theory with two distinct superconducting gap energies $2Δ_{\mathrm{A}}\approx6\ k_{\mathrm{B}}T_{\mathrm{c}}$ and $2Δ_{\mathrm{B}}\approx2.2\ k_{\mathrm{B}}T_{\mathrm{c}}$. The observed un…
Interplay of stripe and double-Q magnetism with superconductivity in $\mathrm{Ba}_{1-x}\mathrm{K}_{x}\mathrm{Fe}_{2}\mathrm{As}_{2}$ under the influence of magnetic fields
Within the $t$--$J$ model Hamiltonian we present a RVB mean field theory directly in terms of dopant particles. We apply this theory to $\mathrm{Na}_{x}\mathrm{CoO_{2}}\cdot y% \mathrm{H_{2}0}$ and show that the resulting phase diagram $T_c$ versus doping is in qualitative agreement with the experimental results.
We report on magnetization, specific heat and resistivity experiments on single crystals of the novel heavy Fermion compound Ce$_3$PdIn$_{11}$. At ambient pressure the compound exhibits two successive transitions at T$_{1}$ = 1.63 K and T$_{\mathrm {N}}$ = 1.49 K into incommensurate and commensurate local moment antiferromagnetic states, respectively, before becoming superconducting below T$_{\mathrm {c}}$ = 0.42 K. The large values of dB$_{\mathrm {c2}}$/dT and B$_{\mathrm {c2}}$ = 2.8 T imply that heavy quasiparticles form the Cooper pairs. Thus, Ce$_{3}$PdIn$_{11}$ is the first ambient pres…
Emergent $s+id$ Superconductivity from the Interplay between Electronic Correlations and Electron-Phonon Coupling in $\mathrm{R}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$
Northeastern University（东北大学）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
We have constructed a pressure$-$temperature ($P-T$) phase diagram of $P$-induced superconductivity in EuFe$_2$As$_2$ single crystals, via resistivity ($ρ$) measurements up to 3.2 GPa. As hydrostatic pressure is applied, an antiferromagnetic (AF) transition attributed to the FeAs layers at $T_\mathrm{0}$ shifts to lower temperatures, and the corresponding resistive anomaly becomes undetectable for $P$ $\ge$ 2.5 GPa. This suggests that the critical pressure $P_\mathrm{c}$ where $T_\mathrm{0}$ becomes zero is about 2.5 GPa. We have found that the AF order of the Eu$^{2+}$ moments survives up to …
Dissecting superconductivity in the Ruddlesden-Popper nickelates: The role of electron correlation and interlayer magnetic exchange
Diamond Light Source（钻石光源）；National Synchrotron Radiation Laboratory and School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院/国家同步辐射实验室）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-Sen University（中山大学物理学院/广东省铁电与磁器件重点实验室）；Department of Physics, University of Oxford（牛津大学物理系）；National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室/物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
A lot of attention has been drawn to superconductivity in UTe$_2$, with suggestions of time-reversal symmetry breaking triplet chiral superconducting order parameter. The chirality of the order parameter has been attributed to an accidental near degeneracy of two superconducting components belonging to 1D irreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it has been argued that the chiral $B_{2u}+iB_{3u}$ combination is selected by ferromagnetic fluctuations. In this work we present a possible explanation of the near-degeneracy as a result of an accidental $C_4$ symmetry o…
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…
We present the pressure-temperature phase diagram of the antiferromagnet CeAg$_2$Si$_2$ established via resistivity and calorimetry measurements under quasi-hydrostatic conditions up to 22.5~GPa. With increasing pressure, the Néel temperature [$T_{\mathrm{N}}(p=0)=8.6$~K] slowly increases up to $T_{\mathrm{N}}=13.4$~K at 9.4~GPa and then vanishes abruptly at the magnetic critical pressure $p_{\mathrm{c}}\sim13$~GPa. For the first time, heavy fermion superconductivity is observed in CeAg$_2$Si$_2$ . Superconductivity emerges at $\sim 11$~GPa and persists over roughly 10~GPa. Partial- and bulk-t…
The Fermi surfaces (FS) of LaOFeAs (in $k_z$=0 plane) consist of two hole-type circles around $Γ$ point, which do not touch each other, and two electron-type co-centered ellipses around M point, which are degenerate along the M-X line. By first-principles calculations, here we show that additional degeneracy exists for the two electron-type FS, and the crucial role of F-doping and pressure is to enhance this orbital degeneracy. It is suggested that the inter-orbital fluctuation is the key point to understand the unconventional superconductivity in these materials.
Electron-lattice interactions play a prominent role in quantum materials, making a deeper understanding of direct routes to phonon-mediated high-transition-temperature ($T_{\mathrm{c}}$) superconductivity desirable. However, it has been known for decades that weak electron-phonon coupling gives rise to low values of $T_{\mathrm{c}}$, while strong electron-phonon coupling leads to lattice instability or formation of bipolarons, generally assumed to be detrimental to superconductivity. Thus, the route to high-$T_{\mathrm{c}}$ materials from phonon-mediated mechanisms has heretofore appeared to b…
The layered bismuth oxy-sulfide materials, which are structurally related to the Fe-pnictides/chalcogenides and cuprates superconductors, have brought substantial attention for understanding the physics of reduced dimensional superconductors. We have examined the pairing symmetry of recently discovered BiCh$_2$-based superconductor, La$_\mathrm{1-x}$Ce$_\mathrm{x}$OBiSSe with $x$ = 0.3, through transverse field (TF) muon spin rotation measurement, in addition we present the results of magnetization, resistivity and zero field (ZF) muon spin relaxation measurements. Bulk superconductivity has b…
The filled skutterudite compound \PrOsSb{} has been found to exhibit superconductivity with a critical temperature $T_\mathrm{c} = 1.85$ K that develops out of a heavy Fermi liquid with an effective mass $m^{*} \approx 50 m_\mathrm{e}$. The current experimental situation regarding the heavy fermion state, the superconducting state, and a high field, low temperature phase that is apparently associated with magnetic or quadrupolar order in \PrOsSb{} is briefly reviewed herein.
Motivated by the bad metal behavior of the iron pnictides, we study a multi-orbital $\mathrm{t-J_1-J_2}$ model and investigate possible singlet superconducting pairings. Magnetic frustration by itself leads to a large degeneracy in the pairing states. The kinetic energy breaks this into a quasi-degeneracy among a reduced set of pairing states. For small electron and hole Fermi pockets, an $A_{1g}$ state dominates over the phase diagram but a $B_{1g}$ state has close-by energy. In addition to the nodeless $A_{1g}$ $s_{x^2y^2}$ channel, the nodal $A_{1g}$ $s_{x^2+y^2}$ and $B_{1g}$ $d_{x^2-y^2}$…
We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_\mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds' paramagnon spectra are nearly identical apart from an energy scale factor of $\sim130\%$ that matches the ratio of $T_\mathrm{c}$'s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer …
Superconductivity in doped symmetric mass generation insulator: a quantum Monte-Carlo study
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, University of California, San Diego（加州大学圣地亚哥分校物理系）
We study the symmetry-broken phases in two- and three-orbital Hubbard models with lifted orbital degeneracy using dynamical mean field theory. On the technical level, we explain how symmetry relations can be exploited to measure the four-point correlation functions needed for the calculation of the lattice susceptibilities. In the half-filled two-orbital model with crystal field splitting, we find an instability of the metallic phase to spin-orbital order with neither spin nor orbital moment. This ordered phase is shown to be related to the recently discovered fluctuating-moment induced spin-t…
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 $T_\ma…
NbRh$_{2}$B$_{2}$ crystallises in a chiral noncentrosymmetric structure and exhibits bulk type-II superconductivity below $7.46(5)$~K. Here we show that the temperature dependence of the upper critical field deviates from the behaviour expected for both Werthamer-Helfand-Hohenberg and the Ginzburg-Landau models and that $μ_{0}H_{\mathrm{c2}}\left(0\right)\approx 18$~T exceeds the Pauli paramagnetic limit, $μ_{0}H_{\mathrm{P}}=13.9$~T. We explore the reasons for this enhancement. Transverse-field muon spectroscopy measurements suggest that the superconducting gap is either $s$-wave or $\left(s+…
Two different ferroelectric materials, Sr$_{0.95}$Ba$_{0.05}$TiO$_3$ and Sr$_{0.985}$Ca$_{0.015}$TiO$_3$, can be turned into polar metals with broken centrosymmetry via electron doping. Systematic substitution of Nb$^{5+}$ for Ti$^{4+}$ has revealed that these polar metals both commonly show a simple superconducting dome with a single convex shape. Interestingly, the superconducting transition temperature $T_\mathrm{c}$ is enhanced more strongly in these polar metals when compared with the nonpolar matrix Sr(Ti,Nb)O$_3$. The maximum $T_\mathrm{c}$ reaches 0.75K, which is the highest reported v…
Superconductivity is observed in the filled skutterudite compound \PrOsSb{} below a critical temperature temperature $T_\mathrm{c} = 1.85$ K and appears to develop out of a nonmagnetic heavy Fermi liquid with an effective mass $m^{*} \approx 50 m_\mathrm{e}$, where $m_\mathrm{e}$ is the free electron mass. Features associated with a cubic crystalline electric field are present in magnetic susceptibility, specific heat, electrical resistivity, and inelastic neutron scattering measurements, yielding a Pr$^{3+}$ energy level scheme consisting of a $Γ_{3}$ nonmagnetic doublet ground state, a low l…
In the d-electron system YFe$_2$Ge$_2$, an unusually high and temperature dependent Sommerfeld ratio of the specific heat capacity $C/T \sim 100~\mathrm{mJ/(molK^2)}$ and an anomalous power law temperature dependence of the electrical resistivity $ρ\simeq ρ_0 + AT^{3/2}$ signal Fermi liquid breakdown, probably connected to a close-by quantum critical point. Full resistive transitions, accompanied by DC diamagnetic screening fractions of up to 80\% suggest that pure samples of YFe$_2$Ge$_2$ superconduct below $1.8~\mathrm{K}$.
We propose a mew picture for superconductivity in $κ-(BEDT-TTF)_2X$ salts arguing that small-{\bf q} electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magnetooptic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless-regions on the FS accounting for the experimental signatures of a Fuld…
Superconducting Dome in $\mathrm{La}_{3-x}\mathrm{Sr}_{x}\mathrm{Ni}_{2}\mathrm{O}_{7-δ}$ Thin Films
National Laboratory of Solid State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University（南京大学工程与应用科学学院，固体微结构物理国家重点实验室，人工功能材料江苏省重点实验室）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
The recently discovered Kagome family ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ (A = K, Rb, Cs) exhibits rich physical phenomena, including non-trivial topological electronic structure, giant anomalous Hall effect, charge density waves (CDW) and superconductivity. Notably, CDW in ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ is evidenced to intertwine with its superconductivity and topology, but its nature remains elusive. Here, we combine x-ray scattering experiments and density-functional theory calculations to investigate the CDWs in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and demonstrate the coexistence of 2 $\times$…
We report muon spin rotation ($μ$SR) and magnetization measurements under pressure on Fe$_{1+δ}$Se$_\mathrm{1\text{-}x}$S$_\mathrm{x}$ with x $\approx 0.11$.Above $p\approx0.6$ GPa we find microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting $T_\mathrm{c}(p)$. The maximum of $T_\mathrm{c}$ corresponds to the onset of mag…
Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pai…
We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave-vector, reflecting the "ferromagnetic-like" SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi s…
The pressure-temperature-phase diagram of the new heavy-fermion superconductor CeAu$_2$Si$_2$ is markedly different from those studied previously. Indeed, superconductivity emerges, not on the verge, but deep inside the magnetic phase. In this context, we have carried out ac-calorimetry, resistivity and thermoelectric power measurements on a CeAu$_2$Si$_2$-single crystal under high-pressure. The principal novelties of this experiment are the observation of a new transition line, presumably a magnetic structure rearrangement at $T_{\mathrm{M}}^{\mathrm{mod}}$ inside the antiferromagnetic phase,…
We used the Hartree-Fock approximation to classify the electronic phases that might occur in a transition metal nanowire. The important features of this situation are orbital degeneracy (or near-degeneracy) and interactions favoring locally high-spin configurations. In this circumstance, spin density wave and triplet superconductivity states are favored. If the interactions favor locally low-spin configurations as in the previously studied spin ladder systems, orbital density wave and singlet superconductivity are observed.
In the family of the iron-based superconductors, the $RE$FeAsO-type compounds (with $RE$ being a rare-earth metal) exhibit the highest bulk superconducting transition temperatures ($T_{\mathrm{c}}$) up to $55\ \textrm{K}$ and thus hold the key to the elusive pairing mechanism. Recently, it has been demonstrated that the intrinsic electronic structure of SmFe$_{0.92}$Co$_{0.08}$AsO ($T_{\mathrm{c}}=18\ \textrm{K}$) is highly nontrivial and consists of multiple band-edge singularities in close proximity to the Fermi level. However, it remains unclear whether these singularities are generic to th…
Anisotropic fully-gapped superconductivity in quasi-one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$
H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学 H.H. 威尔斯物理实验室）；Department of Chemistry and Chemical Biology, Rutgers University（罗格斯大学化学与化学生物学系）；School of Mathematics and Physics, Queen’s University Belfast（贝尔法斯特女王大学数学与物理学院）；Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所学）；High Field Magnet Laboratory (HFML-FELIX) and Institute for Molecules and Materials, Radboud University（拉得堡大学分子与材料研究所及高场磁实验室（HFML-FELIX））
Resistivity and Hall effect measurements of EuFe$_2$As$_2$ up to 3.2\,GPa indicate no divergence of quasiparticle effective mass at the pressure $P_\mathrm{c}$ where the magnetic and structural transition disappears. This is corroborated by analysis of the temperature ($T$) dependence of the upper critical field. $T$-linear resistivity is observed at pressures slightly above $P_\mathrm{c}$. The scattering rates for both electrons and holes are shown to be approximately $T$-linear. When a field is applied, a $T^2$ dependence is recovered, indicating that the origin of the $T$-linear dependence …
We consider the competition between the conventional s-wave and the triplet Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the two contending channels are comparable, we find a simultaneously time-reversal and parity violating $p + is$ state at low temperatures, which provides an example of dynamic axionic state of matter. In contradistinction to the time-reversal invariant, topological B-phase, the $p + is$ state …
Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are st…
The electronic structure of low-density n-type SrTiO3 delta-doped heterostructures is investigated by angular dependent Shubnikov-de Haas oscillations. In addition to a controllable crossover from a three- to two-dimensional Fermi surface, clear beating patterns for decreasing dopant layer thicknesses are found. These indicate the lifting of the degeneracy of the conduction band due to subband quantization in the two-dimensional limit. Analysis of the temperature-dependent oscillations shows that similar effective masses are found for all components, associated with the splitting of the light …
We propose a route to achieve odd-parity spin-triplet superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin-degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfa…
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 …
We consider manifestations of topological order in time-reversal-symmetric fractional topological liquids (TRS-FTLs), defined on planar surfaces with holes. We derive a formula for the topological ground state degeneracy of such a TRS-FTL, which applies to cases where the edge modes on each boundary are fully gapped by appropriate backscattering terms. The degeneracy is exact in the limit of infinite system size, and is given by $q^{N^{\,}_{\mathrm{h}}}$, where $N^{\,}_{\mathrm{h}}$ is the number of holes and $q$ is an integer that is determined by the topological field theory. When the degene…
