From quantum matter to high-temperature superconductivity in copper oxides

Motor guidance by long-range communication on the microtubule highway

Coupling of motor proteins within arrays drives muscle contraction, flagellar beating, chromosome segregation, and other biological processes. Current models of motor coupling invoke either direct mechanical linkage or protein crowding, which rely on short-range motor-motor interactions. In contrast, coupling mechanisms that act at longer length scales remain largely unexplored. Here we report that microtubules can physically couple motor movement in the absence of detectable short-range interactions. The human kinesin-4 Kif4A changes the run length and velocity of other motors on the same microtubule in the dilute binding limit, when approximately 10-nm-sized motors are much farther apart than the motor size. This effect does not depend on specific motor-motor interactions because similar changes in Kif4A motility are induced by kinesin-1 motors. A micrometer-scale attractive interaction potential between motors is sufficient to recreate the experimental results in a biophysical model. Unexpectedly, our theory suggests that long-range microtubule-mediated coupling affects not only binding kinetics but also motor mechanochemistry. Therefore, the model predicts that motors can sense and respond to motors bound several micrometers away on a microtubule. Our results are consistent with a paradigm in which long-range motor interactions along the microtubule enable additional forms of collective motor behavior, possibly due to changes in the microtubule lattice.

Magnetic memory and spontaneous vortices in a van der Waals superconductor

Doped Mott insulators exhibit some of the most intriguing quantum phases of matter, including quantum spin liquids, unconventional superconductors and non-Fermi liquid metals^1-3. Such phases often arise when itinerant electrons are close to a Mott insulating state, and thus experience strong spatial correlations. Proximity between different layers of van der Waals heterostructures naturally realizes a platform for experimentally studying the relationship between localized, correlated electrons and itinerant electrons. Here we explore this relationship by studying the magnetic landscape of tantalum disulfide 4Hb-TaS₂, which realizes an alternating stacking of a candidate spin liquid and a superconductor⁴. We report on a spontaneous vortex phase whose vortex density can be trained in the normal state. We show that time-reversal symmetry is broken in the normal state, indicating the presence of a magnetic phase independent of the superconductor. Notably, this phase does not generate ferromagnetic signals that are detectable using conventional techniques. We use scanning superconducting quantum interference device microscopy to show that it is incompatible with ferromagnetic ordering. The discovery of this unusual magnetic phase illustrates how combining superconductivity with a strongly correlated system can lead to unexpected physics.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Tracking the nematicity in cuprate superconductors: a resistivity study under uniaxial pressure

Overshadowing the superconducting dome in hole-doped cuprates, the pseudogap state is still one of the mysteries that no consensus can be achieved. It has been suggested that the rotational symmetry is broken in this state and may result in a nematic phase transition, whose temperature seems to coincide with the onset temperature of the pseudogap stateT∗around optimal doping level, raising the question whether the pseudogap results from the establishment of the nematic order. Here we report results of resistivity measurements under uniaxial pressure on several hole-doped cuprates, where the normalized slope of the elastoresistivityζcan be obtained as illustrated in iron-based superconductors. The temperature dependence ofζalong particular lattice axis exhibits kink feature atT_kand shows Curie-Weiss-like behavior above it, which may suggest a spontaneous nematic transition. WhileT_kseems to be the same asT∗around the optimal doping and in the overdoped region, they become very different in underdoped La2-xSr_xCuO₄. Our results suggest that the nematic order, if indeed existing, is an electronic phase within the pseudogap state.

Resonant inelastic soft x-ray scattering on LaPt2Si2

X-ray absorption and resonant inelastic x-ray scattering spectra of LaPt₂Si₂single crystal at the Si 2pand La 4dedges are presented. The data are interpreted in terms of density functional theory, showing that the Si spectra can be described in terms of Sisanddlocal partial density of states (LPDOS), and the La spectra are due to quasi-atomic local 4fexcitations. Calculations show that Ptd-LPDOS dominates the occupied states, and a sharp localized Lafstate is found in the unoccupied states, in line with the observations.

Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

Paramagnons and high-temperature superconductivity in a model family of cuprates

Cuprate superconductors have the highest critical temperatures (T_c) at ambient pressure, yet a consensus on the superconducting mechanism remains to be established. Finding an empirical parameter that limits the highest reachable T_c can provide crucial insight into this outstanding problem. Here, in the first two Ruddlesden-Popper members of the model Hg-family of cuprates, which are chemically nearly identical and have the highest T_c among all cuprate families, we use inelastic photon scattering to reveal that the energy of magnetic fluctuations may play such a role. In particular, we observe the single-paramagnon spectra to be nearly identical between the two compounds, apart from an energy scale difference of ~30% which matches their difference in T_c. The empirical correlation between paramagnon energy and maximal T_c is further found to extend to other cuprate families with relatively high T_c’s, hinting at a fundamental connection between them.

Finding a parameter that limits the critical temperature of cuprate superconductors can provide crucial insight on the superconducting mechanism. Here, the authors use inelastic photon scattering on two Ruddlesden-Popper members of the model Hg-family of cuprates to reveal that the energy of magnetic fluctuations may play such a role, and suggest that the Cooper pairing is mediated by paramagnons.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Fermi Surface Expansion above Critical Temperature in a Hund Ferromagnet

Using a cluster extension of the dynamical mean-field theory, we show that strongly correlated metals subject to Hund's physics exhibit significant electronic structure modulations above magnetic transition temperatures. In particular, in a ferromagnet having a large local moment due to Hund's coupling (Hund's ferromagnet), the Fermi surface expands even above the Curie temperature (T_{C}) as if a spin polarization occurred. Behind this phenomenon, effective "Hund's physics" works in momentum space, originating from ferromagnetic fluctuations in the strong-coupling regime. The resulting significantly momentum-dependent (spatially nonlocal) electron correlations induce an electronic structure reconstruction involving a Fermi surface volume change and a redistribution of the momentum-space occupation. Our finding will give a deeper insight into the physics of Hund's ferromagnets above T_{C}.

Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations

The origin of the pseudogap behavior, found in many high-T_c superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a “gap-filling" rather than “gap-closing" behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

The origin of pseudogap in high-T_c superconductors remains a big puzzle. Here, the authors report numerical evidence of pseudogap behavior employing Quantum Monte Carlo algorithm emerging from pairing fluctuations in a quantum-critical non-Fermi liquid, similar to the pseudogap phase observed in cuprate superconductors.

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.

Structural Properties and Hopping Conduction in the Normal State of Electron-Doped Superconductor Cuprate Eu2-x Ce x CuO4+α-δ

Electron-doped superconducting cuprate of Eu_2-x Ce _x CuO_4+α-δ has been studied in the whole doping regime from x = 0.10-0.20 with reducing oxygen content to investigate the relation between the crystal structure and the hopping conduction in the normal state. Parameter of the crystal structure has been extracted from the X-ray diffraction (XRD) measurement while hopping conduction parameters have been obtained from resistivity measurements. The Eu-O bond length decreases with the increasing doping concentration, indicating the successful doping by the partial replacing of Eu³⁺ with Ce⁴⁺. The resistivity increases with decreasing temperature in all measured samples. This is an indication of bad metal-like behavior in the whole regime in the normal state of electron-doped superconducting cuprate of Eu_2-x Ce _x CuO_4+α-δ. The temperature dependence of resistivity was analyzed by the Arrhenius law and the variable range hopping model. It is found that the hopping conduction mechanism more likely follows the variable range hopping rather than the Arrhenius law, indicating that the hopping mechanism occurs in three dimensions. The Cu-O bond length probably plays an important role in decreasing the activation energy. The decreasing value of the activation energy correlates with the increase in the localization radius.

Anisotropic Scattering Caused by Apical Oxygen Vacancies in Thin Films of Overdoped High-Temperature Cuprate Superconductors

There is a hot debate on the anomalous behavior of superfluid density ρ_{s} in overdoped La_{2-x}Sr_{x}CuO_{4} films in recent years. The linear drop of ρ_{s} at low temperatures implies the superconductors are clean, but the linear scaling between ρ_{s} (in the zero temperature limit) and the transition temperature T_{c} is a hallmark of the dirty limit in the Bardeen-Cooper-Schrieffer (BCS) framework [I. Bozovic et al., Nature (London) 536, 309 (2016)NATUAS0028-083610.1038/nature19061]. This dichotomy motivated exotic theories beyond the standard BCS theory. We show, however, that such a dichotomy can be reconciled naturally by the role of increasing anisotropic scattering caused by the apical oxygen vacancies. Furthermore, the anisotropic scattering also explains the "missing" Drude weight upon doping in the optical conductivity, as reported in the THz experiment [F. Mahmood et al., Phys. Rev. Lett. 122, 027003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.027003]. Therefore, the overdoped cuprates can actually be described consistently by the d-wave BCS theory with the unique anisotropic scattering.

Superconductivity in infinite-layer nickelates

The recent discovery of the superconductivity in the doped infinite layer nickelatesRNiO₂(R= La, Pr, Nd) is of great interest since the nickelates are isostructural to doped (Ca, Sr)CuO₂having superconducting transition temperature (T_c) of about 110 K. Verifying the commonalities and differences between these oxides will certainly give a new insight into the mechanism of highT_csuperconductivity in correlated electron systems. In this paper, we review experimental and theoretical works on this new superconductor and discuss the future perspectives for the 'nickel age' of superconductivity.

Comparing Thickness and Doping-Induced Effects on the Normal States of Infinite-Layer Electron-Doped Cuprates: Is There Anything to Learn?

We grew Sr_1-xLa_xCuO₂ thin films and SrCuO₂/Sr_0.9La_0.1CuO₂/SrCuO₂ trilayers by reflection high-energy diffraction-calibrated layer-by-layer molecular beam epitaxy, to study their electrical transport properties as a function of the doping and thickness of the central Sr_0.9La_0.1CuO₂ layer. For the trilayer samples, as already observed in underdoped SLCO films, the electrical resistivity versus temperature curves as a function of the central layer thickness show, for thicknesses thinner than 20 unit cells, sudden upturns in the low temperature range with the possibility for identifying, in the normal state, the T* and a T** temperatures, respectively, separating high-temperature linear behavior and low-temperature quadratic dependence. By plotting the T* and T** values as a function of T_C^onset for both the thin films and the trilayers, the data fall on the same curves. This result suggests that, for the investigated trilayers, the superconducting critical temperature is the important parameter able to describe the normal state properties and that, in the limit of very thin central layers, such properties are mainly influenced by the modification of the energy band structure and not by interface-related disorder.

Interplay between Charge-Density-Wave, Superconductivity, and Ferromagnetism in CuIr2-xCrxTe4 Chalcogenides

We report the crystal structure, charge-density-wave (CDW), superconductivity (SC), and ferromagnetism (FM) in CuIr_2-xCr_xTe₄ (0 ≤ x ≤ 2) chalcogenides. Powder x-ray diffraction (PXRD) results reveal that the CuIr_2-xCr_xTe₄ series are distinguished between two structural types and three different regions: (i) layered trigonal structure region, (ii) mixed phase regions, and (iii) spinel structure region. Besides, Cr substitution for Ir site results in rich physical properties including the collapse of CDW, the formation of dome-shaped like SC, and the emergence of magnetism. Cr doping slightly elevates the superconducting critical temperature (T_sc) to its highest T_sc = 2.9 K around x = 0.06. As x increases from 0.3 to 0.4, the ferromagnetic Curie temperature (T_c) increases from 175 to 260 K. However, the T_c remains unchanged in the spinel range of 1.9 ≤ x ≤ 2. This finding provides a comprehensive material platform for investigating the interplay between CDW, SC, and FM multipartite quantum states.

The Strange-Metal Behavior of Cuprates

Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.

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

The 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 ω/T 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 CePd1−xNi_xAl.

A major mystery in strongly interacting quantum systems is the microscopic origin of the “strange metal” phenomenology, with unconventional metallic behavior that defies Landau’s Fermi liquid framework for ordinary metals. This state is found across a wide range of quantum materials, notably in rare-earth intermetallic compounds at finite temperatures (T) near a magnetic quantum phase transition, and shows a quasilinear-in-temperature resistivity and a logarithmic-in-temperature specific heat coefficient. Recently, an even more enigmatic behavior pointing toward a stable strange metal ground state was observed in CePd1−xNi_xAl, a geometrically frustrated Kondo lattice compound. Here, we propose a mechanism for such phenomena driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlations (spinons) and critical bosonic charge (holons) fluctuations near a Kondo breakdown quantum phase transition. Within a dynamical large-N approach to the Kondo–Heisenberg lattice model, the strange metal phase is realized in transport and thermodynamical quantities. It is manifested as a fluctuating Kondo-scattering–stabilized critical (gapless) fermionic spin-liquid metal. It shows ω/T scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results offer a qualitative understanding of the CePd1−xNi_xAl compound and suggest a possibility of realizing the quantum critical strange metal phase in correlated electron systems in general.

Combinatorial synthesis of heteroepitaxial, multi-cation, thin-films via pulsed laser deposition coupled with in-situ, chemical and structural characterization

Combinatorial synthesis via a continuous composition spread is an excellent route to develop thin-film libraries as it is both time- and cost-efficient. Creating libraries of functional, multicomponent, complex oxide films requires excellent control over the synthesis parameters combined with high-throughput analytical feedback. A reliable, high-throughput, in-situ characterization analysis method is required to meet the crucial need to rapidly screen materials libraries. Here, we report on the combination of two in-situ techniques—(a) Reflection high-energy electron diffraction (RHEED) for heteroepitaxial characterization and a newly developed compositional analysis technique, low-angle x-ray spectroscopy (LAXS), to map the chemical composition profile of combinatorial heteroepitaxial complex oxide films deposited using a continuous composition spread method via pulsed laser deposition. This is accomplished using a unique state-of-the-art combinatorial growth system with a fully synchronized four-axis mechanical substrate stage without shadow masks, alternating acquisition of chemical compositional data using LAXS at various different positions on the $$\sim$$ ∼ 41 mm $$\times$$ × 41 mm range and sequential deposition of multilayers of SrTiO$$_3$$ 3 and $$\hbox {SrTi}_{0.8}\hbox {Ru}_{0.2}\hbox {O}_3$$ SrTi 0.8 Ru 0.2 O 3 on a 2-inch (50.8 mm) $$\hbox {LaAlO}_3$$ LaAlO 3 wafer in a single growth run. Rutherford backscattering spectrometry (RBS) is used to calibrate and validate the compositions determined by LAXS. This study shows the feasibility of combinatorial synthesis of heteroepitaxial, functional complex oxide films at wafer-scale via two essential in-situ characterization tools—RHEED for structural analysis or heteroepitaxy and LAXS for compositional characterization. This is a powerful technique for development of new films with optimized heteroepitaxy and composition.

Metallic and Deconfined Quantum Criticality in Dirac Systems

Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×U(1) symmetry. Using large-scale auxiliary-field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition toward an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data are consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.

Correlation-Consistent Gaussian Basis Sets for Solids Made Simple

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. We find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-ζ correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.

Scaling of the strange-metal scattering in unconventional superconductors

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions^1-4. The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors^5-9. The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity^10-12. However, a clear quantitative picture of the correlation has been lacking. Here we report the observation of precise quantitative scaling laws among the superconducting transition temperature (T_c), the linear-in-T scattering coefficient (A₁) and the doping level (x) in electron-doped copper oxide La_2-xCe_xCuO₄ (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δx = 0.0015. We have uncovered the relations T_c ~ (x_c - x)^0.5 ~ (A₁^□)^0.5, where x_c is the critical doping in which superconductivity disappears and A₁^□ is the coefficient of the linear resistivity per CuO₂ plane. The striking similarity of the T_c versus A₁^□ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems.

Characterization of photoinduced normal state through charge density wave in superconducting YBa2Cu3O6.67

The normal state of high-T_c cuprates has been considered one of the essential topics in high-temperature superconductivity research. However, compared to the high magnetic field study of it, understanding a photoinduced normal state remains elusive. Here, we explore a photoinduced normal state of YBa₂Cu₃O_6.67 through a charge density wave (CDW) with time-resolved resonant soft x-ray scattering, as well as a high magnetic field x-ray scattering. In the nonequilibrium state where people predict a quenched superconducting state based on the previous optical spectroscopies, we experimentally observed a similar analogy to the competition between superconductivity and CDW shown in the equilibrium state. We further observe that the broken pairing states in the superconducting CuO₂ plane via the optical pump lead to nucleation of three-dimensional CDW precursor correlation. Ultimately, these findings provide a critical clue that the characteristics of the photoinduced normal state show a solid resemblance to those under magnetic fields in equilibrium conditions.

Superconductivity in a quintuple-layer square-planar nickelate

Since the discovery of high-temperature superconductivity in copper oxide materials¹, there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials². One prime materials platform has been the rare-earth nickelates and, indeed, superconductivity was recently discovered in the doped compound Nd_0.8Sr_0.2NiO₂ (ref. ³). Undoped NdNiO₂ belongs to a series of layered square-planar nickelates with chemical formula Nd_n+1Ni_nO_2n+2 and is known as the 'infinite-layer' (n = ∞) nickelate. Here we report the synthesis of the quintuple-layer (n = 5) member of this series, Nd₆Ni₅O₁₂, in which optimal cuprate-like electron filling (d^8.8) is achieved without chemical doping. We observe a superconducting transition beginning at ~13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd₆Ni₅O₁₂ interpolates between cuprate-like and infinite-layer nickelate-like behaviour. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors that can be tuned via both doping and dimensionality.

Charge density waves and Fermi surface reconstruction in the clean overdoped cuprate superconductor Tl2Ba2CuO6+δ

Hall effect and quantum oscillation measurements on high temperature cuprate superconductors show that underdoped compositions have small Fermi surface pockets whereas when heavily overdoped, a single much larger pocket is found. The origin of this change in electronic structure has been unclear, but may be related to the high temperature superconductivity. Here we show that the clean overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ (Tl2201) displays CDW order with a remarkably long correlation length ξ ≈ 200 Å which disappears above a hole doping of p_CDW ≈ 0.265. We show that the evolution of the electronic properties of Tl2201 as the doping is lowered may be explained by a Fermi surface reconstruction which accompanies the emergence of the CDW below p_CDW. Our results demonstrate importance of CDW correlations in understanding the electronic properties of overdoped cuprates.

The origin of the Fermi surface reconstruction that occurs in cuprate superconductors as hole doping increases remains unclear. Here, the authors observe long range charge density wave (CDW) order in the overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ, which then disappears above a hole concentration 0.265, suggesting a correlation between Fermi surface reconstruction and the emergence of the CDW.

Unconventional spectral signature of Tc in a pure d-wave superconductor

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap¹. In the high-transition-temperature (high-T_c) cuprates, although the transport, magnetic and thermodynamic signatures of T_c have been known since the 1980s², the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)₂Sr₂CaCu₂O_8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at T_c, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across T_c. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.

Quantum critical points and the sign problem

The "sign problem" (SP) is a fundamental limitation to simulations of strongly correlated matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians because its behavior can be influenced by the choice of algorithm. By contrast, we show that the SP in determinant quantum Monte Carlo (QMC) is quantitatively linked to quantum critical behavior. We demonstrate this through simulations of several models with critical properties that are relatively well understood. We propose a reinterpretation of the low average sign for the Hubbard model on the square lattice away from half filling in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior.

Emerging spin-phonon coupling through cross-talk of two magnetic sublattices

Many material properties such as superconductivity, magnetoresistance or magnetoelectricity emerge from the non-linear interactions of spins and lattice/phonons. Hence, an in-depth understanding of spin-phonon coupling is at the heart of these properties. While most examples deal with one magnetic lattice only, the simultaneous presence of multiple magnetic orderings yield potentially unknown properties. We demonstrate a strong spin-phonon coupling in SmFeO3 that emerges from the interaction of both, iron and samarium spins. We probe this coupling as a remarkably large shift of phonon frequencies and the appearance of new phonons. The spin-phonon coupling is absent for the magnetic ordering of iron alone but emerges with the additional ordering of the samarium spins. Intriguingly, this ordering is not spontaneous but induced by the iron magnetism. Our findings show an emergent phenomenon from the non-linear interaction by multiple orders, which do not need to occur spontaneously. This allows for a conceptually different approach in the search for yet unknown properties.

Iron pnictides and chalcogenides: a new paradigm for superconductivity

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Stripe order enhanced superconductivity in the Hubbard model

The Hubbard model plays a central role in the theory of highly correlated systems. Its simplicity allows conceptual issues—which are generally complicated in the context of experiments on interesting materials—to be sharply posed and definitively answered. Recently, a variety of numerical studies have led to the conclusion that the “pure” Hubbard model on the square lattice at intermediate coupling, U, is not superconducting in the range of electron densities in which many previous approximate treatments had inferred high-temperature superconductivity. Here, using controlled density matrix renormalization group methods, we show that superconductivity is spectacularly enhanced if the hopping matrix elements are periodically modulated in a stripe-like pattern, with important (if suggestive) implications concerning the mechanism of unconventional superconductivity.

Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, Ksc∼1.

Superconductivity in nickel-based 112 systems

Superconductivity has been discovered recently in infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ (R = La, Nd, Pr and A = Sr, Ca). They are isostructural to the infinite-layer cuprate (Ca,Sr)CuO₂ and are supposed to have a formal Ni 3d⁹ valence, thus providing a new platform to study the unconventional pairing mechanism of high-temperature superconductors. This important discovery immediately triggers a huge amount of innovative scientific curiosity in the field. In this paper, we try to give an overview of the recent research progress on the newly found superconducting nickelate systems, both from experimental and theoretical aspects. We mainly focus on the electronic structures, magnetic excitations, phase diagrams and superconducting gaps, and finally make some open discussions for possible pairing symmetries in Ni-based 112 systems.

•

The infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ can host superconductivity up to 15 K

•

R_1−xA_xNiO₂ is a multiband system, in which the short-range antiferromagnetic fluctuations can be detected

•

R_1−xA_xNiO₂ has an unconventional superconducting pairing sate with a robust d-wave gap and a full gap without unified understanding

•

The nickelate system provides a new platform for researching unconventional superconductivity

Quench-drive spectroscopy of cuprates

Cuprates are d-wave superconductors which exhibit a rich phase diagram: they are characterized by superconducting fluctuations even above the critical temperature, and thermal disorder can reduce or suppress the phase...

Signatures of a strange metal in a bosonic system

Fermi liquid theory forms the basis for our understanding of the majority of metals: their resistivity arises from the scattering of well defined quasiparticles at a rate where, in the low-temperature limit, the inverse of the characteristic time scale is proportional to the square of the temperature. However, various quantum materials^1-15-notably high-temperature superconductors^1-10-exhibit strange-metallic behaviour with a linear scattering rate in temperature, deviating from this central paradigm. Here we show the unexpected signatures of strange metallicity in a bosonic system for which the quasiparticle concept does not apply. Our nanopatterned YBa₂Cu₃O_7-δ (YBCO) film arrays reveal linear-in-temperature and linear-in-magnetic field resistance over extended temperature and magnetic field ranges. Notably, below the onset temperature at which Cooper pairs form, the low-field magnetoresistance oscillates with a period dictated by the superconducting flux quantum, h/2e (e, electron charge; h, Planck's constant). Simultaneously, the Hall coefficient drops and vanishes within the measurement resolution with decreasing temperature, indicating that Cooper pairs instead of single electrons dominate the transport process. Moreover, the characteristic time scale τ in this bosonic system follows a scale-invariant relation without an intrinsic energy scale: ħ/τ ≈ a(k_BT + γμ_BB), where ħ is the reduced Planck's constant, a is of order unity^7,8,11,12, k_B is Boltzmann's constant, T is temperature, μ_B is the Bohr magneton and γ ≈ 2. By extending the reach of strange-metal phenomenology to a bosonic system, our results suggest that there is a fundamental principle governing their transport that transcends particle statistics.

Emergent physical properties of perovskite-type oxides prepared under high pressure

The perovskite ABO₃ family demonstrates a wide variety of structural evolutions and physical properties and is arguably the most important family of complex oxides. Chemical substitutions of the A- and/or B-site and modulation of oxygen content can effectively regulate their electronic behaviors and multifunctional performances. In general, the BO₆ octahedron represents the main unit controlling the electronic and magnetic properties while the A-site ion is often not involved. However, a series of unconventional perovskite materials have been recently synthesized under high pressure, such as the s-d level controlled Pb-based perovskite family and quadruple perovskite oxides containing transition metal ions at the A-site. In these compounds, the intersite A-B correlations play an important role in electronic behaviors and further induce many emergent physical properties.

Direct visualization of a static incommensurate antiferromagnetic order in Fe-doped Bi2Sr2CaCu2O8+δ

In cuprate superconductors, due to strong electronic correlations, there are multiple intertwined orders which either coexist or compete with superconductivity. Among them, the antiferromagnetic (AF) order is the most prominent one. In the region where superconductivity sets in, the long-range AF order is destroyed. Yet the residual short-range AF spin fluctuations are present up to a much higher doping, and their role in the emergence of the superconducting phase is still highly debated. Here, by using a spin-polarized scanning tunneling microscope, we directly visualize an emergent incommensurate AF order in the nearby region of Fe impurities embedded in the optimally doped Bi₂Sr₂CaCu₂O_8+δ (Bi2212). Remarkably, the Fe impurities suppress the superconducting coherence peaks with the gapped feature intact, but pin down the ubiquitous short-range incommensurate AF order. Our work shows an intimate relation between antiferromagnetism and superconductivity.

Observation of Cu Spin Fluctuations in High-Tc Cuprate Superconductor Nanoparticles Investigated by Muon Spin Relaxation

The nano-size effects of high-T_c cuprate superconductor La_2-xSr_xCuO₄ with x = 0.20 are investigated using X-ray diffractometry, Transmission electron microscopy, and muon-spin relaxation (μSR). It is investigated whether an increase in the bond distance of Cu and O atoms in the conducting layer compared to those of the bulk state might affect its physical and magnetic properties. The μSR measurements revealed the slowing down of Cu spin fluctuations in La_2-xSr_xCuO₄ nanoparticles, indicating the development of a magnetic correlation at low temperatures. The magnetic correlation strengthens as the particle size reduces. This significantly differs from those observed in the bulk form, which show a superconducting state below T_c. It is indicated that reducing the particle size of La_2-xSr_xCuO₄ down to nanometer size causes the appearance of magnetism. The magnetism enhances with decreasing particle size.

Direct observation of nodeless superconductivity and phonon modes in electron-doped copper oxide Sr1-xNdxCuO2

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study the electron-doped copper oxide compound Sr_1−xNd_xCuO₂, which has only bare cations separating the CuO₂ planes and thus the simplest infinite-layer structure of all cuprate superconductors. Tunneling conductance spectra of the major CuO₂ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. As well as the bosonic modes, with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings reveal the origin of the bosonic modes in lattice vibrations rather than spin excitations.

Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

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.

Competition of Superconductivity and Charge Density Wave in Selective Oxidized CsV_{3}Sb_{5} Thin Flakes

The recently discovered layered kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) with vanadium kagome networks provide a novel platform to explore correlated quantum states intertwined with topological band structures. Here we report the prominent effect of hole doping on both superconductivity and charge density wave (CDW) order, achieved by selective oxidation of exfoliated thin flakes. A superconducting dome is revealed as a function of the effective doping content. The superconducting transition temperature (T_{c}) and upper critical field in thin flakes are significantly enhanced compared with the bulk, which are accompanied by the suppression of CDW. Our detailed analyses establish the pivotal role of van Hove singularities in promoting correlated quantum orders in these kagome metals. Our experiments not only demonstrate the intriguing nature of superconducting and CDW orders, but also provide a novel route to tune the carrier concentration through both selective oxidation and electric gating. This establishes CsV_{3}Sb_{5} as a tunable 2D platform for the further exploration of topology and correlation among 3d electrons in kagome lattices.

Phase fluctuations in conventional superconductors

Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness,J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductorsJis normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors,Jcan drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

Enhancement of Photoresponse on Narrow-Bandgap Mott Insulator α-RuCl3 via Intercalation

Charge doping to Mott insulators is critical to realize high-temperature superconductivity, quantum spin liquid state, and Majorana fermion, which would contribute to quantum computation. Mott insulators also have a great potential for optoelectronic applications; however, they showed insufficient photoresponse in previous reports. To enhance the photoresponse of Mott insulators, charge doping is a promising strategy since it leads to effective modification of electronic structure near the Fermi level. Intercalation, which is the ion insertion into the van der Waals gap of layered materials, is an effective charge-doping method without defect generation. Herein, we showed significant enhancement of optoelectronic properties of a layered Mott insulator, α-RuCl₃, through electron doping by organic cation intercalation. The electron-doping results in substantial electronic structure change, leading to the bandgap shrinkage from 1.2 eV to 0.7 eV. Due to localized excessive electrons in RuCl₃, distinct density of states is generated in the valence band, leading to the optical absorption change rather than metallic transition even in substantial doping concentration. The stable near-infrared photodetector using electronic modulated RuCl₃ showed 50 times higher photoresponsivity and 3 times faster response time compared to those of pristine RuCl₃, which contributes to overcoming the disadvantage of a Mott insulator as a promising optoelectronic device and expanding the material libraries.

Band-selective gap opening by a C 4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-T_C cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr₂VO₃FeAs across a phase transition at T ₀ ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity.

Fragile Pressure-Induced Magnetism in FeSe Superconductors with a Thickness Reduction

The emergence of high transition temperature (T_c) superconductivity in bulk FeSe under pressure is associated with the tuning of nematicity and magnetism. However, sorting out the relative contributions from magnetic and nematic fluctuations to the enhancement of T_c remains challenging. Here, we design and conduct a series of high-pressure experiments on FeSe thin flakes. We find that as the thickness decreases the nematic phase boundary on temperature-pressure phase diagrams remains robust while the magnetic order is significantly weakened. A local maximum of T_c is observed outside the nematic phase region, not far from the extrapolated nematic end point in all samples. However, the maximum T_c value is reduced associated with the weakening of magnetism. No high-T_c phase is observed in the thinnest sample. Our results strongly suggest that nematic fluctuations alone can only have a limited effect while magnetic fluctuations are pivotal on the enhancement of T_c in FeSe.

Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates

Establishing a minimal microscopic model for cuprates is a key step towards the elucidation of a high-T_{c} mechanism. By a quantitative comparison with a recent in situ angle-resolved photoemission spectroscopy measurement in doped 1D cuprate chains, our simulation identifies a crucial contribution from long-range electron-phonon coupling beyond standard Hubbard models. Using reasonable ranges of coupling strengths and phonon energies, we obtain a strong attractive interaction between neighboring electrons, whose strength is comparable to experimental observations. Nonlocal couplings play a significant role in the mediation of neighboring interactions. Considering the structural and chemical similarity between 1D and 2D cuprate materials, this minimal model with long-range electron-phonon coupling will provide important new insights on cuprate high-T_{c} superconductivity and related quantum phases.

Direct evidence for Cooper pairing without a spectral gap in a disordered superconductor above Tc

[Figure: see text].

Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid

[Figure: see text].

Spectroscopy of the frustrated quantum antiferromagnet Cs2CuCl4

We investigate the electronic structure of Cs₂CuCl₄, a material discussed in the framework of a frustrated quantum antiferromagnet, by means of resonant inelastic x-ray scattering (RIXS) and density functional theory (DFT). From the non-dispersive highly localizedddexcitations, we resolve the crystal field splitting of the Cu²⁺ions in a strongly distorted tetrahedral coordination. This allows us to model the RIXS spectrum within the crystal field theory (CFT), assign theddorbital excitations and retrieve experimentally the values of the crystal field splitting parametersD_q,D_sandD_τ. The electronic structure obtainedab-initioagrees with the RIXS spectrum and modelled by CFT, highlighting the potential of combined spectroscopic, cluster and DFT calculations to determine the electronic ground state of complex materials.