A New Spin on Material Properties: Local Magnetic Structure in Functional and Quantum Materials

The past few decades have made clear that the properties and performances of emerging functional and quantum materials can depend strongly on their local atomic and/or magnetic structure, particularly when details of the local structure deviate from the long-range structure averaged over space and time. Traditional methods of structural refinement (e.g., Rietveld) are typically sensitive only to the average structure, creating a need for more advanced structural probes suitable for extracting information about structural correlations on short length- and time-scales. In this Perspective, we describe the importance of local magnetic structure in several classes of emerging materials and present the magnetic pair distribution function (mPDF) technique as a powerful tool for studying short-range magnetism from neutron total-scattering data. We then provide a selection of examples of mPDF analysis applied to magnetic materials of recent technological and fundamental interest, including the antiferromagnetic semiconductor MnTe, geometrically frustrated magnets, and iron-oxide magnetic nanoparticles. The rapid development of mPDF analysis since its formalization a decade ago puts this technique in a strong position for making continued impact in the study of local magnetism in emerging materials.

Enhanced triplet superconductivity in next-generation ultraclean UTe2

The unconventional superconductor UTe[Formula: see text] exhibits numerous signatures of spin-triplet superconductivity-a rare state of matter which could enable quantum computation protected against decoherence. UTe[Formula: see text] possesses a complex phase landscape comprising two magnetic field-induced superconducting phases, a metamagnetic transition to a field-polarized state, along with pair- and charge-density wave orders. However, contradictory reports between studies performed on UTe[Formula: see text] specimens of varying quality have severely impeded theoretical efforts to understand the microscopic origins of the exotic superconductivity. Here, we report a comprehensive suite of high magnetic field measurements on a generation of pristine quality UTe[Formula: see text] crystals. Our experiments reveal a significantly revised high magnetic field superconducting phase diagram in the ultraclean limit, showing a pronounced sensitivity of field-induced superconductivity to the presence of crystalline disorder. We employ a Ginzburg-Landau model that excellently captures this acute dependence on sample quality. Our results suggest that in close proximity to a field-induced metamagnetic transition the enhanced role of magnetic fluctuations-that are strongly suppressed by disorder-is likely responsible for tuning UTe[Formula: see text] between two distinct spin-triplet superconducting phases.

Superconductivity under pressure in a chromium-based kagome metal

Superconductivity in a highly correlated kagome system has been theoretically proposed for years (refs. 1-5), yet the experimental realization is hard to achieve6,7. The recently discovered vanadium-based kagome materials8, which exhibit both superconductivity9-11 and charge-density-wave orders12-14, are nonmagnetic8,9 and weakly correlated15,16. Thus these materials are unlikely to host the exotic superconductivity theoretically proposed. Here we report the discovery of a chromium-based kagome metal, CsCr3Sb5, which is contrastingly featured with strong electron correlations, frustrated magnetism and characteristic flat bands close to the Fermi level. Under ambient pressure, this kagome metal undergoes a concurrent structural and magnetic phase transition at 55 K, with a stripe-like 4a0 structural modulation. At high pressure, the phase transition evolves into two transitions, possibly associated with charge-density-wave and antiferromagnetic spin-density-wave orderings. These density-wave-like orders are gradually suppressed with pressure and, remarkably, a superconducting dome emerges at 3.65-8.0 GPa. The maximum of the superconducting transition temperature, Tcmax = 6.4 K, appears when the density-wave-like orders are completely suppressed at 4.2 GPa, and the normal state exhibits a non-Fermi-liquid behaviour, reminiscent of unconventional superconductivity and quantum criticality in iron-based superconductors17,18. Our work offers an unprecedented platform for investigating superconductivity in correlated kagome systems.

Antiferromagnetic phase transition in a 3D fermionic Hubbard model

The fermionic Hubbard model (FHM)1 describes a wide range of physical phenomena resulting from strong electron-electron correlations, including conjectured mechanisms for unconventional superconductivity. Resolving its low-temperature physics is, however, challenging theoretically or numerically. Ultracold fermions in optical lattices2,3 provide a clean and well-controlled platform offering a path to simulate the FHM. Doping the antiferromagnetic ground state of a FHM simulator at half-filling is expected to yield various exotic phases, including stripe order4, pseudogap5, and d-wave superfluid6, offering valuable insights into high-temperature superconductivity7-9. Although the observation of antiferromagnetic correlations over short10 and extended distances11 has been obtained, the antiferromagnetic phase has yet to be realized as it requires sufficiently low temperatures in a large and uniform quantum simulator. Here we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature and doping concentration are finely tuned to approach their respective critical values, a sharp increase in the spin structure factor is observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class12. At half-filling and with optimal interaction strength, the measured spin structure factor reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results provide opportunities for exploring the low-temperature phase diagram of the FHM.

Light-induced switching between singlet and triplet superconducting states

While the search for topological triplet-pairing superconductivity has remained a challenge, recent developments in optically stabilizing metastable superconducting states suggest a new route to realizing this elusive phase. Here, we devise a testable theory of competing superconducting orders that permits ultrafast switching to an opposite-parity superconducting phase in centrosymmetric crystals with strong spin-orbit coupling. Using both microscopic and phenomenological models, we show that dynamical inversion symmetry breaking with a tailored light pulse can induce odd-parity (spin triplet) order parameter oscillations in a conventional even-parity (spin singlet) superconductor, which when driven strongly can send the system to a competing minimum in its free energy landscape. Our results provide new guiding principles for engineering unconventional electronic phases using light, suggesting a fundamentally non-equilibrium route toward realizing topological superconductivity.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question “is room temperature really achieved?” is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences.

Emergent superconducting fluctuations in compressed kagome superconductor CsV3Sb5

The recent discovery of superconductivity (SC) and charge density wave (CDW) in kagome metals AV₃Sb₅ (A = K, Rb, Cs) provides an ideal playground for the study of emergent electronic orders. Application of moderate pressure leads to a two-dome-shaped SC phase regime in CsV₃Sb₅ accompanied by the destabilizing of CDW phase. Nonetheless, the nature of this pressure-tuned SC state and its interplay with the CDW are yet to be explored. Here, we perform soft point-contact spectroscopy (SPCS) measurements in CsV₃Sb₅ to investigate the evolution of superconducting order parameter with pressure. Surprisingly, we find that the superconducting gap is significantly enhanced between the two SC domes, at which the zero-resistance temperature is suppressed and the transition is remarkably broadened. Moreover, the temperature-dependence of the SC gap in this pressure range severely deviates from the conventional Bardeen-Cooper-Schrieffer (BCS) behavior, evidencing for strong Cooper pair phase fluctuations. These findings reveal the complex intertwining of the CDW with SC in the compressed CsV₃Sb₅, suggesting striking parallel to the cuprate superconductor La_2-xBa_xCuO₄. Our results point to the essential role of charge degree of freedom in the development of intertwining electronic orders, and thus provide new constraints for theories.

Fourfold Symmetric Superconductivity in Spinel Oxide LiTi2O4(001) Thin Films

The charge frustration with the mixed-valence state inherent to LiTi₂O₄, which is found to be the only oxide superconductor with spinel structure, is the impetus for paying special attention to unveil the underlying intriguing superconducting properties. Here, we report a pronounced fourfold rotational symmetry of the superconductivity in high-quality single-crystalline LiTi₂O₄(001) thin films. Both the magnetoresistivity and upper critical field under an applied magnetic field manifest striking fourfold oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute this behavior to the unconventional d-wave superconducting Cooper pairs with the irreducible representation of E_g protected by the O_h point group in cubic LiTi₂O₄. Our findings show the nontrivial character of the pairing interaction in a three-dimensional spinel oxide superconductor.

Fully Two-Dimensional Incommensurate Charge Modulation on the Pd-Terminated Polar Surface of PdCoO2

Here, we use low-temperature scanning tunneling microscopy and spectroscopy to study the polar surfaces of PdCoO₂. On the CoO₂-terminated polar surface, we detect the quasiparticle interference pattern originating from the Rashba-like spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice that has a larger lattice constant than the atomic lattice of PdCoO₂. In comparison with the shape of the hexagonal Fermi surface on the Pd-terminated surface, we identify this regular lattice as a fully two-dimensional incommensurate charge modulation that is driven by the Fermi surface nesting. More interestingly, we also find the moiré pattern induced by the interference between the two-dimensional incommensurate charge modulation in the Pd layer and its atomic lattice. Our results not only show a new charge modulation on the Pd surface of PdCoO₂ but also pave the way for fully understanding the novel electronic properties of this material.

Charge doping to flat AgF2 monolayers in a chemical capacitor setup

Flat monolayers of silver(II) fluoride, which could be obtained by epitaxial deposition on an appropriate substrate, have been recently predicted to exhibit very strong antiferro-magnetic superexchange and to have large potential for ambient pressure superconductivity if doped to an optimal level. It was shown that AgF₂ could become a magnetic glue-based superconductor with a critical superconducting temperature approaching 200 K at optimum doping. In the current work we calculate the optimum doping to correspond to 14% of holes per formula unit, i.e. quite similar to that for oxocuprates(II). Furthermore, using DFT calculations we show that flat [AgF₂] single layers can indeed be doped to a controlled extent using a recently proposed "chemical capacitor" setup. Hole doping associated with the formation of Ag(III) proves to be difficult to achieve in the setup explored in this work as it falls at the verge of charge stability of fluoride anions and does not affect the d(x² - y²) manifold. However, in the case of electron doping, manipulation of different factors - such as the number of dopant layers and the thickness of the separator - permits fine tuning of the doping level (and concomitantly T_C) all the way from the underdoped to overdoped regime (in a similar manner to chemical doping for the Nd₂CuO₄ analogue).

s-wave superconductivity in the noncentrosymmetric W3Al2C superconductor: an NMR study

We report on a microscopic study of the noncentrosymmetric superconductor W₃Al₂C (withT_c= 7.6 K), mostly by means of²⁷Al- and¹³C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5dorbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W₃Al₂C resemble those of a standard metal, but with a Korringa product 1/(T₁T) significantly smaller than that of metallic Al, reflecting the marginal role played bys-electrons. In the superconducting state, we observe a reduction of the Knight shift and an exponential decrease of the NMR relaxation rate 1/T₁, typical ofs-wave superconductivity (SC). This is further supported by the observation of a small but distinct coherence peak just belowT_cin the¹³C NMR relaxation-rate, in agreement with the fully-gapped superconducting state inferred from the electronic specific-heat data well belowT_c. The above features are compared to those of members of the same family, in particular, Mo₃Al₂C, often claimed to exhibit unconventional SC. We discuss why, despite the enhanced SOC, W₃Al₂C does not show spin-triplet features in its superconducting state and consider the broader consequences of our results for noncentrosymmetric superconductors in general.

Giant Viscoelasticity near Mott Criticality in PbCrO_{3} with Large Lattice Anomalies

Coupling of charge and lattice degrees of freedom in materials can produce intriguing electronic phenomena, such as conventional superconductivity where the electrons are mediated by lattice for creating supercurrent. The Mott transition, which is a source for many fascinating emergent behaviors, is originally thought to be driven solely by correlated electrons with an Ising criticality. Recent studies on the known Mott systems have shown that the lattice degree of freedom is also at play, giving rise to either Landau or unconventional criticality. However, the underlying coupling mechanism of charge and lattice degrees of freedom around the Mott critical end point remains elusive, leading to difficulties in understanding the associated Mott physics. Here, we report a study of Mott transition in cubic PbCrO_{3} by measuring the lattice parameter, using high-pressure x-ray diffraction techniques. The Mott criticality in this material is revealed with large lattice anomalies, which is governed by giant viscoelasticity that presumably results from a combination of lattice elasticity and electron viscosity. Because of the viscoelastic effect, the lattice of this material behaves peculiarly near the critical end point, inconsistent with any existing university classes. We argue that the viscoelasticity may play as a hidden degree of freedom behind the Mott criticality.

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.

Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

Pressure-Tuned Superconducting Dome in Chemically-Substituted κ-(BEDT-TTF)2Cu2(CN)3

The quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 has been established as the prime example of a genuine Mott insulator that can be tuned across the first-order insulator–metal transition either by chemical substitution or by physical pressure. Here, we explore the superconducting state that occurs at low temperatures, when both methods are combined, i.e., when κ-[(BEDT-TTF)1−x(BEDT-STF)x]2Cu2(CN)3 is pressurized. We discovered superconductivity for partial BEDT-STF substitution with x = 0.10–0.12 even at ambient pressure, i.e., a superconducting state is realized in the range between a metal and a Mott insulator without magnetic order. Furthermore, we observed the formation of a superconducting dome by pressurizing the substituted crystals; we assigned this novel behavior to disorder emanating from chemical tuning.

New mechanism and exact theory of superconductivity from strong repulsive interaction

We introduce a general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamics of charge carriers is constrained by the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multiparticle tunneling processes that favor two itinerant carriers to be close together. Our analytically controlled theory provides a quantitative formula relating Tc to microscopic parameters, with maximum Tc reaching about 10% of the Fermi temperature. Our work demonstrates a powerful method for studying strong coupling superconductivity with unconventional pairing symmetry. It also offers a realistic new route to realizing finite angular momentum superfluidity of spin-polarized fermions in optical lattice.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

The Superconducting Critical Temperature

Two principles govern the critical temperature for superconducting transitions: (1) intrinsic strength of the pair coupling and (2) the effect of the many-body environments on the efficiency of that coupling. Most discussions take into account only the former, but we argue that the properties of unconventional superconductors are governed more often by the latter, through dynamical symmetry relating to normal and superconducting states. Differentiating these effects is essential to charting a path to the highest-temperature superconductors.

Emergence of a Pressure-Driven Superconducting Phase in Ba0.77Na0.23Ti2Sb2O

We investigated the pressure dependence of electric transport in a superconducting sample, Ba_0.77Na_0.23Ti₂Sb₂O, to complete the phase diagram of superconducting transition temperature (T_c) against pressure (p). This superconducting sample exhibits a T_c value of 5.8 K at ambient pressure. Here, the superconductivity of the recently reported sample was investigated over a wide pressure range. The T_c value monotonously decreased with pressure below 8 GPa. Interestingly, the T_c value rapidly increased above 8 GPa and slowly declined with pressure above 11 GPa. Thus, a new superconducting phase was discovered above ∼9 GPa. The crystal structure of Ba_0.77Na_0.23Ti₂Sb₂O was also elucidated at 0-22.0 GPa with synchrotron X-ray powder diffraction. Consequently, an evident relation between the crystal structure and the superconductivity was revealed, namely, a clear structural phase transition was observed at 8-11 GPa, where the T_c value rapidly increased against pressure. This study provides detailed information on the superconductivity of Ba_0.77Na_0.23Ti₂Sb₂O under pressure, which will lead to a comprehensive understanding of pressure-driven superconductivity.

Mixed temperature-dependent order parameters in the extended Hubbard model

The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below T _c. Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.

Strong In-Plane Magnetic Field-Induced Reemergent Superconductivity in the van der Waals Heterointerface of NbSe2 and CrCl3

A magnetic field is generally considered to be incompatible with superconductivity as it tends to spin-polarize electrons and breaks apart the opposite-spin singlet superconducting Cooper pairs. Here, an experimental phenomenon is observed that an intriguing reemergent superconductivity evolves from a conventional superconductivity undergoing a hump-like intermediate phase with a finite electric resistance in the van der Waals heterointerface of layered NbSe₂ and CrCl₃ flakes. This phenomenon merely occurred when the applied magnetic field is parallel to the sample plane and perpendicular to the electric current direction as compared to the reference sample of a NbSe₂ thin flake. The strong anisotropy of the reemergent superconducting phase is pointed to the nature of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state driven by the strong interfacial spin-orbit coupling between NbSe₂ and CrCl₃ layers. The theoretical picture of FFLO state nodes induced by Josephson vortices collectively pinning is presented for well understanding the experimental observation of the reemergent superconductivity. This finding sheds light on an opportunity to search for the exotic FFLO state in the van der Waals heterostructures with strong interfacial spin-orbit coupling.

Superconducting behavior of BaTi2Bi2O and its pressure dependence

A new superconducting sample, BaTi2Bi2O, was synthesized and characterized over a wide pressure range. The superconducting transition temperature, Tc, of BaTi2Bi2O was 4.33 K at ambient pressure. The crystal structure was tetragonal (space group of P4/mmm (No. 123)), according to the X-ray diffraction (XRD) pattern at ambient pressure. The XRD pattern was analyzed using the Le Bail method. The magnetic-field dependence of the magnetization at different temperatures was precisely investigated to elucidate the characteristics of the superconductivity. The pressure-dependent XRD patterns showed absence of structural phase transitions up to 19.8 GPa. The superconducting properties of BaTi2Bi2O were investigated under pressure. Tc monotonously increased with the pressure (p) up to 4.0 GPa and saturated above 4.0 GPa. The variations in the Tc-p plot were thoroughly analyzed. The Cooper pair symmetry (or superconducting pairing mechanism) was analyzed based on the magnetic field dependence of the superconductivity at ambient and high pressures, which indicated a sign of p-wave pairing for the superconductivity of BaTi2Bi2O, i.e., topologically nontrivial sign was suggested for BaTi2Bi2O.

Quasiparticle Lifetime of the Repulsive Fermi Polaron

We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is dominated by many-body dephasing within the upper repulsive branch rather than by relaxation from the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.

Pairing mechanism in multiband superconductors

It has been a long-standing puzzle why electrons with repulsive interactions can form pairs in unconventional superconductors. Here we develop an analytic solution for renormalization group analysis in multiband superconductors, which agrees with the numerical results exceedingly well. The analytic solution allows us to construct soluble effective theory and answers the pairing puzzle: electrons form pairs resonating between different bands to compensate the energy penalty for bring them together, just like the resonating chemical bonds in benzene. The analytic solutions allow us to explain the peculiar features of critical temperatures, spin uctuations in unconventional superconductors and can be generalized to cuprates where the notion of multibands is replaced by multipatches in momentum space.

Refined symmetry indicators for topological superconductors in all space groups

Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing fourfold symmetric superconductors with or without inversion symmetry and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.

Nature of the spin resonance mode in CeCoIn5

Spin-fluctuation-mediated unconventional superconductivity can emerge at the border of magnetism, featuring a superconducting order parameter that changes sign in momentum space. Detection of such a sign-change is experimentally challenging, since most probes are not phase-sensitive. The observation of a spin resonance mode (SRM) from inelastic neutron scattering is often seen as strong phase-sensitive evidence for a sign-changing superconducting order parameter, by assuming the SRM is a spin-excitonic bound state. Here we show that for the heavy fermion superconductor CeCoIn5, its SRM defies expectations for a spin-excitonic bound state, and is not a manifestation of sign-changing superconductivity. Instead, the SRM in CeCoIn5 likely arises from a reduction of damping to a magnon-like mode in the superconducting state, due to its proximity to magnetic quantum criticality. Our findings emphasize the need for more stringent tests of whether SRMs are spin-excitonic, when using their presence to evidence sign-changing superconductivity.

Anisotropic effect of a magnetic field on the neutron spin resonance in FeSe

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (E r = 3.6 meV) of superconducting FeSe (T c = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasiparticle excitations between the hole and electron Fermi surfaces.

First-principles studies of spin-orbital physics in pyrochlore oxides

The pyrochlore oxides [Formula: see text]O₇ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B  =  Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA)  +  U and LDA  +  dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.

Anomalous isotope effect in iron-based superconductors

The role of electron-phonon interactions in iron-based superconductor is currently under debate with conflicting experimental reports on the isotope effect. To address this important issue, we employ the renormalization-group method to investigate the competition between electron-electron and electron-phonon interactions in these materials. The renormalization-group analysis shows that the ground state is a phonon-dressed unconventional superconductor: the dominant electronic interactions account for pairing mechanism while electron-phonon interactions are subdominant. Because of the phonon dressing, the isotope effect of the critical temperature can be normal or reversed, depending on whether the retarded intra- or inter-band interactions are altered upon isotope substitutions. The connection between the anomalous isotope effect and the unconventional pairing symmetry is discussed at the end.

Scaling of magnetotransport in the Ba(Fe1-x Co x )2As2 series

We present magnetotransport studies of the parent, an underdoped and an optimally doped composition of the Ba(Fe_1-x Co _x )₂As₂ series. We observe that both the Kohler's and modified Kohler's scaling is typically violated in these systems. A notable exception is the magnetically ordered state of the underdoped composition where the modified Kohler's scaling is observed to be valid, indicating its relative similarity to the cuprates and some heavy fermion systems. This composition also exhibits a feature in the Hall angle, which could signify the opening of a pseudogap before the onset of long range magnetic order. The implications of our observations are discussed in the context of magnetotransport of metals with incipient magnetic fluctuations.

Discrete Superconducting Phases in FeSe-Derived Superconductors

A general feature of unconventional superconductors is the existence of a superconducting dome in the phase diagram. Here we report a series of discrete superconducting phases in the simplest iron-based superconductor, FeSe thin flakes, by continuously tuning the carrier concentration through the intercalation of Li and Na ions with a solid ionic gating technique. Such discrete superconducting phases are robust against the substitution of 20% S for Se, but they are vulnerable to the substitution of 2% Cu for Fe, highlighting the importance of the iron site being intact. The superconducting phase diagram for FeSe derivatives is given, which is distinct from that of other unconventional superconductors.

Enhanced superconductivity of Ba0.5K0.5Fe2As2 under surface potassium dosing

Surface potassium dosing has been proven to be an effective method in tuning the electron doping and enhancing the superconducting transition temperatures in both iron chalcogenides and electron doped iron pnictides. However, it is not clear how surface potassium dosing affects the hole doping and superconductivity in hole doped Fe-based superconductors. Here we performed K-dosing on Ba_0.5K_0.5Fe₂As₂, a prototypical hole-doped iron pnictide compound, and explored the electronic structure by in situ angle-resolved photoemission spectroscopy measurements. Starting from the slightly over-doped Ba_0.5K_0.5Fe₂As₂, surface K-dosing effectively reduces the hole concentration towards optimal doping and enhances the superconductivity. Intriguingly, the enhancement of superconductivity does not slow down at optimal doping, and the gap further increases with K dosing even when the carrier doping effect is saturated. Meanwhile, the quasiparticle coherence of the inner hole pockets is enhanced by higher K dosing. Our results uncover a novel scattering-reduction effect of K-dosing in Ba_1-x K _x Fe₂As₂, which collaborates with the carrier doping effect and enhances superconductivity.

Frustrated Structural Instability in Superconducting Quasi-One-Dimensional K_{2}Cr_{3}As_{3}

We present density functional theory and neutron total scattering studies on quasi-one-dimensional superconducting K_{2}Cr_{3}As_{3} revealing a frustrated structural instability. Our first principles calculations find a significant phonon instability, which, under energy minimization, corresponds to a frustrated orthorhombic distortion. In neutron diffraction studies we find large atomic displacement parameters with anomalous temperature dependencies, which result from highly localized orthorhombic distortions of the CrAs sublattice and coupled K displacements. These results suggest a more complex phase diagram than previously assumed for K_{2}Cr_{3}As_{3} with subtle interplays of structure, electron-phonon, and magnetic interactions.

From Ising Resonant Fluctuations to Static Uniaxial Order in Antiferromagnetic and Weakly Superconducting CeCo(In_{1-x}Hg_{x})_{5}(x=0.01)

CeCo(In_{0.990}Hg_{0.010})_{5} is a charge doped variant of the d-wave CoCoIn_{5} superconductor with coexistent antiferromagnetic and superconducting transitions occurring at T_{N}=3.4 and T_{c}=1.4  K, respectively. We use neutron diffraction and spectroscopy to show that the magnetic resonant fluctuations present in the parent superconducting phase are replaced by collinear c-axis magnetic order with three-dimensional Ising critical fluctuations. No low-energy transverse spin fluctuations are observable in this doping-induced antiferromagnetic phase and the dynamic resonant spectral weight predominately shifts to the elastic channel. Static (τ>0.2  ns) collinear Ising order is proximate to superconductivity in CeCoIn_{5} and is stabilized through hole doping with Hg.

Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5

Layered material structures play a key role in enhancing electron–electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn₅. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

The electronic properties along the out-of-plane direction of layered materials are often inferred indirectly. Here, Gyenis et al. directly probe in cross-section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn₅.

Distinct domain switching in Nd0.05Ce0.95CoIn5 at low and high fields

Nd_0.05Ce_0.95CoIn₅ features a magnetic field-driven quantum phase transition that separates two antiferromagnetic phases with an identical magnetic structure inside the superconducting condensate. Using neutron diffraction we demonstrate that the population of the two magnetic domains in the two phases is affected differently by the rotation of the magnetic field in the tetragonal basal plane. In the low-field SDW-phase the domain population is only weakly affected while in the high-field Q-phase they undergo a sharp switch for fields around the a-axis. Our results provide evidence that the anisotropic spin susceptibility in both phases arises ultimately from spin-orbit interactions but are qualitatively different in the two phases. This provides evidence that the electronic structure is changed at the quantum phase transition, which yields a modified coupling between magnetism and superconductivity in the Q-phase.

Spin Resonance and Magnetic Order in an Unconventional Superconductor

Unconventional superconductivity in many materials is believed to be mediated by magnetic fluctuations. It is an open question how magnetic order can emerge from a superconducting condensate and how it competes with the magnetic spin resonance in unconventional superconductors. Here we study a model d-wave superconductor that develops spin-density wave order, and find that the spin resonance is unaffected by the onset of static magnetic order. This result suggests a scenario, in which the resonance in Nd_{0.05}Ce_{0.95}CoIn_{5} is a longitudinal mode with fluctuating moments along the ordered magnetic moments.

Superconductivity Induced by Oxygen Doping in Y2 O2 Bi

When doped with oxygen, the layered Y₂ O₂ Bi phase becomes a superconductor. This finding raises questions about the sites for doped oxygen, the mechanism of superconductivity, and practical guidelines for discovering new superconductors. We probed these questions in terms of first-principles calculations for undoped and O-doped Y₂ O₂ Bi. The preferred sites for doped O atoms are the centers of Bi₄ squares in the Bi square net. Several Bi 6p x/y bands of Y₂ O₂ Bi are raised in energy by oxygen doping because the 2p x/y orbitals of the doped oxygen make antibonding possible with the 6p x/y orbitals of surrounding Bi atoms. Consequently, the condition necessary for the "flat/steep" band model for superconductivity is satisfied in O-doped Y₂ O₂ Bi.

Stepwise Bose-Einstein Condensation in a Spinor Gas

We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization m_{z} and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin-1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading, for instance, to condensation in m_{F}=±1, a phenomenon that cannot occur for an ideal gas with q>0.

Observation of a bi-critical point between antiferromagnetic and superconducting phases in pressurized single crystal Ca0.73La0.27FeAs2

One of the most strikingly universal features of the high-temperature superconductors is that the superconducting phase emerges in the close proximity of the antiferromagnetic phase, and the interplay between these two phases poses a long-standing challenge. It is commonly believed that, as the antiferromagnetic transition temperature is continuously suppressed to zero, there appears a quantum critical point, around which the existence of antiferromagnetic fluctuation is responsible for the development of the superconductivity. In contrast to this scenario, we report the observation of a bi-critical point identified at 2.88GPa and 26.02K in the pressurized high-quality single crystal Ca_0.73La_0.27FeAs₂ by complementary in-situ high pressure measurements. At the critical pressure, we find that the antiferromagnetism suddenly disappears and superconductivity simultaneously emerges at almost the same temperature, and that the external magnetic field suppresses the superconducting transition temperature but hardly affects the antiferromagnetic transition temperature.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

Europium-based iron pnictides: a unique laboratory for magnetism, superconductivity and structural effects

Despite decades of intense research, the origin of high-temperature superconductivity in cuprates and iron-based compounds is still a mystery. Magnetism and superconductivity are traditionally antagonistic phenomena; nevertheless, there is basically no doubt left that unconventional superconductivity is closely linked to magnetism. But this is not the whole story; recently, also structural effects related to the so-called nematic phase gained considerable attention. In order to obtain more information about this peculiar interplay, systematic material research is one of the most important attempts, revealing from time to time unexpected effects. Europium-based iron pnictides are the latest example of such a completely paradigmatic material, as they display not only spin-density-wave and superconducting ground states, but also local Eu²⁺ magnetism at a similar temperature scale. Here we review recent experimental progress in determining the complex phase diagrams of europium-based iron pnictides. The conclusions drawn from the observations reach far beyond these model systems. Thus, although europium-based iron pnictides are very peculiar, they provide a unique platform to study the common interplay of structural-nematic, magnetic and electronic effects in high-temperature superconductors.

Theory of scanning tunneling spectroscopy: from Kondo impurities to heavy fermion materials

Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments-the differential conductance and the quasi-particle interference spectrum-however, has been complicated by the fact that electrons tunneling from the STS tip into the system can tunnel either into the heavy magnetic moment or the light conduction band states. In this article, we briefly review the theoretical progress made in understanding how quantum interference between these two tunneling paths affects the experimental STS results. We show how this theoretical insight has allowed us to interpret the results of STS experiments on a series of heavy fermion materials providing detailed knowledge of their complex electronic structure. It is this knowledge that is a conditio sine qua non for developing a deeper understanding of the fascinating properties exhibited by heavy fermion materials, ranging from unconventional superconductivity to non-Fermi-liquid behavior in the vicinity of quantum critical points.

Anomalous Damping of a Microelectromechanical Oscillator in Superfluid ^{3}He-B

The mechanical resonance properties of a microelectromechanical oscillator with a gap of 1.25  μm was studied in superfluid ^{3}He-B at various pressures. The oscillator was driven in the linear damping regime where the damping coefficient is independent of the oscillator velocity. The quality factor of the oscillator remains low (Q≈80) down to 0.1T_{c}, 4 orders of magnitude less than the intrinsic quality factor measured in vacuum at 4 K. In addition to the Boltzmann temperature dependent contribution to the damping, a damping proportional to temperature was found to dominate at low temperatures. We propose a multiple scattering mechanism of the surface Andreev bound states to be a possible cause for the anomalous damping.