Sixfold enhancement of superconductivity in a tunable electronic nematic system

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.

Double Superconducting Dome of Quasi Two-Dimensional TaS2 in Non-Centrosymmetric van der Waals Heterostructure

Two-dimensional van der Waals heterostructures (2D-vdWHs) based on transition metal dichalcogenides (TMDs) provide unparalleled control over electronic properties. However, the interlayer coupling is challenged by the interfacial misalignment and defects, which hinders a comprehensive understanding of the intertwined electronic orders, especially superconductivity and charge density wave (CDW). Here, by using pressure to regulate the interlayer coupling of non-centrosymmetric 6R-TaS2 vdWHs, we observe an unprecedented phase diagram in TMDs. This phase diagram encompasses successive suppression of the original CDW states from alternating H-layer and T-layer configurations, the emergence and disappearance of a new CDW-like state, and a double superconducting dome induced by different interlayer coupling effects. These results not only illuminate the crucial role of interlayer coupling in shaping the complex phase diagram of TMD systems but also pave a new avenue for the creation of a novel family of bulk heterostructures with customized 2D properties.

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.

Precursor region with full phonon softening above the charge-density-wave phase transition in 2H-TaSe2

Research on charge-density-wave (CDW) ordered transition-metal dichalcogenides continues to unravel new states of quantum matter correlated to the intertwined lattice and electronic degrees of freedom. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of the canonical CDW compound 2H-TaSe2 complemented by angle-resolved photoemission spectroscopy and density functional perturbation theory. Our results rule out the formation of a central-peak without full phonon softening for the CDW transition in 2H-TaSe2 and provide evidence for a novel precursor region above the CDW transition temperature TCDW, which is characterized by an overdamped phonon mode and not detectable in our photoemission experiments. Thus, 2H-TaSe2 exhibits structural before electronic static order and emphasizes the important lattice contribution to CDW transitions. Our ab-initio calculations explain the interplay of electron-phonon coupling and Fermi surface topology triggering the CDW phase transition and predict that the CDW soft phonon mode promotes emergent superconductivity near the pressure-driven CDW quantum critical point.

Potential Lifshitz transition at optimal substitution in nematic pnictide Ba1-xSrxNi2As2

BaNi2As2 is a structural analog of the pnictide superconductor BaFe2As2, which, like the iron-based superconductors, hosts a variety of ordered phases including charge density waves (CDWs), electronic nematicity, and superconductivity. Upon isovalent Sr substitution on the Ba site, the charge and nematic orders are suppressed, followed by a sixfold enhancement of the superconducting transition temperature (Tc). To understand the mechanisms responsible for enhancement of Tc, we present high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements of the Ba1-xSrxNi2As2 series, which agree well with our density functional theory (DFT) calculations throughout the substitution range. Analysis of our ARPES-validated DFT results indicates a Lifshitz transition and reasonably nested electron and hole Fermi pockets near optimal substitution where Tc is maximum. These nested pockets host Ni dxz/dyz orbital compositions, which we associate with the enhancement of nematic fluctuations, revealing unexpected connections to the iron-pnictide superconductors. This gives credence to a scenario in which nematic fluctuations drive an enhanced Tc.

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge-Density Wave in ScV6Sn6

The kagome metals display an intriguing variety of electronic and magnetic phases arising from the connectivity of atoms on a kagome lattice. A growing number of these materials with vanadium-kagome nets host charge-density waves (CDWs) at low temperatures, including ScV6Sn6, CsV3Sb5, and V3Sb2. Curiously, only the Sc version of the RV6Sn6 materials with a HfFe6Ge6-type structure hosts a CDW (R = Gd-Lu, Y, Sc). In this study, we investigate the role of rare earth size in CDW formation in the RV6Sn6 compounds. Magnetization measurements on our single crystals of (Sc,Lu)V6Sn6 and (Sc,Y)V6Sn6 establish that the CDW is suppressed by substituting Sc by larger Lu or Y. Single-crystal X-ray diffraction reveals that compressible Sn-Sn bonds accommodate the larger rare earth atoms within loosely packed R-Sn-Sn chains without significantly expanding the lattice. We propose that Sc provides extra room in these chains crucial to CDW formation in ScV6Sn6. Our rattling chain model explains why both physical pressure and substitution by larger rare earth atoms hinder CDW formation despite opposite impacts on lattice size. We emphasize the cooperative effect of pressure and rare earth size by demonstrating that pressure further suppresses the CDW in a Lu-doped ScV6Sn6 crystal. Our model not only addresses why a CDW only forms in the RV6Sn6 materials with tiny Sc but also advances our understanding of why unusual CDWs form in the kagome metals.

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.

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.

Soft-Phonon and Charge-Density-Wave Formation in Nematic BaNi_{2}As_{2}

We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi_{2}As_{2}, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, Q_{I-CDW}. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around Q_{I-CDW}. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position are well captured by our ab initio calculations. These, however, indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.

Emergent charge order in pressurized kagome superconductor CsV3Sb5

The discovery of several electronic orders in kagome superconductors AV₃Sb₅ (A means K, Rb, Cs) provides a promising platform for exploring unprecedented emergent physics^1-9. Under moderate pressure (<2.2 GPa), the triple-Q charge density wave (CDW) order is monotonically suppressed by pressure, while the superconductivity shows a two-dome-like behaviour, suggesting an unusual interplay between superconductivity and CDW order^10,11. Given that time-reversal symmetry breaking and electronic nematicity have been revealed inside the triple-Q CDW phase^8,9,12,13, understanding this CDW order and its interplay with superconductivity becomes one of the core questions in AV₃Sb₅ (refs. ^3,5,6). Here, we report the evolution of CDW and superconductivity with pressure in CsV₃Sb₅ by ⁵¹V nuclear magnetic resonance measurements. An emergent CDW phase, ascribed to a possible stripe-like CDW order with a unidirectional 4a₀ modulation, is observed between P_c1 ≅ 0.58 GPa and P_c2 ≅ 2.0 GPa, which explains the two-dome-like superconducting behaviour under pressure. Furthermore, the nuclear spin-lattice relaxation measurement reveals evidence for pressure-independent charge fluctuations above the CDW transition temperature and unconventional superconducting pairing above P_c2. Our results not only shed new light on the interplay of superconductivity and CDW, but also reveal new electronic correlation effects in kagome superconductors AV₃Sb₅.

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.

An electronic nematic liquid in BaNi2As2

Understanding the organizing principles of interacting electrons and the emergence of novel electronic phases is a central endeavor of condensed matter physics. Electronic nematicity, in which the discrete rotational symmetry in the electron fluid is broken while the translational one remains unaffected, is a prominent example of such a phase. It has proven ubiquitous in correlated electron systems, and is of prime importance to understand Fe-based superconductors. Here, we find that fluctuations of such broken symmetry are exceptionally strong over an extended temperature range above phase transitions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{\rm{Ba}}}}}}{{{{{{\rm{Ni}}}}}}}_{2}{({{{{{{\rm{As}}}}}}}_{1-x}{{{{{{\rm{P}}}}}}}_{x})}_{2}$$\end{document}BaNi2(As1−xPx)2, the nickel homologue to the Fe-based systems. This lends support to a type of electronic nematicity, dynamical in nature, which exhibits a particularly strong coupling to the underlying crystal lattice. Fluctuations between degenerate nematic configurations cause splitting of phonon lines, without lifting degeneracies nor breaking symmetries, akin to spin liquids in magnetic systems.

Electronic nematicity is typically associated with the breaking of rotational symmetry. Here the authors report unusual nematicity in BaNi2As2, manifested in a large splitting of the optical phonon mode above the structural transition temperature, and link it to the coupling between the lattice and nematic fluctuations.

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.

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.

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.

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.