Measurement of the magnetic octupole susceptibility of PrV2Al20

Revealing the presence of magnetic octupole order and associated octupole fluctuations in solids is a highly challenging task due to the lack of simple external fields that can couple to magnetic octupoles. Here, we demonstrate a methodology for probing the magnetic octupole susceptibility of a candidate material, PrV2Al20, using a product of magnetic field Hi and shear strain ϵjk as a composite effective field, while employing an adiabatic elastocaloric effect to probe the response. We observe Curie-Weiss behavior in the obtained octupolar susceptibility down to approximately 3 K. Although octupole order does not appear to be the leading multipolar channel in PrV2Al20, our results nevertheless reveal the presence of strong magnetic octupole fluctuations and hence demonstrate that octupole order is at least a competing state. More broadly, our results highlight how anisotropic strain can be combined with magnetic fields to probe elusive 'hidden' electronic orders.

Light-induced electronic polarization in antiferromagnetic Cr2O3

In a solid, the electronic subsystem can exhibit incipient order with lower point group symmetry than the crystal lattice. Ultrafast external fields that couple exclusively to electronic order parameters have rarely been investigated, however, despite their potential importance in inducing exotic effects. Here we show that when inversion symmetry is broken by the antiferromagnetic order in Cr2O3, transmitting a linearly polarized light pulse through the crystal gives rise to an in-plane rotational symmetry-breaking (from C3 to C1) via optical rectification. Using interferometric time-resolved second harmonic generation, we show that the ultrafast timescale of the symmetry reduction is indicative of a purely electronic response; the underlying spin and crystal structures remain unaffected. The symmetry-broken state exhibits a dipole moment, and its polar axis can be controlled with the incident light. Our results establish a coherent nonlinear optical protocol by which to break electronic symmetries and produce unconventional electronic effects in solids.

Spin Echo, Fidelity, and the Quantum Critical Fan in TmVO_{4}

Using spin-echo nuclear magnetic resonance in the model transverse field Ising system TmVO_{4}, we show that low frequency quantum fluctuations at the quantum critical point have a very different effect on ^{51}V nuclear spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point. Spin echoes filter out the low-frequency classical noise but not the quantum fluctuations. This allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO_{4} to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence.

Emergent tetragonality in a fundamentally orthorhombic material

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe3, for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.

Perspective: probing elasto-quantum materials with x-ray techniques andin situanisotropic strain

Anisotropic lattice deformation plays an important role in the quantum mechanics of solid state physics. The possibility of mediating the competition and cooperation among different order parameters by applyingin situstrain/stress on quantum materials has led to discoveries of a variety of elasto-quantum effects on emergent phenomena. It has become increasingly critical to have the capability of combining thein situstrain tuning with x-ray techniques, especially those based on synchrotrons, to probe the microscopic elasto-responses of the lattice, spin, charge, and orbital degrees of freedom. Herein, we briefly review the recent studies that embarked on utilizing elasto-x-ray characterizations on representative material systems and demonstrated the emerging opportunities enabled by this method. With that, we further discuss the promising prospect in this rising area of quantum materials research and the bright future of elasto-x-ray techniques.

Colossal c-Axis Response and Lack of Rotational Symmetry Breaking within the Kagome Planes of the CsV_{3}Sb_{5} Superconductor

The kagome materials AV_{3}Sb_{5} (A=K, Rb, Cs) host an intriguing interplay between unconventional superconductivity and charge-density waves. Here, we investigate CsV_{3}Sb_{5} by combining high-resolution thermal-expansion, heat-capacity, and electrical resistance under strain measurements. We directly unveil that the superconducting and charge-ordered states strongly compete, and that this competition is dramatically influenced by tuning the crystallographic c axis. In addition, we report the absence of additional bulk phase transitions within the charge-ordered state, notably associated with rotational symmetry breaking within the kagome planes. This suggests that any breaking of the C_{6} invariance occurs via different stacking of C_{6}-symmetric kagome patterns. Finally, we find that the charge-density-wave phase exhibits an enhanced A_{1g}-symmetric elastoresistance coefficient, whose large increase at low temperature is driven by electronic degrees of freedom.

Charge density waves tuned by biaxial tensile stress

The precise arrangement and nature of atoms drive electronic phase transitions in condensed matter. To explore this tenuous link, we developed a true biaxial mechanical deformation device working at cryogenic temperatures, compatible with x-ray diffraction and transport measurements, well adapted to layered samples. Here we show that a slight deformation of TbTe3 can have a dramatic influence on its Charge Density Wave (CDW), with an orientational transition from c to a driven by the a/c parameter, a tiny coexistence region near a = c, and without space group change. The CDW transition temperature Tc displays a linear dependence witha / c - 1 while the gap saturates out of the coexistence region. This behaviour is well accounted for within a tight-binding model. Our results question the relationship between gap and Tc in RTe3 systems. This method opens a new route towards the study of coexisting or competing electronic orders in condensed matter.

Signatures of a surface spin-orbital chiral metal

The relation between crystal symmetries, electron correlations and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism1-6. The detection of such hidden orders is an important goal in condensed-matter physics. However, until now, non-standard forms of magnetism with chiral electronic ordering have been difficult to detect experimentally7. Here we develop a theory for symmetry-broken chiral ground states and propose a methodology based on circularly polarized, spin-selective, angular-resolved photoelectron spectroscopy to study them. We use the archetypal quantum material Sr2RuO4 and reveal spectroscopic signatures that, despite being subtle, can be reconciled with the formation of spin-orbital chiral currents at the surface of the material8-10. As we shed light on these chiral regimes, our findings pave the way for a deeper understanding of ordering phenomena and unconventional magnetism.

Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200  K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

Giant lattice softening at a Lifshitz transition in Sr2RuO4

The interplay of electronic and structural degrees of freedom in solids is a topic of intense research. More than 60 years ago, Lifshitz discussed a counterintuitive possibility: lattice softening driven by conduction electrons at topological Fermi surface transitions. The effect that he predicted, however, was small and has not been convincingly observed. Using a piezo-based uniaxial pressure cell to tune the ultraclean metal strontium ruthenate while measuring the stress-strain relationship, we reveal a huge softening of the Young's modulus at a Lifshitz transition of a two-dimensional Fermi surface and show that it is indeed driven entirely by the conduction electrons of the relevant energy band.

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

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

Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide

Electronic anisotropy ("nematicity") has been detected in cuprate superconductors by various experimental techniques. Using angle-resolved transverse resistance (ARTR) measurements, a very sensitive and background-free technique that can detect 0.5% anisotropy in transport, we have observed it also in La2-xSrxCuO4 (LSCO) for 0.02 ≤ x ≤ 0.25. A central enigma in LSCO is the rotation of the nematic director (orientation of the largest longitudinal resistance) with temperature; this has not been seen before in any material. Here, we address this puzzle by measuring the angle-resolved transverse magnetoresistance (ARTMR) in LSCO. We report the discovery of colossal transverse magnetoresistance (CTMR)-an order-of-magnitude drop in the transverse resistivity in the magnetic field of 6 T. We show that the apparent rotation of the nematic director is caused by anisotropic superconducting fluctuations, which are not aligned with the normal electron fluid, consistent with coexisting bond-aligned and diagonal nematic orders. We quantify this by modeling the (magneto-)conductivity as a sum of normal (Drude) and paraconducting (Aslamazov-Larkin) channels but extended to contain anisotropic Drude and Cooper-pair effective mass tensors. Strikingly, the anisotropy of Cooper-pair stiffness is much larger than that of the normal electrons. It grows dramatically on the underdoped side, where the fluctuations become quasi-one-dimensional. Our analysis is general rather than model dependent. Still, we discuss some candidate microscopic models, including coupled strongly-correlated ladders where the transverse (interladder) phase stiffness is low compared with the longitudinal intraladder stiffness, as well as the anisotropic superconducting fluctuations expected close to the transition to a pair-density wave state.

Optimized superconductivity in the vicinity of a nematic quantum critical point in the kagome superconductor Cs(V1-xTix)3Sb5

CsV3Sb5 exhibits superconductivity at Tc = 3.2 K after undergoing intriguing two high-temperature transitions: charge density wave order at ~98 K and electronic nematic order at Tnem ~ 35 K. Here, we investigate nematic susceptibility in single crystals of Cs(V1-xTix)3Sb5 (x = 0.00-0.06) where double-dome-shaped superconducting phase diagram is realized. The nematic susceptibility typically exhibits the Curie‒Weiss behaviour above Tnem, which is monotonically decreased with x. Moreover, the Curie‒Weiss temperature is systematically suppressed from ~30 K for x = 0 to ~4 K for x = 0.0075, resulting in a sign change at x = ~0.009. Furthermore, the Curie constant reaches a maximum at x = 0.01, suggesting drastically enhanced nematic susceptibility near a putative nematic quantum critical point (NQCP) at x = ~0.009. Strikingly, Tc is enhanced up to ~4.1 K with full Meissner shielding realized at x = ~0.0075-0.01, forming the first superconducting dome near the NQCP. Our findings directly point to a vital role of nematic fluctuations in enhancing the superconducting properties of Cs(V1-xTix)3Sb5.

Verwey transition as evolution from electronic nematicity to trimerons via electron-phonon coupling

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step toward controlling material's properties. Since the proposal of charge order-induced MIT in magnetite Fe3O4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive. Recently, a trimeron order was found in the low-temperature structure of Fe3O4; however, the expected transition entropy change in forming trimeron is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here, we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature structure of bulk Fe3O4 and that, upon cooling, a competitive intertwining of charge and lattice orders arouses the Verwey transition. Our findings discover an unconventional type of electronic nematicity in correlated materials and offer innovative insights into the transition mechanism in Fe3O4 via the electron-phonon coupling.

Real-Space Observation of Unidirectional Charge Density Wave and Complex Structural Modulation in the Pnictide Superconductor Ba1-xSrxNi2As2

Here we use low-temperature and variable-temperature scanning tunneling microscopy to study the pnictide superconductor, Ba_1-xSr_xNi₂As₂. In the low-temperature phase (triclinic phase) of BaNi₂As₂, we observe the unidirectional charge density wave (CDW) with Q = 1/3 on both the Ba and NiAs surfaces. On the NiAs surface of the triclinic BaNi₂As₂, there are structural-modulation-induced chain-like superstructures with distinct periodicities. In the high-temperature phase (tetragonal phase) of BaNi₂As₂, the NiAs surface appears as the periodic 1 × 2 superstructure. Interestingly, in the triclinic phase of Ba_0.5Sr_0.5Ni₂As₂, the unidirectional CDW is suppressed on both the Ba/Sr and NiAs surfaces, and the Sr substitution stabilizes the periodic 1 × 2 superstructure on the NiAs surface, which enhance the superconductivity in Ba_0.5Sr_0.5Ni₂As₂. Our results provide important microscopic insights for the interplay among the unidirectional CDW, structural modulation, and superconductivity in this class of pnictide superconductors.

Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.

In situ uniaxial pressure cell for x-ray and neutron scattering experiments

We present an in situ uniaxial pressure device optimized for small angle x-ray and neutron scattering experiments at low-temperatures and high magnetic fields. A stepper motor generates force, which is transmitted to the sample via a rod with an integrated transducer that continuously monitors the force. The device has been designed to generate forces up to 200 N in both compressive and tensile configurations, and a feedback control allows operating the system in a continuous-pressure mode as the temperature is changed. The uniaxial pressure device can be used for various instruments and multiple cryostats through simple and exchangeable adapters. It is compatible with multiple sample holders, which can be easily changed depending on the sample properties and the desired experiment and allow rapid sample changes.

Nematic-Fluctuation-Mediated Superconductivity Revealed by Anisotropic Strain in Ba(Fe_{1-x}Co_{x})_{2}As_{2}

Anisotropic strain is an external field capable of selectively addressing the role of nematic fluctuations in promoting superconductivity. We demonstrate this using polarization-resolved elasto-Raman scattering by probing the evolution of nematic fluctuations under strain in the normal and superconducting state of the paradigmatic iron-based superconductor Ba(Fe_{1-x}Co_{x})_{2}As_{2}. In the parent compound BaFe_{2}As_{2} we observe a strain-induced suppression of the nematic susceptibility which follows the expected behavior of an Ising order parameter under a symmetry breaking field. For the superconducting compound, the suppression of the nematic susceptibility correlates with the decrease of the critical temperature T_{c}, indicating a significant contribution of nematic fluctuations to electron pairing. Our results validate theoretical scenarios of enhanced T_{c} near a nematic quantum critical point.

Controllable Emergent Spatial Spin Modulation in Sr_{2}IrO_{4} by In Situ Shear Strain

Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that the competition of anisotropic interactions of orthogonal irreducible representations can be a general route to obtain new exotic magnetic states. We demonstrate it here by observing the emergence of a continuously tunable 12-layer spatial spin modulation when distorting the square-lattice planes in the quasi-two-dimensional antiferromagnetic Sr_{2}IrO_{4} under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain-activated anisotropic interaction which is at the fourth order and competing with the inherent quadratic anisotropic interaction. Such a mechanism of competing anisotropy is distinct from that among the ferromagnetic, antiferromagnetic, and/or the Dzyaloshinskii-Moriya interactions, and it could be widely applicable and highly controllable in low-dimensional magnets.

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.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Te_x. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Reversible strain-induced magnetic phase transition in a van der Waals magnet

Mechanical deformation of a crystal can have a profound effect on its physical properties. Notably, even small modifications of bond geometry can completely change the size and sign of magnetic exchange interactions and thus the magnetic ground state. Here we report the strain tuning of the magnetic properties of the A-type layered antiferromagnetic semiconductor CrSBr achieved by designing a strain device that can apply continuous, in situ uniaxial tensile strain to two-dimensional materials, reaching several percent at cryogenic temperatures. Using this apparatus, we realize a reversible strain-induced antiferromagnetic-to-ferromagnetic phase transition at zero magnetic field and strain control of the out-of-plane spin-canting process. First-principles calculations reveal that the tuning of the in-plane lattice constant strongly modifies the interlayer magnetic exchange interaction, which changes sign at the critical strain. Our work creates new opportunities for harnessing the strain control of magnetism and other electronic states in low-dimensional materials and heterostructures.

Comparison of temperature and doping dependence of elastoresistivity near a putative nematic quantum critical point

Strong electronic nematic fluctuations have been discovered near optimal doping for several families of Fe-based superconductors, motivating the search for a possible link between these fluctuations, nematic quantum criticality, and high temperature superconductivity. Here we probe a key prediction of quantum criticality, namely power-law dependence of the associated nematic susceptibility as a function of composition and temperature approaching the compositionally tuned putative quantum critical point. To probe the ‘bare’ quantum critical point requires suppression of the superconducting state, which we achieve by using large magnetic fields, up to 45 T, while performing elastoresistivity measurements to follow the nematic susceptibility. We performed these measurements for the prototypical electron-doped pnictide, Ba(Fe_1−xCo_x)₂As₂, over a dense comb of dopings. We find that close to the putative quantum critical point, the elastoresistivity appears to obey power-law behavior as a function of composition over almost a decade of variation in composition. Paradoxically, however, we also find that the temperature dependence for compositions close to the critical value cannot be described by a single power law.

Evidence for quantum criticality in Fe-based superconductors is still being accumulated. Here, the authors observe power-law behavior of the elastoresistivity as a function of composition in Ba(Fe_1−xCo_x)₂As₂ near a putative nematic quantum critical point, consistent with expectations for quantum criticality, while the temperature dependence near the critical doping deviates from a power law.

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Electronic nematicity, in which rotational symmetry is spontaneously broken by electronic degree of freedom, has been demonstrated as a ubiquitous phenomenon in correlated quantum fluids including high-temperature superconductors (HTS) and quantum Hall systems^1,2. More strikingly, the electronic nematicity in HTS exhibits an intriguing entanglement with superconductivity, generating complicated superconducting pairing and intertwined electronic orders. Recently, an unusual competition between superconductivity and a charge-density-wave (CDW) order has been found in AV₃Sb₅ (A = K, Rb, Cs) family with two-dimensional vanadium kagome nets^3-8. Whether these phenomena involve electronic nematicity is still elusive. Here, we report compelling evidence for the existence of electronic nematicity in CsV₃Sb₅, using a combination of elastoresistance measurements, nuclear magnetic resonance (NMR) and scanning tunnelling microscopy/spectroscopy (STM/S). The temperature-dependent elastoresistance coefficient (m₁₁-m₁₂) and NMR spectrum clearly demonstrate that, besides a C₂ structural distortion of 2a₀×2a₀ supercell due to out-of-plane modulation, significant nematic fluctuations emerge immediately below the CDW transition (T_CDW ~ 94 K) and finally a nematic transition occurs below T_nem ~ 35 K. STM experiment directly visualizes the C₂-structure-pinned long-range nematic order below T_nem, suggesting a novel nematicity described by a three-state Potts model. Our findings unambiguously prove an intrinsic electronic nematicity in the normal state of CsV₃Sb₅, which sets a new paradigm for revealing the role of electronic nematicity on pairing mechanism in unconventional superconductors.

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.

Unveiling unconventional magnetism at the surface of Sr2RuO4

Materials with strongly correlated electrons often exhibit interesting physical properties. An example of these materials is the layered oxide perovskite Sr₂RuO₄, which has been intensively investigated due to its unusual properties. Whilst the debate on the symmetry of the superconducting state in Sr₂RuO₄ is still ongoing, a deeper understanding of the Sr₂RuO₄ normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of surface magnetism in Sr₂RuO₄ in its normal state. We detect static weak dipolar fields yet manifesting at an onset temperature higher than 50 K. We ascribe this unconventional magnetism to orbital loop currents forming at the reconstructed Sr₂RuO₄ surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence electron pairing with broken time reversal symmetry.

Elastocaloric signature of nematic fluctuations

The elastocaloric effect (ECE) relates changes in entropy to changes in strain experienced by a material. As such, ECE measurements can provide valuable information about the entropy landscape proximate to strain-tuned phase transitions. For ordered states that break only point symmetries, bilinear coupling of the order parameter with strain implies that the ECE can also provide a window on fluctuations above the critical temperature and hence, in principle, can also provide a thermodynamic measure of the associated susceptibility. To demonstrate this, we use the ECE to sensitively reveal the presence of nematic fluctuations in the archetypal Fe-based superconductor Ba([Formula: see text])₂[Formula: see text] By performing these measurements simultaneously with elastoresistivity in a multimodal fashion, we are able to make a direct and unambiguous comparison of these closely related thermodynamic and transport properties, both of which are sensitive to nematic fluctuations. As a result, we have uncovered an unanticipated doping dependence of the nemato-elastic coupling and of the magnitude of the scattering of low-energy quasi-particles by nematic fluctuations-while the former weakens, the latter increases dramatically with increasing doping.

Emerging symmetric strain response and weakening nematic fluctuations in strongly hole-doped iron-based superconductors

Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong electronic correlations and the sensitivity of these correlations to strain. We find weakened remnants of the nematic fluctuations that are present at optimal doping, but no change in the symmetry channel of nematic fluctuations with hole doping. Furthermore, we find no indication of a nematic-ordered state in the AFe2As2 (A = K, Rb, Cs) superconductors. These results revise the current understanding of nematicity in hole-doped iron-based superconductors.

Multiple Charge Density Waves and Superconductivity Nucleation at Antiphase Domain Walls in the Nematic Pnictide Ba_{1-x}Sr_{x}Ni_{2}As_{2}

How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba_{1-x}Sr_{x}Ni_{2}As_{2} (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a sixfold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at x_{c}=0.7) [1]. The superconductivity is, however, anomalous, with the resistive transition for 0.4<x<x_{c} occurring at a higher temperature than the specific heat anomaly. Using x-ray scattering, we discovered a new charge density wave (CDW) in BSNA in this composition range. The CDW is commensurate with a period of two lattice parameters, and is distinct from the two CDWs previously reported in this material [1,2]. We argue that the anomalous transport behavior arises from heterogeneous superconductivity nucleating at antiphase domain walls in this CDW. We also present new data on the incommensurate CDW, previously identified as being unidirectional [2], showing that it is a rotationally symmetric "4Q" state with C_{4} symmetry. Our study establishes BSNA as a rare material containing three distinct CDWs, and an exciting test bed for studying coupling between CDW, nematic, and SC orders.

Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure

CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94  K and superconductivity (SC) at T_{c}=2.5  K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9  GPa before it vanishes completely at P_{c2}≈2  GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around P_{c1} has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise T_{c} of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning

Quantum criticality may be essential to understanding a wide range of exotic electronic behavior; however, conclusive evidence of quantum critical fluctuations has been elusive in many materials of current interest. An expected characteristic feature of quantum criticality is power-law behavior of thermodynamic quantities as a function of a nonthermal tuning parameter close to the quantum critical point (QCP). Here, we observed power-law behavior of the critical temperature of the coupled nematic/structural phase transition as a function of uniaxial stress in a representative family of iron-based superconductors, providing direct evidence of quantum critical nematic fluctuations in this material. These quantum critical fluctuations are not confined within a narrow regime around the QCP but rather extend over a wide range of temperatures and compositions.

Quadrupolar charge dynamics in the nonmagnetic FeSe1-x S x superconductors

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

Learning the Fuzzy Phases of Small Photonic Condensates

Phase transitions, being the ultimate manifestation of collective behavior, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behavior in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and nonequilibrium regimes, including Bose-Einstein condensation or laserlike emission are identified. However, the small photon number and the presence of large relative fluctuations places major difficulties in identifying different phases and phase transitions. We overcome this limitation by employing unsupervised learning and fuzzy clustering algorithms to systematically construct the fuzzy phase diagram of our small photonic condensate. Our results thus demonstrate the rich and complex phase structure of even small collections of photons, making them an ideal platform to investigate equilibrium and nonequilibrium physics at the few particle level.

Strain-Stabilized (π, π) Order at the Surface of Fe1+xTe

A key property of many quantum materials is that their ground state depends sensitively on small changes of an external tuning parameter, e.g., doping, magnetic field, or pressure, creating opportunities for potential technological applications. Here, we explore tuning of the ground state of the nonsuperconducting parent compound, Fe_1+xTe, of the iron chalcogenides by uniaxial strain. Iron telluride exhibits a peculiar (π, 0) antiferromagnetic order unlike the (π, π) order observed in the Fe-pnictide superconductors. The (π, 0) order is accompanied by a significant monoclinic distortion. We explore tuning of the ground state by uniaxial strain combined with low-temperature scanning tunneling microscopy. We demonstrate that, indeed under strain, the surface of Fe_1.1Te undergoes a transition to a (π, π)-charge-ordered state. Comparison with transport experiments on uniaxially strained samples shows that this is a surface phase, demonstrating the opportunities afforded by 2D correlated phases stabilized near surfaces and interfaces.

Incommensurate smectic phase in close proximity to the high-Tc superconductor FeSe/SrTiO3

Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO₃, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists and gradually fades away with increasing film thickness, while it suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase transition. Surface alkali-metal doping can suppress the smectic phase and induce high-T_c superconductivity in bilayer FeSe. Our observations provide evidence that the monolayer FeSe is in close proximity to the smectic phase, and its superconductivity is likely enhanced by this electronic instability as well.

The relation between enhanced superconductivity in monolayer FeSe grown on SrTiO₃ and the large nematicity in multilayer FeSe on SrTiO₃ remains not well understood. Here, the authors observe a long-range smectic phase in bilayer FeSe films but vanishes in monolayer FeSe, providing a new instability to help enhance the superconductivity.

Short-Range Nematic Fluctuations in Sr_{1-x}Na_{x}Fe_{2}As_{2} Superconductors

Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr_{1-x}Na_{x}Fe_{2}As_{2} measured via inelastic x-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped (x=0.36) sample, which harbors a magnetically ordered tetragonal phase, we find it hosts a short nematic correlation length ξ∼10  Å and a large nematic susceptibility χ_{nem}. The optimal-doped (x=0.55) sample exhibits weaker phonon softening effects, indicative of both reduced ξ and χ_{nem}. Our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.

Nanoscale decoupling of electronic nematicity and structural anisotropy in FeSe thin films

In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to spatially varying strain. We map local anisotropic strain by analyzing scanning tunneling microscopy topographs, and visualize electronic nematic domains from concomitant spectroscopic maps. While the domains form so that the energy of nemato-elastic coupling is minimized, we observe distinct regions where electronic nematic ordering fails to flip direction, even though the underlying structural anisotropy is locally reversed. The findings point towards a nanometer-scale stiffness of the nematic order parameter.

In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe2As2

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe2As2, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature Ts. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature TN ( < Ts) and create in-plane resistivity anisotropy above Ts. Here we use neutron polarization analysis to show that such a strain on BaFe2As2 also induces a static or quasi-static out-of-plane (c-axis) AF order and its associated critical spin fluctuations near TN/Ts. Therefore, uniaxial pressure necessary to detwin single crystals of BaFe2As2 actually rotates the easy axis of the collinear AF order near TN/Ts, and such effects due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.

Momentum dependent [Formula: see text] band splitting in LaFeAsO

The nematic phase in iron based superconductors (IBSs) has attracted attention with a notion that it may provide important clue to the superconductivity. A series of angle-resolved photoemission spectroscopy (ARPES) studies were performed to understand the origin of the nematic phase. However, there is lack of ARPES study on LaFeAsO nematic phase. Here, we report the results of ARPES studies of the nematic phase in LaFeAsO. Degeneracy breaking between the [Formula: see text] and [Formula: see text] hole bands near the [Formula: see text] and M point is observed in the nematic phase. Different temperature dependent band splitting behaviors are observed at the [Formula: see text] and M points. The energy of the band splitting near the M point decreases as the temperature decreases while it has little temperature dependence near the [Formula: see text] point. The nematic nature of the band shift near the M point is confirmed through a detwin experiment using a piezo device. Since a momentum dependent splitting behavior has been observed in other iron based superconductors, our observation confirms that the behavior is a universal one among iron based superconductors.

Dominant In-Plane Symmetric Elastoresistance in CsFe_{2}As_{2}

We study the elastoresistance of the highly correlated material CsFe_{2}As_{2} in all symmetry channels. Neutralizing its thermal expansion by means of a piezoelectric-based strain cell is demonstrated to be essential. The elastoresistance response in the in-plane symmetric channel is found to be large, while the response in the symmetry-breaking channels is weaker and provides no evidence for a divergent nematic susceptibility. Rather, our results can be interpreted naturally within the framework of a coherence-incoherence crossover, where the low-temperature coherent state is sensitively tuned by the in-plane atomic distances.

Three-state nematicity in the triangular lattice antiferromagnet Fe1/3NbS2

Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such 'Ising-nematic' systems is a simple scalar. Here, using a spatially resolved optical polarimetry technique, we show that a qualitatively distinct nematic state arises in the triangular lattice antiferromagnet Fe_1/3NbS₂. The crucial difference is that the nematic order on the triangular lattice is a [Formula: see text] or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously reoriented by external perturbations. This discovery lays the groundwork for devices that exploit analogies with nematic liquid crystals.

Superconductivity in undoped BaFe2As2 by tetrahedral geometry design

Fe-based superconductors exhibit a diverse interplay between charge, orbital, and magnetic ordering. Variations in atomic geometry affect electron hopping between Fe atoms and the Fermi surface topology, influencing magnetic frustration and the pairing strength through changes of orbital overlap and occupancies. Here, we experimentally demonstrate a systematic approach to realize superconductivity without chemical doping in BaFe₂As₂, employing geometric design within an epitaxial heterostructure. We control both tetragonality and orthorhombicity in BaFe₂As₂ through superlattice engineering, which we experimentally find to induce superconductivity when the As-Fe-As bond angle approaches that in a regular tetrahedron. This approach to superlattice design could lead to insights into low-dimensional superconductivity in Fe-based superconductors.

Comprehensive Electrical Control of Metamagnetic Transition of a Quasi-2D Antiferromagnet by In Situ Anisotropic Strain

Effective nonmagnetic control of the spin structure is at the forefront of the study for functional quantum materials. This study demonstrates that, by applying an anisotropic strain up to only 0.05%, the metamagnetic transition field of spin-orbit-coupled Mott insulator Sr₂ IrO₄ can be in situ modulated by almost 300%. Simultaneous measurements of resonant X-ray scattering and transport reveal that this drastic response originates from the complete strain-tuning of the transition between the spin-flop and spin-flip limits, and is always accompanied by large elastoconductance and magnetoconductance. This enables electrically controllable and electronically detectable metamagnetic switching, despite the antiferromagnetic insulating state. The obtained strain-magnetic field phase diagram reveals that C₄ -symmetry-breaking anisotropy is introduced by strain via pseudospin-lattice coupling, directly demonstrating the pseudo-Jahn-Teller effect of spin-orbit-coupled complex oxides. The extracted coupling strength is much weaker than the superexchange interactions, yet crucial for the spontaneous symmetry-breaking, affording the remarkably efficient strain-control.

Uniaxial-strain control of nematic superconductivity in SrxBi2Se3

Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. In nematic superconductivity, multiple superconducting domains with different nematic orientations can exist, and these domains can be controlled by a conjugate external stimulus. Domain engineering is quite common in magnets but has not been achieved in superconductors. Here, we report control of the nematic superconductivity and their domains of SrxBi2Se3, through externally-applied uniaxial stress. The suppression of subdomains indicates that it is the Δ4y state that is most favoured under compression along the basal Bi-Bi bonds. This fact allows us to determine the coupling parameter between the nematicity and lattice distortion. These results provide an inevitable step towards microscopic understanding and future utilization of the unique topological nematic superconductivity.

Evolution of the Nematic Susceptibility in LaFe_{1-x}Co_{x}AsO

We report a systematic elastoresistivity study on LaFe_{1-x}Co_{x}AsO single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss-like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of LaFe_{1-x}Co_{x}AsO.

Frequency-dependent sensitivity of AC elastocaloric effect measurements explored through analytical and numerical models

We present a comprehensive study of the frequency-dependent sensitivity for measurements of the AC elastocaloric effect by applying both exactly soluble models and numerical methods to the oscillating heat flow problem. These models reproduce the finer details of the thermal transfer functions observed in experiments, considering here representative data for single-crystal Ba(Fe_1-xCo_x)₂As₂. Based on our results, we propose a set of practical guidelines for experimentalists using this technique. This work establishes a baseline against which the frequency response of the AC elastocaloric technique can be compared and provides intuitive explanations of the detailed structure observed in experiments.

Rigid platform for applying large tunable strains to mechanically delicate samples

Response to uniaxial stress has become a major probe of electronic materials. Tunable uniaxial stress may be applied using piezoelectric actuators, and so far two methods have been developed to couple samples to actuators. In one, actuators apply force along the length of a free, beam-like sample, allowing very large strains to be achieved. In the other, samples are affixed directly to piezoelectric actuators, allowing the study of mechanically delicate materials. Here, we describe an approach that merges the two: thin samples are affixed to a substrate, which is then pressurized uniaxially using piezoelectric actuators. Using this approach, we demonstrate the application of large elastic strains to mechanically delicate samples: the van der Waals-bonded material FeSe and a sample of CeAuSb₂ that was shaped with a focused ion beam.

Fluctuations and pairing in Fe-based superconductors: light scattering experiments

Inelastic scattering of visible light (Raman effect) offers a window into properties of correlated metals such as spin, electron and lattice dynamics as well as their mutual interactions. In this review we focus on electronic and spin excitations in Fe-based pnictides and chalcogenides, in particular but not exclusively superconductors. After a general introduction to the basic theory including the selection rules for the various scattering processes we provide an overview over the major experimental results. In the superconducting state below the transition temperatureTcthe pair-breaking effect can be observed, and the gap energies may be derived and associated with the gaps on the electron and hole bands. In spite of the similarities of the overall band structures the results are strongly dependent on the family and may even change qualitatively within one family. In some of the compounds strong collective modes appear belowTc. In Ba1-xKxFe2As2, which has the most isotropic gap of all Fe-based superconductors, there are indications that these modes are exciton-like states appearing in the presence of a hierarchy of pairing tendencies. The strong in-gap modes observed in Co-doped NaFeAs are interpreted in terms of quadrupolar orbital excitations which become undamped in the superconducting state. The doping dependence of the scattering intensity in Ba(Fe1-xCox)2As2is associated with a nematic resonance above a quantum critical point and interpreted in terms of a critical enhancement at the maximalTc. In the normal state the response from particle-hole excitations reflects the resistivity. In addition, there are strongly temperature-dependent contributions from presumably critical fluctuations in the energy range ofkBTwhich can be compared to the elastic properties. Currently it is not settled whether the fluctuations observed by light scattering are related to spin or charge. Another controversy relates to putative two-magnon excitations, typically in the energy range below 0.5 eV. Whereas this response presumably originates from charge excitations in most of the Fe-based compounds theory and experiment suggest that the excitations in the 60 meV range in FeSe stem from localized spins in a nearly frustrated system.

Electronic Nematicity in URu_{2}Si_{2} Revisited

The nature of the hidden-order (HO) state in URu_{2}Si_{2} remains one of the major unsolved issues in heavy-fermion physics. Recently, torque magnetometry, x-ray diffraction, and elastoresistivity data have suggested that the HO phase transition at T_{HO}≈ 17.5  K is driven by electronic nematic effects. Here, we search for thermodynamic signatures of this purported structural instability using anisotropic thermal expansion, Young's modulus, elastoresistivity, and specific-heat measurements. In contrast to the published results, we find no evidence of a rotational symmetry breaking in any of our data. Interestingly, our elastoresistivity measurements, which are in full agreement with published results, exhibit a Curie-Weiss divergence, which we however attribute to a volume and not to a symmetry-breaking effect. Finally, clear evidence for thermal fluctuations is observed in our heat-capacity data, from which we estimate the HO correlation length.