UCoGe is reported as a weak ferromagnetic (FM) two-band superconductor (SC) with the critical temperature, $T_{\mathrm{SC}}\sim$ 0.7 K and the Curie temperature, $T_{\mathrm{C}}\sim$ 3 K at ambient pressure. We report exotic attributes of the SC and FM state in moderate magnetic fields. The observed phenomena clearly demonstrate that the SC regime is superior to the paramagnetic state in the vicinity of $T_{\mathrm{SC}}$. Above $T_{\mathrm{SC}}$, the zero-field state is characterized by a regime with strong FM spin fluctuations, suggesting proximity of the FM quantum critical point (FM-QCP). In addition, we observed that the robust SC regime develops independently on the existence or lack of the long-range FM ordering.
Identification of pairing mechanisms leading to the unconventional superconductivity realized in copper-oxide, heavy-fermions, and organic compounds is one of the most challenging issues in condensed-matter physics. Clear evidence for an electron-phonon mechanism in conventional superconductors is seen by the isotope effect on the superconducting transition temperatures $T_{\rm SC}$, since isotopic substitution varies the phonon frequency without affecting the electronic states. In unconventional superconductors, magnetic fluctuations have been proposed to mediate superconductivity, and consid…
The mechanism of unconventional superconductivity, such as high-temperature-cuprate, Fe-based, and heavy-fermion superconductors, has been studied as a central issue in condensed-matter physics. Spin fluctuations, instead of phonons, are considered to be responsible for the formation of Cooper pairs, and many efforts have been made to confirm this mechanism experimentally. Although a qualitative consensus seems to have been obtained, experimental confirmation has not yet been achieved. This is owing to a lack of the quantitative comparison between theory and experiments. Here, we show a semi-q…
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. We find that the fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are strikingly different for $d$- and $s^*$ symmetries in the crossover region. The chemical potential and the gaps functions for both pairing symmetries show several interesting features as a function of interaction. Fermion…
High-temperature superconductivity emerges in a host of different quantum materials, often in a region of the phase diagram where the electronic kinetic energy is comparable in magnitude with the electron-electron Coulomb repulsion. Describing such an intermediate-coupling regime has proven challenging, as standard perturbative approaches are inapplicable. Hence, it is of enormous interest to find models that are amenable to be solved using exact methods. While important advances have been made in elucidating the properties of one such minimal model -- the Hubbard model -- via numerical simula…
Superconductors are classified by their pairing mechanism and the coupling strength, measured as the ratio of the energy gap to the critical temperature, Tc. We present an extensive comparison of the gap ratios among many single- and multiband superconductors from simple metals to high-Tc cuprates and iron pnictides. Contrary to the recently suggested universality of this ratio in Fe-based superconductors, we find that the coupling in pnictides ranges from weak, near the BCS limit, to strong, as in cuprates, bridging the gap between these two extremes. Moreover, for Fe- and Cu-based materials,…
The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after the discovery of superconductivity it has been expected to be close to a ferromagnetic instability showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. The competition between different types of magnetic interactions and the duality between the local and itinerant character…
Ultrasound velocity measurements of the unconventional superconductor CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an unusual structural transformation of the flux line lattice (FLL) in the vicinity of the upper critical field. The transition field coincides with that at which heat capacity measurements reveal a second order phase transition. The lowering of the sound velocity at the transition is consistent with the collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL pinning. These results provide a strong evidence that the high field state …
The phase diagram of the layered organic superconductor $κ$-(ET)$_{2}$Cu[N(CN)$_{2}$]Cl has been accurately measured from a combination of $^{1}$H NMR and AC susceptibility techniques under helium gas pressure. The domains of stability of antiferromagnetic and superconducting long-range orders in the pressure {\it vs} temperature plane have been determined. Both phases overlap through a first-order boundary that separates two regions of inhomogeneous phase coexistence. The boundary curve is found to merge with another first order line related to the metal-insulator transition in the paramagnet…
Ubiquity of unconventional phenomena observed in a series of heavy fermion metals is discussed on the basis of an idea of critical valence fluctuations. After surveying experimental aspects of these unconventional behaviors in prototypical compounds, CeCu_2(Si,Ge)_2, under pressure, we propose that sharp valence crossover phenomena are realized in CeCu_6, CeRhIn_5, and Ce(Ir,Rh)Si_3 by tuning the pressure and the magnetic field simultaneously, on the basis of previous results for an extended Anderson lattice model with the Coulomb repulsion U_fc between localized f-electron and itinerant condu…
The nature of quantum criticality in CeCoIn$_5$ is studied by low-temperature thermal expansion $α(T)$. At the field-induced quantum critical point at H=5 T a crossover scale $T^\star\approx 0.3$ K is observed, separating $α(T)/T\propto T^{-1}$ from a weaker $T^{-1/2}$ divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn$_{5-x}$Sn$_x$ ($0\leq x\leq 0.18$), shifts $T^\star$ towards higher temp…
By means of density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled $J_{\rm{eff}}=3/2$ insulator GaTa$_4$Se$_8$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry $J_{\rm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of $J_{\rm{eff}}$ at the Ta $L_2$-edge up to 10.4 GPa. Our exact diagonalization based DFT+DMFT calculations includ…
The pairing of interacting fermions leading to superfluidity has two limiting regimes: the Bardeen-Cooper-Schrieffer (BCS) scheme for weakly interacting degenerate fermions and the Bose-Einstein condensation (BEC) of bosonic pairs of strongly interacting fermions. While the superconductivity that emerges in most metallic systems is the BCS-like electron pairing, strongly correlated electrons with poor Fermi liquidity can condense into the unconventional BEC-like pairs. Quantum spin liquids harbor extraordinary spin correlation free from order and the superconductivity that possibly emerges by …
The strange-metal state is a crucial problem in condensed matter physics highlighted by its ubiquity in almost all major correlated systems[1-7]. Its understanding could provide important insight into high-Tc superconductivity[2] and quantum criticality[8]. However, with the Fermi liquid theory failing in strange metals, understanding the highly unconventional behaviors has been a long-standing challenge. Fundamental aspects of strange metals remain elusive, including the nature of their charge carriers[1]. Here, we report the observation of a giant Nernst response in the strange-metal state i…
We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-$1/2$ Heisenberg antiferromagnetic ladder compound $\mathrm{(C_7H_{10}N)_2CuBr_4}$. The staggered order was previously evidenced from a continuous and symmetric splitting of $^{14}$N NMR spectral lines on lowering temperature below $T_c\simeq 330$ mK, with a saturation towards $\simeq 150$ mK. Unexpectedly, the split lines begin to further separate away below $T^*\sim 100$ mK while the line width and shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxatio…
A theory for treating the unconventional non-Fermi liquid temperature dependence of physical quantities, such as the resistivity, in the Pr-based two-channel Anderson impurities system is developed. It is shown that their temperature dependences are essentially the same as those in the pure lattice system except for the case of extremely low concentration of Pr ions that is difficult to realize by a controlled experiments. This result is consistent with recent observations in diluted Pr-1-2-20 system Y$_{1-x}$Pr$_x$Ir$_2$Zn$_{20}$ ($x=0.024,\,0.044,\,0.085,$ and $0.44$) reported in Yamane $et\…
Kitaev quantum spin liquids host Majorana fermions via the fractionalization of spins. In a magnetic field, the Majorana fermions were predicted to comprise a topological state, which has attracted great attention by the discovery of the half-quantized thermal Hall conductivity. Nevertheless, a reliable theory remains elusive for the field effect, especially at finite temperature. Here we present unbiased large-scale numerical results for the Kitaev model in a wide range of magnetic field and temperature. We find that the unconventional paramagnetic region showing fractional spin dynamics exte…
The understanding of strongly-correlated materials, and in particular unconventional superconductors, has puzzled physicists for decades. Such difficulties have stimulated new research paradigms, such as ultra-cold atom lattices for simulating quantum materials. Here we report on the realization of intrinsic unconventional superconductivity in a 2D superlattice created by stacking two graphene sheets with a small twist angle. For angles near $1.1^\circ$, the first `magic' angle, twisted bilayer graphene (TBG) exhibits ultra-flat bands near charge neutrality, which lead to correlated insulating…
We study the critical behavior of dc magnetization in the uranium ferromagnet URhSi around the paramagnetic to ferromagnetic phase transition at T_C~ 10 K with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis and the scaling analysis. URhSi is isostructural to uranium ferromagnetic superconductors URhGe and UCoGe. The critical exponent beta for the temperature dependence of the spontaneous magnetization below TC, gamma for the magnetic susceptibility, and delta for the magnetic isotherm at T_C in URhSi have been determined as beta = 0.300 +- 0.002, gamma = 1.00 +- 0…
The condensation of electron-hole (e-h) pairs is studied at zero temperature and in the presence of a weak spin-orbit coupling (SOC) in the inversion-layer quantum wells. Under realistic conditions, a perturbative SOC can have observable effects in the order parameter of the experimentally long-searched-for excitonic condensate. Firstly, the fermion exchange symmetry is absent for the e-h pairs indicating a counterexample to the known classification schemes of fermion pairing. With the lack of fermion exchange, the condensate spin has no definite parity. Additionally, the excitonic SOC breaks …
In the scientific description of unconventional transport properties of oxides (spin-dependent transport, superconductivity etc.), the spin-state degree of freedom plays a fundamental role. Because of this, temperature- or magnetic field-induced spin-state transitions are in the focus of solid-state physics. Cobaltites, e.g. LaCoO3, are prominent examples showing these spin transitions. However, the microscopic nature of the spontaneous spin crossover in LaCoO3 is still controversial. Here we report magnetostriction measurements on LaCoO3 in magnetic fields up to 70 T to study the sharp, field…
The interplay between multiple bands, sizable multi-band electronic correlations and strong spin-orbit coupling may conspire in selecting a rather unusual unconventional pairing symmetry in layered Sr$_{2}$RuO$_{4}$. This mandates a detailed revisit of the normal state and, in particular, the $T$-dependent incoherence-coherence crossover. Using a modern first-principles correlated view, we study this issue in the actual structure of Sr$_{2}$RuO$_{4}$ and present a unified and quantitative description of a range of unusual physical responses in the normal state. Armed with these, we propose tha…
The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structu…
Quantum critical systems derive their finite temperature properties from the influence of a zero temperature quantum phase transition. The paradigm is essential for understanding unconventional high-Tc superconductors and the non-Fermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated. Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behavior to distinct Fermi liquid ground states in a hi…
One of the major themes in the physics of condensed matter is unconventional superconductivity in correlated electronic systems. The symmetry structure of Cooper pairs is thought to be the key to the understanding of the pairing mechanism of their superconductivity. In iron pnictide superconductors, the precise symmetry of the order parameter as well its evolution with doping remains highly controversial. There is no general consensus on the nature of pairing in iron-based superconductors leaving the perspectives ranging from $s^{++}$ wave, to $s^{\pm}$, and $d$ wave. Here we show that doping …
Recent experiments in unconventional superconductors, and in particular iron-based materials, have reported evidence of an antiferromagnetic quantum critical point (AFM-QCP) emerging inside the superconducting dome of the phase diagram. Fluctuations associated with such an AFM-QCP are expected to promote unusual temperature dependencies of thermodynamic quantities. Here, we compute the $T$ dependence of the specific heat $C(T)$ deep inside a fully gapped $s^{+-}$ superconducting state as the AFM-QCP is approached. We find that, at the AFM-QCP, the specific heat $C(T)$ vanishes quadratically wi…
Crossover and Changeover in Spin-1 Kitaev-$Γ$ Chain with Uniaxial Single-ion Anisotropy
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Nankai University（南开大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Lanzhou University（兰州大学）；Zhejiang University（浙江大学）
We report the temperature and magnetic field dependence of resistivity ($ρ$) for single-crystalline EuTi$_{1-x}$Nb$_{x}$O$_3$ ($x$=0.10$-$0.20), an itinerant ferromagnetic system with very low Curie temperature ($T_C$). The detailed analysis reveals that the charge conduction in EuTi$_{1-x}$Nb$_{x}$O$_3$ is extremely sensitive to Nb concentration and dominated by several scattering mechanisms. Well below the $T_C$, where the spontaneous magnetization follows the Bloch's $T^{3/2}$ law, $ρ$ exhibits $T^2$ dependence with a large coefficient $\sim$10$^{-8}$ $Ω$ cm K$^{-2}$ due to the electron-mag…
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…
Superconductivity with a remarkably high $T_c$ has recently been found in Sr-doped NdNiO$_2$ thin films. While this system bears strong similarities to the cuprates, some differences, such as a weaker antiferromagnetic exchange coupling and possible high-spin moments on the doped Ni sites have been pointed out. Here, we investigate the effect of Hund coupling and crystal field splitting in a simple model system and argue that a multiorbital description of nickelate superconductors is warranted, especially in the strongly hole-doped regime. We then look at this system from the viewpoint of the …
Quantum criticality of metal-insulator transitions in correlated electron systems is shownto belong to an unconventional universality class with violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square latticesare capable…
We report detailed Knight shift measurements of the two indium sites in the heavy fermion compound CeIrIn$_5$ as a function of temperature and field orientation. We find that the Knight shift anomaly is orientation-dependent, with a crossover temperature $T^*$ that varies by 50% as the field is rotated from (001) to (100). This result suggests that the hybridization between the Ce 4f states and the itinerant conduction electrons is anisotropic, a result that reflects its collective origin, and may lead to anisotropic Kondo liquid behavior and unconventional superconductivity.
Heavy fermion metals provide a prototype setting to study quantum criticality. Experimentally, quantum critical points have been identified and studied in a growing list of heavy fermion compounds. Theoretically, Kondo destruction has provided a means to characterize a class of unconventional quantum critical points that goes beyond the Landau framework of order-parameter fluctuations. Among the prominent evidence for such local quantum criticality have been measurements in YbRh$_2$Si$_2$. A rapid crossover is observed at finite temperatures in the isothermal field dependence of the Hall coeff…
The NMR results in iron pnictides BaFe2(As1-xPx)2 and Ba(Fe1-xCox)2As2 are analyzed based on the self-consistent renormalization (SCR) spin fluctuation theory. The temperature dependence of the NMR relaxation rate (T_1)^{-1} as well as the electrical resistivity is well reproduced by a SCR model where two-dimensional antiferromagnetic (AF) spin fluctuations are dominant. The successful description of the crossover feature from non-Fermi liquid to Fermi liquid behavior strongly suggests that low-lying spin fluctuations in BaFe2(As1-xPx)2 and Ba(Fe1-xCox)2As2 possess an itinerant AF nature, and …
The intermetallic FeSi exhibits an unusual temperature dependence in its electronic and magnetic degrees of freedom, epitomized by the crossover from a low temperature non-magnetic semiconductor to a high temperature paramagnetic metal with a Curie-Weiss like susceptibility. Many proposals for this unconventional behavior have been advanced, yet a consensus remains elusive. Using realistic many-body calculations, we here reproduce the signatures of the metal-insulator crossover in various observables: the spectral function, the optical conductivity, the spin susceptibility, and the Seebeck coe…
Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critic…
The emergent behavior of spin liquids that are born out of geometrical frustration makes them an intriguing state of matter. We show that in the quantum kagome antiferromagnet ZnCu$_3$(OH)$_6$SO$_4$ several different correlated, yet fluctuating states exist. By combining complementary local-probe techniques with neutron scattering, we discover a crossover from a critical regime into a gapless spin-liquid phase with decreasing temperature. An additional unconventional instability of the latter phase leads to a second, distinct spin-liquid state that is stabilized at the lowest temperatures. We …
Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh2Si2, a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the qua…
The energetics of the interplay between superconductivity and the pseudogap in high temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two dimensional Hubbard model. Two regimes of superconductivity are found: a weak coupling/large doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong coupling regime in which superconductivity is associated with an increase in potential energy and decrease in kinetic energy. The crossover between the two regimes is found to …
Influence of quantum critical point (QCP) of first-order valence transition (FOVT) on Ce- and Yb-based heavy fermions is discussed as a key origin of anomalies such as non-Fermi liquid, metamagnetism, and unconventional superconductivity. Even in intermediate-valence materials, the QCP of the FOVT is shown to be induced by applying a magnetic field, which creates a new characteristic energy distinct from the Kondo temperature. It is stressed that the key concept is closeness to the QCP of the FOVT by pointing out that the proximity of the QCP explains sharp contrast between X=Ag and X=Cd in Yb…
The layered van der Waals ferromagnetic Fe$_3$GeTe$_2$ harbours an unconventional interplay between topology and magnetism, leading to a large anomalous Hall conductivity at low temperatures. Here, we investigate the temperature dependence of its charge dynamics and reveal that upon entering the ferromagnetic state at $T_C \sim 200$ K and further lowering the temperature there is the onset of a gradual spectral weight reshuffling from the mid-infrared range towards far- as well as near-infrared frequencies. This two-fold spectral weight transfer indicates the important role of the Hund's coupl…
Unconventional superconductivity from heavy fermion (HF) is always observed in f-electron systems, in which Kondo physics between localized f-electrons and itinerant electrons plays an essential role. Whether HF superconductivity could be achieved in other systems without f electrons, especially for d-electron systems, is still elusive. Here, we experimentally study the origin of d-electron HF behavior in iron-based superconductors (FeSCs) AFe2As2 (A = K, Rb, Cs). Nuclear magnetic resonance on 75As reveals a universal coherent-incoherent crossover with a characteristic temperature T*. Below T*…
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear therma…
We study a model of $N$ fermions in a quantum dot, coupled to $M$ bosons by a disorder-induced complex Yukawa coupling (Yukawa-SYK model), in order to explore the interplay between non-Fermi liquid and superconductivity in a strongly coupled, (quantum-)critical environment. We analyze the phase diagram of the model for an arbitrary complex interaction and arbitrary ratio of $N/M$, with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like behavior with a power-law frequency dependence of the fermionic self-energy and an impurity-like behavior with frequency independent sel…
The interplay between dimensionality and various phases of matter is a central inquiry in condensed matter physics. New phases are often discovered through spontaneously broken symmetry. Understanding the dimensionality of superconductivity in the high-temperature cuprate analogue $-$ layered nickelates and revealing a new symmetry-breaking state are the keys to deciphering the underlying pairing mechanism. Here, we demonstrate the highly-tunable dimensionality and a broken rotational symmetry state in the superconductivity of square-planar layered nickelates. The superconducting state, probed…
