Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS and Migdal-Eliashberg theories. We consider the problem of obtaining closed-form analytical lower and upper bounds on transition temperatures for such systems. We focus mainly on a class of models known as the gamma-model, a variation of the Eliashberg theory of superconductivity where the effective interaction potential scales as V(Omega) proportional to 1/|Omega|^gamma. Building on a recent reformulation of Migdal-Eliashberg theory expressed as a classical infinite spin chain with nonlocal interactions [1,2], and employing a linear algebra analysis of the Hessian matrix obtained from the free energy functional, we derive rigorous, closed-form expressions for upper and lower bounds on the superconducting transition temperature for any gamma > 0. The main result of the paper is to establish an analytical upper bound on the transition temperature in closed form. Our upper bound is significantly tighter than those currently available in the literature and demonstrates rapid convergence toward results from prior numerical studies. Also, by applying the singularity condition directly to the unbounded Hessian matrix, our independently performed calculations confirm the lower bounds previously established in the literature [3].
We determine the behavior of the critical temperature of magnetically mediated p-wave superconductivity near a ferromagnetic quantum critical point in three dimensions, distinguishing universal and non-universal aspects of the result. We find that the transition temperature is non-zero at the critical point, raising the possibility of superconductivity in the ferromagnetic phase.
We report a high-pressure single crystal study of the superconducting ferromagnet UCoGe. Ac-susceptibility and resistivity measurements under pressures up to 2.2 GPa show ferromagnetism is smoothly depressed and vanishes at a critical pressure $p_c = 1.4$ GPa. Near the ferromagnetic critical point superconductivity is enhanced. Upper-critical field measurements under pressure show $B_{c2}(0)$ attains remarkably large values, which provides solid evidence for spin-triplet superconductivity over the whole pressure range. The obtained $p-T$ phase diagram reveals superconductivity is closely conne…
Transverse-field muon spin relaxation measurements have been carried out on the heavy-fermion superconductor UPt3 doped with small amounts of Pd. We find that the critical Pd concentration for the emergence of the large-moment antiferromagnetic phase is ~0.6 at.%Pd. At the same Pd content, superconductivity is completely suppressed. The existence of a magnetic quantum critical point in the phase diagram, which coincides with the critical point for superconductivity, provides evidence for ferromagnetic spin-fluctuation mediated odd-parity superconductivity, which competes with antiferromagnetic…
We investigate the influence of critical spin fluctuations on electromagnetic responses in the odd-frequency superconductivity. It is shown that the Meissner kernel of the odd-frequency superconductivity is strongly reduced by the critical spin fluctuation or the massless spin wave mode in the antiferromagnetic phase. These results imply that the superfluid density is reduced, and the London penetration depth is lengthened for the odd-frequency pairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikov pairing is spontaneously realized both for even- and odd-frequency in th…
Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between superconductivity and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconductivity always develops above a quantum-critical point, no matter how strong the fermionic self-energy is. We argue that superconductivity sho…
We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermio…
We study how an inversion-breaking quantum critical point affects the ground state of a one-dimensional electronic liquid with repulsive interaction and spin-orbit coupling. We find that regardless of the interaction strength, the critical fluctuations always lead to a gap in the electronic spin-sector. The origin of the gap is a two-particle backscattering process, which becomes relevant due to renormalization of the Luttinger parameter near the critical point. The resulting spin-gapped state is a one-dimensional version of spin triplet superconductivity. Interestingly, in the case of a ferro…
Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optic phonons decouple from the electron charge. In the resulting vacuum, the residual interactions between quasiparticles are carried by energy fluctuations of the polar medium, resembling the gravitational interactions of a dark matter universe. Here we demonstrate that pairing inevitably emerges from "gravitational'…
We will examine the possible link between spin fluctuations and the superconducting mechanism in the iron-based high temperature superconductor Ba(Fe,Co)2As2 based on NMR and high pressure transport measurements.
Departing from the assumption that pairing is induced by an retarded external 'bosonic glue', we reformulate the Bardeen-Cooper-Schrieffer theory of superconductivity as a scaling theory. Conventional superconductors correspond with the asymptotically free case but the theory can be effortlessly generalized to handle quantum critical metals. We find that superconducting Tc's are strongly enhanced in the latter when retardation is strong while the coupling is weak. It appears that this simple scaling theory does account quite well for superconducting properties near quantum critical points.
We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range supe…
We analyze an asymptotically exact solution for the transition temperature of p-wave superconductivity near ferromagnetic criticality on the basis of the three-dimensional electron systems in which scattering processes are dominated by exchange interactions with small momentum transfers. Taking into account all Feynman diagrams in the gap equation, we show that vertex corrections neglected in the conventional Eliashberg's formalism enhance the dynamical retarded effect of the pairing interaction, and raise the superconducting transition temperature significantly, though they just give subleadi…
Superconductivity mediated by spin fluctuations in weak and nearly ferromagnetic metals is studied close to the zero-temperature magnetic transition. We solve analytically the Eliashberg equations for p-wave pairing and obtain the normal state quasiparticle self-energy and the superconducting transition temperature $T_c$ as a function of the distance to the quantum critical point. We show that the reduction of quasiparticle coherence and life-time due to scattering by quasistatic spin fluctuations is the dominant pair-breaking process, which leads to a rapid suppression of $T_c$ to a nonzero v…
Weakly correlated electrons on a square lattice are studied by angle-resolved functional renormalization group. Upon renormalization the interaction starts to depend on momenta and has pole-like solutions near a doping-dependent characteristic critical energy scale. Near half-filling this scale is the pseudogap temperature T*. In the overdoped regime the critical scale is the mean-field like critical temperature for d-wave superconductivity.
75As-zero-field nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements are performed on CaFe2As2 under pressure. At P = 4.7 and 10.8 kbar, the temperature dependences of nuclear-spin-lattice relaxation rate (1/T1) measured in the tetragonal phase show no coherence peak just below Tc(P) and decrease with decreasing temperature. The superconductivity is gapless at P = 4.7 kbar but evolves to that with multiple gaps at P = 10.8 kbar. We find that the superconductivity appears near a quantum critical point under pressures in the range 4.7 kbar < P < 10.8 kbar. Both el…
Pressure-induced superconductivity beyond magnetic quantum criticality in a Kondo ferromagnet
New Cornerstone Science Laboratory, Center for Correlated Matter and School of Physics, Zhejiang University（浙江大学物理学院关联物质中心新基石科学实验室）；Hubei Key Laboratory of Photoelectric Materials and Devices, School of Materials Science and Engineering, Hubei Normal University（湖北师范大学材料科学与工程学院光电材料与器件湖北省重点实验室）
We discover superconductivity (SC) in LaAgSb$_2$ at ambient pressure and its close correlation with a charge density wave (CDW) under pressure. The superconducting transition temperature ($T_c$) exhibits a sharp peak at the CDW critical pressure of 3.2 GPa. We demonstrate that the carriers inhabiting the Sb-square net is crucial not only in the formation of CDW but also in SC for their relatively strong electron-phonon coupling (EPC). Furthermore, theoretical EPC strength in pristine LaAgSb$_2$ cannot explain the observed peak with $T_c\sim 1$ K, which indicates that an additional mechanism re…
We report bulk superconductivity induced by an isovalent doping of phosphorus in BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$. The P-for-As substitution results in shrinkage of lattice, especially for the FeAs block layers. The resistivity anomaly associated with the spin-density-wave (SDW) transition in the undoped compound is gradually suppressed by the P doping. Superconductivity with the maximum $T_c$ of 30 K emerges at $x$=0.32, coinciding with a magnetic quantum critical point (QCP) which is evidenced by the disappearance of SDW order and the linear temperature-dependent resistivity in the normal…
Measurements of specific heat and electrical resistivity in magnetic fields up to 9 T along [001] and temperatures down to 50 mK of Sn-substituted CeCoIn5 are reported. The maximal -ln(T) divergence of the specific heat at the upper critical field H_{c2} down to the lowest temperature characteristic of non-Fermi liquid systems at the quantum critical point (QCP), the universal scaling of the Sommerfeld coefficient, and agreement of the data with spin-fluctuation theory, provide strong evidence for quantum criticality at H_{c2} for all x < 0.12 in CeCoIn5-xSnx. These results indicate the "accid…
We study electron correlation driven superconductivity on a decorated honeycomb lattice (DHL), which has a low-energy flat band. On doping, we find singlet superconductivity with extended-s, extended-d and f-wave symmetry mediated by magnetic exchange. f-wave singlet pairing is enabled by the lattice decoration. The critical temperature is predicted to be significantly higher than on similar lattices lacking flat bands. We discuss how high-temperature superconductivity could be realized in the DHL materials such as Rb3TT. 2 H2O and Mo3S7(dmit)3.
Measurements of the upper critical field $H_{c2}$ near $T_c$ of Pr$_{1- x}$La$_{x}$Os$_{4}$Sb$_{12}$ were performed by specific heat. A positive curvature in $H_{c2}$ versus $T$ was observed in samples and concentrations exhibiting two superconducting transitions. These results argue against this curvature being due to two-band superconductivity. The critical field slope - $dH_{c2}/dT$ suggests the existence of a crossover concentration $x_{cr} \approx 0.25$, below which there is a rapid suppression of effective electron mass with La-alloying. This crossover concentration was previously detect…
A possibility of the realization of the p-wave spin-singlet superconductivity ($p$SS), whose gap function is odd both in momentum and in frequency, is investigated by solving the gap equation with the phenomenological interaction mediated by the antiferromagnetic spin fluctuation. The $p$SS is realized prevailing over the d-wave singlet superconductivity ($d$SS) in the vicinity of antiferromagnetic quantum critical pint (QCP) both on the paramagnetic and on the antiferromagnetic sides. Off the QCP in the paramagnetic phase, however, the $d$SS with line-nodes is realized as \textit{conventional…
We consider a strongly spin-orbit-coupled metal, one of whose Fermi surfaces is close to a Lifshitz (topological) transition. Via a renormalization group analysis of the square-lattice Hubbard model with strong Rashba spin-orbit coupling, we show that such a metal is generically unstable to the formation of mixed-parity superconductivity with a helical triplet component.
Superconductivity and magnetism are mutually exclusive in most alloys and elements, so it is striking that superconductivity emerges around a magnetic quantum critical point (QCP) in many strongly correlated electron systems (SCES). In the latter case superconductivity is believed to be unconventional and directly influenced by the QCP. However, experimentally unconventional superconductivity has neither been established nor directly been linked to any mechanism of the QCP. Here we report measurements in the heavy-fermion superconductors CeIrSi$_3$ and CeRhSi$_3$. The measurements were perform…
We consider an s-wave superconductor in the vicinity of a second-order ferromagnetic (FM) or spin-density-wave (SDW) quantum critical point (QCP), where the superconductivity and magnetism arise from separate mechanisms. The quantum critical spin fluctuations reduce the superconducting T_c. Near a FM QCP, we find that T_c falls to zero as 1/|ln kappa| in 3D and as kappa in 2D, where kappa ~ |J-J_c|^nu is the inverse correlation length of the spin fluctuations, and measures the distance |J-J_c| from the quantum critical point. SDW quantum critical fluctuations, on the other hand, suppress T_c t…
Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor CeCoIn_5 at pressures to 4.2 GPa reveal a strong crossover in transport properties near P^* \approx 1.6 GPa, where T_c is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.
We investigate reentrant superconductivity in an Ising ferromagnetic superconductor URhGe under a transverse magnetic field h_x. The superconducting transition temperature for p-wave order parameters T_{sc} is calculated and shows two domes as a function of h_x. We find strong enhancement of T_{sc} in the high-field dome near a saturation field h_s where the spins align in the transverse direction. Soft magnons generate strong attractive interactions there. Spin components of the pairing show a significant change between h_x<h_s and h_x>h_s. We also discuss the appearance of superconductivity …
A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on a single-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. The FM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below $P_c$ showed phase separation of the FM and paramagnetic (PM) phases below Curie temperature $T_{\textrm{Curie}}$, suggesting first-order FM quantum phase transition (QPT). We found that the internal field was absent above $P_c$, but the superconductivity is almost unchanged. This result suggests the existence of the nonunitary to unitary transition of the superconductivit…
The interplay between magnetism and superconductivity has been a central issue in unconventional superconductors. While the dynamic magnetism could be the source of electron pairing, the static magnetism is generally believed to compete with superconductivity. In this sense, the observation of Q phase, the coupled spin-density wave order and superconductivity, in the heavy-fermion superconductor CeCoIn5 is very puzzling. Whether this Q phase origins from the novel Fulde-Ferrel-Larkin-Ovchinnikov state is under hot debate. Here we report the resistivity and thermal conductivity study of a newly…
Spin dynamics evolution of BaFe$_2$(As$_{1-x}$P$_x$)$_2$ was probed as a function of P concentration via $^{31}$P NMR. Our NMR study reveals that two-dimensional antiferromagnetic (AF) fluctuations are notably enhanced with little change in static susceptibility on approaching the AF phase from the superconducting dome. Moreover, magnetically ordered temperature $θ$ deduced from the relaxation rate vanishes at optimal doping. These results provide clear-cut evidence for a quantum-critical point (QCP), suggesting that the AF fluctuations associated with the QCP play a central role in the high-$…
Superconductors close to quantum phase transitions often exhibit a simultaneous increase of electronic correlations and superconducting transition temperatures. Typical examples are given by the recently discovered iron-based superconductors. We investigated the band-specific quasiparticle masses of AFe2As2 single crystals with A = K, Rb, and Cs and determined their pressure dependence. The evolution of electronic correlations could be tracked as a function of volume and hole doping. The results indicate that with increasing alkali-metal ion radius a quantum critical point is approached. The c…
Many unconventional superconductors exhibit a common set of anomalous charge transport properties that characterize them as `strange metals', which provides hope that there is single theory that describes them. However, model-independent connections between the strange metal and superconductivity have remained elusive. In this letter, we show that the Hall effect of the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ contains an anomalous contribution arising from the correlations within the strange metal. This term has a distinctive dependence on magnetic field, which allows us to…
The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground-state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find …
We consider possible routes to superconductivity in hydrated cobaltates Na_xCoO_2.yH_2O on the basis of the t-J-V model plus phonons on the triangular lattice. We studied the stability conditions for the homogeneous Fermi liquid (HFL) phase against different broken symmetry phases. Besides the sqrt(3)xsqrt(3)-CDW phase, triggered by the nearest-neighbour Coulomb interaction V, we have found that the HFL is unstable, at very low doping, against a bond-ordered phase due to J. We also discuss the occurrence of phase separation at low doping and V. The interplay between the electron-phonon interac…
Superconductivity in lanthanide- and actinide-based heavy-fermion metals can have different microscopic origins. Among others, Cooper pair formation based on fluctuations of the valence, of the quadrupole moment or of the spin of the localized 4f/5f shell have been proposed. Spin-fluctuation mediated superconductivity in CeCu2Si2 was demonstrated by inelastic neutron scattering to exist in the vicinity of a spin-density-wave quantum critical point. The isostructural HF compound YbRh2Si2 which is prototypical for a Kondo-breakdown quantum critical point has so far not shown any sign of supercon…
We report the magnetoresistance in the novel spin-triplet superconductor UTe2 under pressure close to the critical pressure Pc, where the superconducting phase terminates, for field along the three a, b and c-axes in the orthorhombic structure. The superconducting phase for H // a-axis just below Pc shows a field-reentrant behavior due to the competition with the emergence of magnetic order at low fields. The upper critical field Hc2 for H // c-axis shows a quasi-vertical increase in the H-T phase diagram just below Pc, indicating that superconductivity is reinforced by the strong fluctuations…
We report the discovery of superconductivity at a pressure-induced magnetic quantum critical point in the Kondo-lattice system CeSb2, sustained up to magnetic fields that exceed the conventional Pauli limit eight-fold. Like CeRh2As2, CeSb2 is locally non-centrosymmetric around the Ce-site, but the evolution of critical fields and normal state properties as CeSb2 is tuned through the quantum critical point motivates a fundamentally different explanation for its resilience to applied field.
We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition from an anti-ferromagnetic Néel ordered state to a VBS-like state. We argue further that the symplectic fermions capture the proper degrees of freedom in the zero temperature phase that is the parent to the superconducting phase in the cuprates. We then show that our model reproduces some features found recently in experiments and also i…
With understood exceptions, conventional superconductivity does not coexist with long-range magnetic order[1]. In contrast, unconventional superconductivity develops near a boundary separating magnetically ordered and magnetically disordered phases[2,3]. A maximum in the superconducting transition temperature Tc develops where this boundary extrapolates to T=0 K, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity[4,5]. Invariably though, unconventional superconductivity hides the magnetic boundary when T < Tc, pr…
In heavy fermion systems, higher-rank multipole operators are active thanks to the strong spin-orbit interaction (SOI), and the role of diverse multipole fluctuations on the pairing mechanism attracts a lot of attention. Here, we study a mechanism of superconductivity in heavy fermion systems, by focusing on the impact of vertex corrections (VCs) for the pairing interaction going beyond the Migdal approximation. In heavy fermion systems, strong interference between multipole fluctuations cause significant VCs, that represent many-body effects beyond mean-field-type approximations. Especially, …
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 …
An intriguingly complex phase diagram of Na-doped SrFe2As2 is uncovered using high-resolution thermal-expansion, magnetization and heat-capacity measurements. The detailed temperature dependence of the orthorhombic distortion and the anisotropy of the uniform magnetic susceptibility provide evidence for nine distinct electronic phases near the transition region between stripe antiferromagnetism and unconventional superconductivity. In particular, we report the finding of a new magnetic phase which competes surprisingly strongly with superconductivity. From theoretical studies we propose that t…
By first-principles calculations, we present a doping-dependent phase diagram of LaO{\it M}As ({\it M}=V--Cu) family. It is characterized as antiferromagnetic semiconductor around LaOMnAs side and ferromagnetic metal around LaOCoAs. Both LaOFeAs and LaONiAs, where superconductivity were discovered, are located at the borderline of magnetic phases. Extensive Fermi surface analysis suggests that the observed superconductivity is of electron-type in its origin. We discuss possible pairing mechanisms in the context of competing ferromagnetic phases found in this work and the ferromagnetic spin flu…
A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transit…
We report a study on the interplay between antiferromagnetism (AFM) and superconductivity (SC) in a heavy-fermion compound CeRhIn$_5$ under pressure $P=1.75$ GPa. The onset of the magnetic order is evidenced from a clear split of $^{115}$In-NQR spectrum due to the spontaneous internal field below the Néel temperature $T_N=2.5$ K. Simultaneously, bulk SC below $T_c=2.0$ K is demonstrated by the observation of the Meissner diamagnetism signal whose size is the same as in the exclusively superconducting phase. These results indicate that the AFM coexists homogeneously with the SC at a microscopic…
Motivated by recent experiments reporting superconductivity only at very low temperature in a class of heavy fermion compounds, we study the impact of energy fluctuations with small momentum transfer on the pairing instability near an antiferromagnetic quantum critical point. While these fluctuations, formed by composite spin fluctuations, were proposed to explain the thermodynamic and transport properties near the quantum critical point of compounds such as YbRh$_{2}$Si$_{2}$ and CeCu$_{6-x}$Au$_{x}$ at $x\approx0.1$, here they are found to strongly suppress $T_{c}$ of the $d$-wave pairing of…
Superconductivity in many strongly correlated materials appears in proximity to a density-wave or nematic order and is believed to be mediated by quantum-critical (QC) fluctuations of the corresponding order parameter. We argue that fingerprints of QC pairing can be extracted from the angular dependence of the gap $Δ(θ)$. We consider pairing by QC nematic fluctuations and show that there exist multiple pairing instabilities within the same symmetry ($s-$wave in our case), with closely spaced transition temperatures $T_{c,n}$. The corresponding $Δ_n (θ)$ change sign $8n$ times along the FS. Onl…
The nature of the quantum valence transition is studied in the one-dimensional periodic Anderson model with Coulomb repulsion between f and conduction electrons by the density-matrix renormalization group method. It is found that the first-order valence transition emerges with the quantum critical point and the crossover from the Kondo to the mixed-valence states is strongly stabilized by quantum fluctuation and electron correlation. It is found that the superconducting correlation is developed in the Kondo regime near the sharp valence increase. The origin of the superconductivity is ascribed…
We use the two fluid model to determine the conditions under which the nuclear spin-lattice lattice relaxation rate, $T_1$, of candidate heavy quantum critical superconductors can exhibit scaling behavior and find that it can occur if and only if their "hidden" quantum critical spin fluctuations give rise to a temperature-independent intrinsic heavy electron spin-lattice relaxation rate. The resulting scaling of $T_1$ with the strength of the heavy electron component and the coherence temperature, $T^*$, provides a simple test for their presence at pressures at which the superconducting transi…
To understand the role of electron-phonon interaction in superconducting MgCNi$_{3}$ we have performed density functional based linear response calculations of its lattice dynamical properties. A large coupling constant $% λ$= 1.51 is predicted and contributing phonons are identified as displacements of Ni atoms towards octahedral interstitials of the perovskite lattice. Instabilities found for some vibrational modes emphasize the role of anharmonic effects in resolving experimental controversies.
The in-plane resistivity $ρ$ and thermal conductivity $κ$ of FeAs-based superconductor KFe$_2$As$_2$ single crystal were measured down to 50 mK. We observe non-Fermi-liquid behavior $ρ(T) \sim T^{1.5}$ at $H_{c_2}$ = 5 T, and the development of a Fermi liquid state with $ρ(T) \sim T^2$ when further increasing field. This suggests a field-induced quantum critical point, occurring at the superconducting upper critical field $H_{c_2}$. In zero field there is a large residual linear term $κ_0/T$, and the field dependence of $κ_0/T$ mimics that in d-wave cuprate superconductors. This indicates that…
The tetragonal heavy-fermion metal YbRh$_2$Si$_2$ orders antiferromagnetically at $T_{\rm N} = 70$ mK and exhibits an unconventional quantum critical point (QCP) of Kondo-destroying type at $B_{\rm N} = 60$ mT, for the magnetic field applied within the basal ($a,b$) plane. Ultra-low-temperature magnetization and heat-capacity measurements at very low fields indicate that the 4$f$-electronic antiferromagnetic (AF) order is strongly suppressed by a nuclear-dominated hybrid order (`A-phase') at $T_{\rm A} \le 2.3$ mK, such that quantum critical fluctuations develop at $B \approx 0$ (Schuberth et …
In several unconventional superconductors, the highest superconducting transition temperature $T_{c}$ is found in a region of the phase diagram where the antiferromagnetic transition temperature extrapolates to zero, signaling a putative quantum critical point. The elucidation of the interplay between these two phenomena - high-$T_{c}$ superconductivity and magnetic quantum criticality - remains an important piece of the complex puzzle of unconventional superconductivity. In this paper, we combine sign-problem-free Quantum Monte Carlo simulations and field-theoretical analytical calculations t…
The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum dependent quasiparticles as in many materials near the Mott insulator. Among all, the mode-coupling theory of the density fl…
This paper shows the existence of a duality between an unidirectional charge density wave order and a superconducting order. This duality predicts the existence of charge density wave near a superconducting vortex, and the existence of superconductivity near a charge density wave dislocation.
The isostructural transition in the tetragonal phase, with sizable change in the anion-height, is realized in heavily H-doped LaFeAsO and (La,P) co-doped CaFe$_2$As$_2$. In these compounds, the superconductivity with higher-Tc (40~50 K) is realized near the isostructural transition. To reveal the origin of the anion-height instability and its important role in realizing the higher-Tc state, we develop the orbital-spin fluctuation theory by including the vertex correction. It is found that the non-nematic orbital fluctuations, which induce the anion-height instability, can develop near the magn…
Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressure-induced enhancement of superconductivity in CeCu$_2$Si$_2$ away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu$_2$Si$_2$ and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature $T_{\rm cr}$. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical…
