Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus.

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands.

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at "ghost crossings" of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron-electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

Quantum criticality enabled by intertwined degrees of freedom.

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice.

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

CoTe2 : A Quantum Critical Dirac Metal with Strong Spin Fluctuations.

Quantum critical points separating weak ferromagnetic and paramagnetic phases trigger many novel phenomena. Dynamical spin fluctuations not only suppress the long-range order, but can also lead to unusual transport and even superconductivity. Combining quantum criticality with topological electronic properties presents a rare and unique opportunity. Here, by means of ab initio calculations and magnetic, thermal, and transport measurements, it is shown that the orthorhombic CoTe2 is close to ferromagnetism, which appears suppressed by spin fluctuations. Calculations and transport measurements reveal nodal Dirac lines, making it a rare combination of proximity to quantum criticality and Dirac topology.

High Pressure-Driven Magnetic Disorder and Structural Transformation in Fe3 GeTe2 : Emergence of a Magnetic Quantum Critical Point.

Among the recently discovered 2D intrinsic van der Waals (vdW) magnets, Fe3 GeTe2 (FGT) has emerged as a strong candidate for spintronics applications, due to its high Curie temperature (130 - 220 K) and magnetic tunability in response to external stimuli (electrical field, light, strain). Theory predicts that the magnetism of FGT can be significantly modulated by an external strain. However, experimental evidence is needed to validate this prediction and understand the underlying mechanism of strain-mediated vdW magnetism in this system. Here, the effects of pressure (0 - 20 GPa) are elucidated on the magnetic and structural properties of Fe3 GeTe2 by means of synchrotron Mössbauer source spectroscopy, X-ray powder diffraction and Raman spectroscopy over a wide temperature range of 10 - 290 K. A strong suppression of ferromagnetic ordering is observed with increasing pressure, and a paramagnetic ground state emerges when pressure exceeds a critical value, PPM ≈ 15 GPa. The anomalous pressure dependence of structural parameters and vibrational modes is observed at PC ≈ 7 GPa and attributed to an isostructural phase transformation. Density functional theory calculations complement these experimental findings. This study highlights pressure as a driving force for magnetic quantum criticality in layered vdW magnetic systems.

Multicomponent odd-parity superconductivity in UAu2 at high pressure.

We report that high-quality single crystals of the hexagonal heavy fermion material uranium diauride (UAu2) become superconducting at pressures above 3.2 GPa, the pressure at which an unusual antiferromagnetic state is suppressed. The antiferromagnetic state hosts a marginal fermi liquid and the pressure evolution of the resistivity within this state is found to be very different from that approaching a standard quantum phase transition. The superconductivity that appears above this transition survives in high magnetic fields with a large critical field for all field directions. The critical field also has an unusual angle dependence suggesting that the superconductivity may have an order parameter with multiple components. An order parameter consistent with these observations is predicted to host half-quantum vortices (HQVs). Such vortices can be topologically entangled and have potential applications in quantum computing.

Two-dimensional quantum universality in the spin-1/2 triangular-lattice quantum antiferromagnet Na2BaCo(PO4)2.

An interplay of geometrical frustration and strong quantum fluctuations in a spin-1/2 triangular-lattice antiferromagnet (TAF) can lead to exotic quantum states. Here, we report the neutron-scattering, magnetization, specific heat, and magnetocaloric studies of the recently discovered spin-1/2 TAF Na2BaCo(PO4)2, which can be described by a spin-1/2 easy axis XXZ model. The zero-field neutron diffraction experiment reveals an incommensurate antiferromagnetic ground state with a significantly reduced ordered moment of about 0.54(2) µB/Co. Different magnetic phase diagrams with magnetic fields in the ab plane and along the easy c-axis were extracted based on the magnetic susceptibility, specific heat, and elastic neutron-scattering results. In addition, two-dimensional (2D) spin dispersion in the triangular plane was observed in the high-field polarized state, and microscopic exchange parameters of the spin Hamiltonian have been determined through the linear spin wave theory. Consistently, quantum critical behaviors with the universality class of d = 2 and νz = 1 were established in the vicinity of the saturation field, where a Bose-Einstein condensation (BEC) of diluted magnons occurs. The newly discovered quantum criticality and fractional magnetization phase in this ideal spin-1/2 TAF present exciting opportunities for exploring exotic quantum phenomena.

Direct measurement of the evolution of magnetism and superconductivity toward the quantum critical point.

Nontrivial quantum states can be realized in the vicinity of the quantum critical point (QCP) in many strongly correlated electron systems. In particular, an emergence of unconventional superconductivity around the QCP strongly suggests that the quantum critical fluctuations play a central role in the superconducting pairing mechanism. However, a clear signature of the direct coupling between the superconducting pairing states and the quantum criticality has not yet been elucidated by the microscopic probes. Herein, we present muon spin rotation/relaxation and neutron diffraction measurements in the superconducting dome of CeCo(In1 - xZnx)5. It was found that a magnetically ordered state develops at x≥ 0.03, coexisting with the superconductivity. The magnitude of the ordered magnetic moment is continuously reduced with decreasing x, and it disappears below x∼ 0.03, indicating a second-order phase transition and the presence of the QCP at this critical Zn concentration. Furthermore, the magnetic penetration depth diverges toward the QCP. These facts provide evidence for the intimate coupling between quantum criticality and Cooper pairing.

Are Heavy Fermion Strange Metals Planckian?

Strange metal behavior refers to a linear temperature dependence of the electrical resistivity that is not due to electron-phonon scattering. It is seen in numerous strongly correlated electron systems, from the heavy fermion compounds, via transition metal oxides and iron pnictides, to magic angle twisted bi-layer graphene, frequently in connection with unconventional or "high temperature" superconductivity. To achieve a unified understanding of these phenomena across the different materials classes is a central open problem in condensed matter physics. Tests whether the linear-in-temperature law might be dictated by Planckian dissipation-scattering with the rate ∼ k B T / ℏ -are receiving considerable attention. Here we assess the situation for strange metal heavy fermion compounds. They allow to probe the regime of extreme correlation strength, with effective mass or Fermi velocity renormalizations in excess of three orders of magnitude. Adopting the same procedure as done in previous studies, i.e., assuming a simple Drude conductivity with the above scattering rate, we find that for these strongly renormalized quasiparticles, scattering is much weaker than Planckian, implying that the linear temperature dependence should be due to other effects. We discuss implications of this finding and point to directions for further work.

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4.

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO4, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4f orbitals of the thulium (Tm[Formula: see text]) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

Critical structure and emergent symmetry of Dirac fermion systems.

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-orderεexpansion in4-ϵdimensions, we study the critical structure and emergent symmetry of theO(N)-GNY model withNfflavors of four-component Dirac fermions coupled strongly to anO(N) scalar field under a smallO(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for generalNandNf. Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point forN⩾4on the basis ofO(N)-GNY model. It turns out that theO(N)-GNY universality class is physically meaningful if and only ifN<2Nf+4. On this premise, the smallO(N)-symmetry breaking perturbation is always irrelevant in theO(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limitO(2Nf+3), depending on the flavor numbersNf. As a result, the emergent-O(4) andO(5) symmetries are possible to be found in Dirac systems with fermion flavorNf=1, and the emergent-O(4),O(5),O(6) andO(7) symmetries are expected to be found in the systems with fermion flavorNf=2. Our result suggests some richer transitions with emergent-Z2×O(2)×O(3)symmetry, and so on. Interestingly, in theO(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavorNf=1.

Fingerprints of Critical Phenomena in a Quantum Paraelectric Ensemble of Nanoconfined Water Molecules.

We have studied the radio frequency dielectric response of a system consisting of separate polar water molecules periodically arranged in nanocages formed by the crystal lattice of the gemstone beryl. Below T = 20-30 K, quantum effects start to dominate the properties of the electric dipolar system as manifested by a crossover between the Curie-Weiss and the Barrett regimes in the temperature-dependent real dielectric permittivity ε'(T). When analyzing in detail the temperature evolution of the reciprocal permittivity (ε')-1 down to T ≈ 0.3 K and comparing it with the data obtained for conventional quantum paraelectrics, like SrTiO3, KTaO3, we discovered clear signatures of a quantum-critical behavior of the interacting water molecular dipoles: Between T = 6 and 14 K, the reciprocal permittivity follows a quadratic temperature dependence and displays a shallow minimum below 3 K. This is the first observation of "dielectric fingerprints" of quantum-critical phenomena in a paraelectric system of coupled point electric dipoles.

Superconductivity from repulsion in the doped 2D electronic Hubbard model: an entanglement perspective.

We employ the momentum space entanglement renormalization group (MERG) scheme developed in references (Mukherjeeet al2021J. High Energy Phys.JHEP04(2021)148; Patra and Lal 2021Phys. Rev.B104144514) for the study of various insulating, superconducting and normal phases of the doped and the undoped 2D Hubbard model on a square lattice found recently by us (Mukherjee and Lal 2020New J. Phys.22063007; Mukherjee and Lal 2020New J. Phys.22063008). At each MERG step, disentanglement of particular degrees of freedom, transforms the tensor network representation of the many-particle states. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Neél antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling, clarifying the essence of the entanglement phase transitions that separates the three phases. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is concomitant with the emergence of d-wave superconductivity.

A mechanism for the strange metal phase in rare-earth intermetallic compounds.

SignificanceThe elusive strange metal phase (ground state) was observed in a variety of quantum materials, notably in f-electron-based rare-earth intermetallic compounds. Its emergence has remained unclear. Here, we propose a generic mechanism for this phenomenon driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlation and critical bosonic charge fluctuations near a Kondo breakdown quantum phase transition. It is manifested as a fluctuating Kondo-scattering-stabilized critical (gapless) fermionic spin liquid. It shows [Formula: see text] scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results on quasilinear-in-temperature scattering rate and logarithmic-in-temperature divergence in specific heat coefficient as temperature vanishes were recently seen in CePd[Formula: see text]NixAl.

Non-Fermi liquid behavior below the Néel temperature in the frustrated heavy fermion magnet UAu2.

The term Fermi liquid is almost synonymous with the metallic state. The association is known to break down at quantum critical points (QCPs), but these require precise values of tuning parameters, such as pressure and applied magnetic field, to exactly suppress a continuous phase transition temperature to the absolute zero. Three-dimensional non-Fermi liquid states, apart from superconductivity, that are unshackled from a QCP are much rarer and are not currently well understood. Here, we report that the triangular lattice system uranium diauride (UAu2) forms such a state with a non-Fermi liquid low-temperature heat capacity [Formula: see text] and electrical resistivity [Formula: see text] far below its Néel temperature. The magnetic order itself has a novel structure and is accompanied by weak charge modulation that is not simply due to magnetostriction. The charge modulation continues to grow in amplitude with decreasing temperature, suggesting that charge degrees of freedom play an important role in the non-Fermi liquid behavior. In contrast with QCPs, the heat capacity and resistivity we find are unusually resilient in magnetic field. Our results suggest that a combination of magnetic frustration and Kondo physics may result in the emergence of this novel state.

Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors.

During the last decade, translational and rotational symmetry-breaking phases-density wave order and electronic nematicity-have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor [Formula: see text] (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.

Emergence of quenched disorder as a dominant control for complex phase diagram of rare-earth nickelates.

Competing interactions in complex materials tend to induce multiple quantum phases of comparable energetics close to the ground state stability. This requires novel strategies and tools to segregate such phases with desired control to manipulate the properties relevant for contemporary technologies. Here, we show 'quenched disorder (QD)' as a predominant control parameter to realize a broad range of the quantum phases of bulkRNiO3(R= rare-earth ion) phase diagram in a LaxEu1-xNiO3compounds by systematic introduction of QD. Using static and terahertz dynamic transport studies on epitaxial thin films, we demonstrate various phases such as Fermi to non-Fermi liquid crossover, bad metallic behavior, quantum criticality, preservation of orbital and charge order symmetry and increased electronic inhomogeneity responsible for Maxwell-Wagner type of dielectric response, etc. The underlying mechanisms are unveiled by the anomalous responses of microscopic quantities such as scattering rate, plasma frequency, spectral weight, effective mass, and disorder. The results and methodology implemented here can be a generic pursuit of disorder based unified control to extract quantum phases submerged in competing energetics in all complex materials.

Magnetic-Field Tunable Intertwined Checkerboard Charge Order and Nematicity in the Surface Layer of Sr2 RuO4.

In strongly correlated electron materials, the electronic, spin, and charge degrees of freedom are closely intertwined. This often leads to the stabilization of emergent orders that are highly sensitive to external physical stimuli promising opportunities for technological applications. In perovskite ruthenates, this sensitivity manifests in dramatic changes of the physical properties with subtle structural details of the RuO6 octahedra, stabilizing enigmatic correlated ground states, from a hotly debated superconducting state via electronic nematicity and metamagnetic quantum criticality to ferromagnetism. Here, it is demonstrated that the rotation of the RuO6 octahedra in the surface layer of Sr2 RuO4 generates new emergent orders not observed in the bulk material. Through atomic-scale spectroscopic characterization of the low-energy electronic states, four van Hove singularities are identified in the vicinity of the Fermi energy. The singularities can be directly linked to intertwined nematic and checkerboard charge order. Tuning of one of these van Hove singularities by magnetic field is demonstrated, suggesting that the surface layer undergoes a Lifshitz transition at a magnetic field of ≈32T. The results establish the surface layer of Sr2 RuO4 as an exciting 2D correlated electron system and highlight the opportunities for engineering the low-energy electronic states in these systems.

Observation of thickness-tuned universality class in superconducting ß-W thin films.

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we observe the thickness-tuned universality class of superconductor-metal transition by changing the disorder strength in ß-W films with varying thickness. The finite-size scaling uncovers the switch of universality class: quantum Griffiths singularity to multiple quantum criticality at a critical thickness of tc⊥1~8nm and then from multiple quantum criticality to single criticality at tc⊥2~16nm. Moreover, the superconducting-metal transition is observed for the first time under in-plane magnetic fields and the universality class is changed at tc‖~8nm. The observation of thickness-tuned universality class under both out-of-plane and in-plane magnetic fields provides broad information for the disorder effect on superconducting-metal transitions and quantum criticality.