We have investigated the bulk and microscopic properties of the rhombohedral intermediate valence superconductor CeIr$_3$ by employing magnetization, heat capacity, and muon spin rotation and relaxation ($μ$SR) measurements. The magnetic susceptibility indicates bulk superconductivity below $T_\mathrm{C} = 3.1$~K. Heat capacity data also reveal a bulk superconducting transition at $T_\mathrm{C} = 3.1$~K with a second weak anomaly near 1.6~K. At $T_{\mathrm{C}}$, the jump in heat capacity $ΔC$/$γT_{\mathrm{C}} \sim 1.39(1)$, is slightly less than the BCS weak coupling limit of 1.43. Transverse-field $μ$SR measurements suggest a fully gapped, isotropic, $s$-wave superconductivity with 2$Δ(0)/k_{\mathrm{B}}T_{\mathrm{C}} = 3.76(3)$, very close to 3.56, the BCS gap value for weak-coupling superconductors. From the temperature variation of magnetic penetration depth, we have also determined the London penetration depth $λ_{\mathrm{L}}(0) = 435(2)$~nm, the carriers' effective mass enhancement $m^{*} = 1.69(1)m_{\mathrm{e}}$ and the superconducting carrier density $n_{\mathrm{s}} = 2.5(1)\times 10^{26}$ carriers m$^{-3}$. The fact that LaIr$_3$, with no $4f$-electrons, and CeIr$_3$ with $4f^{n}$ electrons where $n \le 1$-electron (Ce ion in a valence fluctuating state), both exhibit the same $s$-wave gap symmetry indicates that the physics of these two compounds is governed by the Ir-$d$ band near the Fermi-level, which is in agreement with previous band structure calculations.
Transverse-field muon spin rotation measurements in the vortex-lattice mixed state of the heavy-fermion (HF) superconductor PrOs4Sb12 yield a temperature dependence of the penetration depth indicative of an isotropic or nearly isotropic energy gap. This is not seen to date in any other HF superconductor and is a signature of isotropic pairing symmetry, possibly related to a novel nonmagnetic "quadrupolar Kondo" HF mechanism in PrOs4Sb12. The T = 0 relaxation rate σ_s(0) = 0.91(1) μs^-1 yields an estimated penetration depth λ(0) = 3440(20) Å, which is considerably shorter than in other HF super…
We report the results of a zero-field muon spin relaxation (ZF-muSR) study of superconducting Ba1-xKxFe2As2 (0.5 < x < 0.9) in search of weak spontaneous internal magnetic fields associated with proposed time-reversal-symmetry breaking mixed pairing states. The measurements were performed on polycrystalline samples, which do not exhibit the mesoscopic phase separation previously observed in single crystals of Ba1-xKxFe2As2. No evidence of spontaneous internal magnetic fields is found in any of the samples at temperatures down to T ~ 0.02 K.
Muon spin relaxation/rotation (muSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super-conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based su…
We have investigated the superconducting state of the non-centrosymmetric compound Re6Zr using magnetization, heat capacity, and muon-spin relaxation/rotation (muSR) measurements. Re6Zr has a superconducting transition temperature, Tc = 6.75 K. Transverse-field muSR experiments, used to probe the superfluid density, suggest an s-wave character for the superconducting gap. However, zero and longitudinal-field muSR data reveal the presence of spontaneous static magnetic fields below Tc indicating that time-reversal symmetry is broken in the superconducting state and an unconventional pairing mec…
Conventional Cooper pairing arises from attractive interaction of electrons in the metallic bands. Recent experiment on Co-doped LiFeAs shows superconductivity in the insulating valence band, which is evolved from a metallic hole band upon doping. Here we examine this phenomenon by studying superconductivity in a three-orbital Hamiltonian relevant to the doped LiFeAs. We show explicitly that Cooper pairing of the insulating hole band requires a finite pairing interaction strength. For strong coupling, the superconductivity in the hole band is robust against the sink of the hole band below the …
Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce "symplectic Hubbard operators": an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-cohere…
Nonunitary triplet superconductivity in the Z2 topological metal SrPd2As2
University of Petroleum and Energy Studies（石油能源大学）；Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；Ariel University（阿里埃勒大学）；Rutherford Appleton Laboratory（卢瑟福阿普顿实验室）；University of Johannesburg（约翰内斯堡大学）；Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心）；Ramakrishna Mission Vivekananda Educational and Research Institute（罗摩克里希纳使命维韦卡南达教育与研究机构）
Many cerium-based heavy fermion (HF) compounds have pressure-temperature phase diagrams in which a superconducting region extends far from a magnetic quantum critical point. In at least two compounds, CeCu2Si2 and CeCu2Ge2, an enhancement of the superconducting transition temperature was found to coincide with an abrupt valence change, with strong circumstantial evidence for pairing mediated by critical valence, or charge transfer, fluctuations. This pairing mechanism, and the valence instability, is a consequence of a f-c Coulomb repulsion term U_fc in the hamiltonian. While some non-supercon…
Conventional and unconventional superconductivity, respectively, arise from attractive (electron-phonon) and repulsive (many-body Coulomb) interactions with fixed-sign and sign-reversal pairing symmetries. Although heavy-fermions, cuprates, and pnictides are widely believed to be unconventional superconductors, recent evidence in one of the heavy fermion superconductor (CeCu$_2$Si$_2$) indicate the presence of a novel conventional type pairing symmetry beyond the electron-phonon coupling. We present a new mechanism of attractive potential between electrons, mediated by emergent boson fields (v…
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…
To explain the high-temperature superconductivity of hole-doped copper-oxide high-temperature superconductors (HDCO-HTSCs), Anderson proposed a theory: (A) the pseudogap state is a resonating valence-bond (RVB) state below T* and (B) the RVB state translates itself into high-temperature superconducting state below Tc. In this paper we abandon Anderson theory B but still retain Anderson theory A and add three new hypotheses. Jointed three hypotheses with Anderson theory A, we construct an effective Hamiltonian of HDCO-HTSCs and explain why Tc-line is a dome in phase diagram and why HDCO-HTSCs h…
Resonating valence bond pairing energy in graphene by quantum Monte Carlo
University of Manchester（曼彻斯特大学）；Center for Advanced Systems Understanding（先进系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；TU Dresden（德累斯顿工业大学）
Superconductivity in the pseudo-binary pnictides Ru0.55Rh0.45P and Ru0.75Rh0.25As is probed by muon spin relaxation and rotation (muSR) measurements in conjuction with magnetic susceptibility, heat capacity and electrical resistivity measurements. Powder x-ray diffraction confirmed the MnP-type orthorhombic structure (space group Pnma) and showed a nearly single phase nature with small impurity phase(s) of about 5% for both the samples. The occurence of bulk superconductivity is confirmed with Tc = 3.7 K for Ru0.55Rh0.45P and T = 1.6 K for Ru0.75Rh0.25As. The superconducting state electronic h…
Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here we use the muon spin rotation/relaxation (muSR) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier muSR studies on powders and crystals, we show that while the superconducting gap is m…
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhibits better agreement with muSR data at higher fields, thereby demonstrating the importance of reproducing the field profile near the vortex cores when the intervortex distance becomes closer to the GL coherence length. The temperature and field dependence of magnetic penetration depth ($λ$) does not show any hint of nonlocal effect nor of low-lyin…
An estimation shows that the interband pairing channel between the valence band components of doped graphane can support a superconducting transition temperature (or a contribution into this expected event) of the order of 100 K at the coupling strength near 1 eV.
Low-temperature (T) heat-capacity measurements under hydrostatic pressure of up to p=2.1 GPa have been performed on single-crystalline CeCu2Si2. A broad superconducting (SC) region exists in the T-p phase diagram. In the low-pressure region antiferromagnetic spin fluctuations and in the high-pressure region valence fluctuations had previously been proposed to mediate Cooper pairing. We could identify these two distinct SC regions. We found different thermodynamic properties of the SC phase in both regions, supporting the proposal that different mechanisms might be implied in the formation of s…
Triplet pairing, orbital selectivity and correlations in Iron-based superconductors
University of Cincinnati（辛辛那提大学）；Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Rutgers University（罗格斯大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
The results of heat capacity C_p(T, H) and electrical resistivity ρ(T,H) measurements down to 0.35 K as well as muon spin relaxation and rotation (\muSR) measurements on a noncentrosymmetric superconductor LaIrSi3 are presented. Powder neutron diffraction confirmed the reported noncentrosymmetric body-centered tetragonal BaNiSn3-type structure (space group I4\,mm) of LaIrSi3. The bulk superconductivity is observed below T_c = 0.72(1) K. The intrinsic ΔC_e/γ_n T_c = 1.09(3) is significantly smaller than the BCS value of 1.43, and this reduction is accounted by the α-model of BCS superconductivi…
We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the t-J model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short range antiferromagnetic correlations.
Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $\vert 0 \rangle$ and $\vert 1 \rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an…
Combining symmetry based considerations with inputs from available experimental results, we make the case that a novel spin-triplet superconductivity triggered by antiferromagnetic fluctuations may be realized in the newly discovered layered cobaltide Na$_x$CoO$_{2}\cdot y$H$_2$O. In the proposed picture, unaccessable via resonating-valence-bond physics extrapolated from half-filling, the pairing process is similar to that advanced for Sr$_{2}$RuO$_4$, but enjoys a further advantage coming from the hexagonal structure of the Fermi-surface which gives a stronger pairing tendency.
A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method. Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics. In this work, we further investigate the ground state of two holes by VMC. It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations. A unique …
We have synthesized AgSn1-xBixSe2 polycrystalline samples to investigate the effect of partial substitution of mixed-valence Sn by Bi3+ to the superconductivity of the valence-skip superconductor AgSnSe2. The Bi-substituted AgSn1-xBixSe2 were obtained up to x = 0.2, but an insulating phase Ag2SnBi2Se5 with a NaCl-type structure showed up above x = 0.3. The superconducting transition temperature increased from 4.5 K (x = 0) to 5.0 K (x = 0.1) by Bi substitution. The enhancement of superconductivity by the suppression of the valence-skip states of Sn suggests that the valence-skip states of Sn a…
Intermetallic compounds containing f-electron elements display a wealth of superconducting phases, that are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferro- and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconductivity near valence transitions, or in the vicinity of magneto-polar order are candidates for new superconductive pairing interactions such as fluctuations of the condu…
We outline key elements of a theory that accounts for anomalous properties of the PuCoGa$_5$ and PuRhGa$_5$ compounds as a consequence of a two-body interference between two Kondo screening channels. Virtual valence fluctuations of the magnetic Pu configurations create two conduction channels of different symmetry. Using the symplectic large-N approach, we are able to demonstrate our pairing mechanism in an exactly solvable large-N limit. The critical temperature reaches its maximum when the energy levels of excited valence configurations are almost degenerate. The symmetry of the order parame…
We use the Hubbard Hamiltonian $H$ on the honeycomb lattice to represent the valence bands of carbon single-wall $(N,N)$ nanotubes. A detailed symmetry analysis shows that the model allows W=0 pairs which we define as two-body singlet eigenstates of $H$ with vanishing on-site repulsion. By means of a non-perturbative canonical transformation we calculate the effective interaction between the electrons of a W=0 pair added to the interacting ground state. We show that the dressed W=0 pair is a bound state for resonable parameter values away from half filling. Exact diagonalization results for th…
Paired valence electrons forming covalent bonds in molecues are confined cooper pair correlations. High pressure dissociates molecules in solid H2S, SiH4, H2 etc. and form extended structures. However, valence electrons are resilient and continue to bond and sometimes resonate. It is suggested that some structures contain emergent Mott insulators (EMI) and support superconductivity and other phases, under special conditions. In pressurized solid H2S, we propose presence of a sublattice of relatively narrow, nearly half filled band of H atoms, trapped in ordered interstitials of colvalently bon…
We have investigated the superconducting state of the noncentrosymmetric superconductor Re6Ti (Tc = 6.0 K) using muon-spin rotation/relaxation (muSR) technique. The zero-field muon experiment shows the presence of spontaneous magnetic fields in the superconducting state, indicating time-reversal symmetry breaking (TRSB). However, the low-temperature transverse field muon measurements suggest nodeless s-wave superconductivity. The time reversal symmetry breaking further confirmed in the stoichiometric composition Re24Ti5. These results indicate that the pairing symmetry is not affected by spin-…
The enigmatic pseudogap phase in underdoped cuprate high T_c superconductors has long been recognized as a central puzzle of the T_c problem. Recent data show that the pseudogap is likely a distinct phase, characterized by a medium range and quasi-static charge ordering. However, the origin of the ordering wavevector and the mechanism of the charge order is unknown. At the same time, earlier data show that precursive superconducting fluctuations are also associated with this phase. We propose that the pseudogap phase is a novel pairing state where electrons on the same side of the Fermi surfac…
Magnetic measurements have been carried out in the superconducting and normal states of the optimally doped nonmagnetic bismuthate superconductor Ba0.63K0.37BiO3. The magnetic data along with previous muSR, resistivity, and tunneling data consistently show that there is a large polaronic enhancement in the density of states and effective electron-phonon coupling constant. The first-principle calculation within the density-functional theory indicates a small electron-phonon coupling constant of about 0.3-0.4, which can only lead to about 1 K superconductivity within the conventional phonon-medi…
Nonequilibrium conditions offer novel routes to superconductivity that are not available at equilibrium. For example, by engineering nonequilibrium electronic populations, pairing may develop between electrons in different energy bands. A concrete proposal has been made to photo-induce superconductivity in a semiconductor, where pairing occurs between electrons in the conduction and valence bands, even for repulsive interactions. Here, we calculate the superfluid density for such a nonequilibrium paired state, and find it to be positive for repulsive interactions and interband pairing. The pos…
The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitud…
We report the discovery of a self-doped multi-layer high Tc superconductor Ba2Ca3Cu4O8F2(F0234) which contains distinctly different superconducting gap magnitudes along its two Fermi surface(FS) sheets. While formal valence counting would imply this material to be an undoped insulator, it is a self-doped superconductor with a Tc of 60K, possessing simultaneously both electron- and hole-doped FS sheets. Intriguingly, the FS sheet characterized by the much larger gap is the electron-doped one, which has a shape disfavoring two electronic features considered to be important for the pairing mechan…
The two superconducting phases recently discovered in skutterudite PrOs4Sb12 are discussed by using the phenomenological Ginzburg-Landau theory in the cubic (tetrahedral) crystal symmetry T_h. Building on experimental imput coming from the recent thermal conductivity measurements, the structure of the gap functions for these two phases are considered for the spin singlet pairing case. One of the phases lying in the high temperature and high field region (the A phase) is a strongly "anisotropic s-wave" state and another phase (the B phase) is "anisotropic s"+ i d-wave state. The B phase breaks …
PuCoGa$_5$ has emerged as a prototypical heavy-fermion superconductor, with its transition temperature ($T_c\simeq18.5$ K) being the highest amongst such materials. Nonetheless, a clear description as to what drives the superconducting pairing is still lacking, rendered complicated by the notoriously intricate nature of plutonium's 5$f$ valence electrons. Here, we present a detailed $^{69,71}$Ga nuclear quadrupole resonance (NQR) study of PuCoGa$_5$, concentrating on the system's normal state properties near to $T_c$ and aiming to detect distinct signatures of possible pairing mechanisms. In p…
Giant amplification of Berezinskii-Kosterlitz-Thouless transition temperature in superconducting systems characterized by cooperative interplay of small-gapped valence and conduction bands
The recent discovery of superconductivity in NaSn$_2$As$_2$ with a van der Waals layered structure raises immediate questions on its pairing mechanism and underlying electronic structure. Here, we present measurements of the temperature-dependent magnetic penetration depth $λ(T)$ in single crystals of NaSn$_2$As$_2$ down to $\sim40$ mK. We find a very long penetration depth $λ(0) = 960$ nm, which is strongly enhanced from the estimate of first-principles calculations. This enhancement comes from a short mean free path $\ell \approx 1.7$ nm, indicating atomic scale disorder possibly associated …
The question of pairing glue for the cuprate superconductors (SC)is revisited and its determination through the angle resolved photo-emission spectroscopy (ARPES) is discussed in detail. There are two schools of thoughts about the pairing glue question: One argues that superconductivity in the cuprates emerges out of doping the spin singlet resonating valence bond (RVB) state. Since singlet pairs are already formed in the RVB state there is no need for additional boson glue to pair the electrons. The other instead suggests that the d-wave pairs are mediated by the collective bosons like the co…
Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap $E_g$. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the BEC regime at low densities. At a given larger density, a band gap $E_g\sim 40$-$60$ …
Superconductivity and its underlying mechanisms are one of the most active research fields in condensed-matter physics. An important question is how to enhance the transition temperature $T_{\rm c}$ of a superconductor. In this respect, the possibly positive role of valence-skipping elements in the pairing mechanism has been attracting considerable interest. Here we follow this pathway and successfully enhance $T_{\rm c}$ up to almost 6 K in the simple chalcogenide SnTe known as topological crystalline insulator by doping the valence-skipping element In and codoping Se. A high-pressure synthes…
Topological superconductors (SCs) are novel phases of matter with nontrivial bulk topology. They host at their boundaries and vortex cores zero-energy Majorana bound states, potentially useful in fault-tolerant quantum computation. Chiral SCs are particular examples of topological SCs with finite angular momentum Cooper pairs circulating around a unique chiral axis, thus spontaneously breaking time-reversal symmetry (TRS). They are rather scarce and usually feature triplet pairing: best studied examples in bulk materials are UPt3 and Sr2RuO4 proposed to be f-wave and p-wave SCs respectively, a…
We introduce a minimal model for 2D cuprates with the on-site Hilbert space reduced to only three effective valence centers CuO$_4^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) and make use of the S=1 pseudospin formalism. Despite its seeming simplicity the model is believed to capture the salient features both of the hole- and electron-doped cuprates. The pseudospin formalism elucidates an unique fermion-boson duality of the doped cuprates, does provide an unified standpoint for classification of the "myriad"\, of electronic phases in cuprates and the evolution of the CuO$_2$ planes under a nonisov…
