Enhancement of superconductivity near a nematic 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.

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.

Atomic-Scale Andreev Probe of Unconventional Superconductivity

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

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.

Synergetic Ferroelectricity and Superconductivity in Zero-Density Dirac Semimetals near Quantum Criticality

We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., Pb_{x}Sn_{1-x}Te, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

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.

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4

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

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.

Quasiparticle Scattering in a Superconductor near a Nematic Critical Point: Resonance Mode and Multiple Attractive Channels

We analyze the scattering rate for 2D fermions interacting via soft nematic fluctuations. The ground state is an s-wave superconductor, but other pairing channels are almost equally attractive. This strongly alters the scattering rate: At energies beyond the pairing gap Δ, it is renormalized by contributions from all pairing channels. At energies of order Δ, it is determined by the competition between scattering into a gapped continuum and dispersing nematic resonance. The outcome is a "peak-peak-dip-hump" spectrum, similar, but not identical, to the "peak-dip-hump" structure in the cuprates.

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

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

The transport-structural correspondence across the nematic phase transition probed by elasto X-ray diffraction

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and X-ray diffraction measurements with in-situ tunable strain (elasto X-ray diffraction) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of Ba(Fe_0.96Co_0.04)₂As₂. The ratio of transport to structural quantities is nearly temperature independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto X-ray diffraction is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of the mean-field description reveals the intertwined nature of nematicity.

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.

Specific Heat of a Quantum Critical Metal

We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

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.

Mössbauer spectroscopy study of nematicity in Ba(Fe0.962Cu0.038)2As2single crystal: enhanced orbital effect

The origin of the nematic order remains unclear due to the strong coupling between orbital, spin and lattice degrees of freedom in iron-based superconductors. Although the driving force of hole-doped BeFe₂As₂is still controversial, the nematic fluctuation of electron-doped compounds is generally believed to be spin fluctuation driven. Here, we present a comprehensive study of the nematic phase transition in Ba(Fe_0.962Cu_0.038)₂As₂single crystal by using Mössbauer spectroscopy. The electric field gradient and its in-plane asymmetry on Fe nucleus, which are directly determined by the occupation of individualt_2gorbital, are sensitive to the local nematicity of Fe ions. The nematic phase transition happens atT_nem≈ 73.8 K in the compound while the band splitting betweend_xz/d_yzorbitals begins far aboveT_nemand reaches 18.8 meV at 30 K. The temperature evolution of the hyperfine parameters proves the existence of electron-phonon interaction and non-Fermi-liquid behaviour nearT_nem. However, the spin-lattice relaxation signal is only evident belowT_nem. These observations show that the role of orbital degrees of freedom is more active in driving nematicity than in Co- or Ni-doped BaFe₂As₂compounds, and can be attributed to enhanced electronic localization caused by Cu doping.

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.

High-pressure phase diagrams of FeSe1-xTex: correlation between suppressed nematicity and enhanced superconductivity

The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe_1−xS_x superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe_1−xTe_x. When Te composition x(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to x(Te) ≈ 0.5. In contrast to FeSe_1−xS_x, enhanced superconductivity in FeSe_1−xTe_x does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.

Despite studies in FeSe_1−xS_x, it is yet unconfirmed whether nematic fluctuation can induce superconductivity. Here, the authors study single crystals of FeSe_1−xTe_x showing enhanced superconductivity upon suppression of nematicity.

Raman Study of Cooper Pairing Instabilities in (Li_{1-x}Fe_{x})OHFeSe

We studied the electronic Raman spectra of (Li_{1-x}Fe_{x})OHFeSe as a function of light polarization and temperature. In the B_{1g} spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T_{c}. The nearly resolution-limited peak at 110  cm^{-1} (13.6 meV) is identified as a collective mode. The peak at 190  cm^{-1} (23.6 meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band structure of (Li_{1-x}Fe_{x})OHFeSe, the most plausible explanations include conventional spin-fluctuation pairing between the electron bands and the incipient hole band and pairing between the hybridized electron bands. The absence of gap features in A_{1g} and B_{2g} symmetry favors the second case. Thus, in spite of various differences between the pnictides and chalcogenides, this Letter demonstrates the proximity of pairing states and the importance of band structure effects in the Fe-based compounds.

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.

Electronic nematicity in Sr2RuO4

We have measured the angle-resolved transverse resistivity (ARTR), a sensitive indicator of electronic anisotropy, in high-quality thin films of the unconventional superconductor Sr₂RuO₄ grown on various substrates. The ARTR signal, heralding the electronic nematicity or a large nematic susceptibility, is present and substantial already at room temperature and grows by an order of magnitude upon cooling down to 4 K. In Sr₂RuO₄ films deposited on tetragonal substrates the highest-conductivity direction does not coincide with any crystallographic axis. In films deposited on orthorhombic substrates it tends to align with the shorter axis; however, the magnitude of the anisotropy stays the same despite the large lattice distortion. These are strong indications of actual or incipient electronic nematicity in Sr₂RuO₄.

Solvable Strong-Coupling Quantum-Dot Model with a Non-Fermi-Liquid Pairing Transition

We show that a random interacting model exhibits solvable non-Fermi-liquid behavior and exotic pairing behavior. This model, dubbed as the Yukawa-SYK model, describes the random Yukawa coupling between M quantum dots each hosting N flavors of fermions and N^{2} bosons that self-tune to criticality at low energies. The diagrammatic expansion is controlled by 1/MN, and the results become exact in a large-M, large-N limit. We find that pairing only develops within a region of the (M,N) plane-even though the pairing interaction is strongly attractive, the incoherence of the fermions can spoil the forming of Cooper pairs, rendering the system a non-Fermi liquid down to zero temperature. By solving the Eliashberg equation and the renormalization group equation, we show that the transition into the pairing phase exhibits Kosterlitz-Thouless quantum-critical behavior.

Sixfold enhancement of superconductivity in a tunable electronic nematic system

The electronic nematic phase-in which electronic degrees of freedom lower the crystal rotational symmetry-is commonly observed in high-temperature superconductors. However, understanding the role of nematicity and nematic fluctuations in Cooper pairing is often made more complicated by the coexistence of other orders, particularly long-range magnetic order. Here we report the enhancement of superconductivity in a model electronic nematic system that is not magnetic, and show that the enhancement is directly born out of strong nematic fluctuations associated with a quantum phase transition. We present measurements of the resistance as a function of strain in Ba_1-x Sr _x Ni₂As₂ to show that strontium substitution promotes an electronically driven nematic order in this system. In addition, the complete suppression of that order to absolute zero temperature leads to an enhancement of the pairing strength, as evidenced by a sixfold increase in the superconducting transition temperature. The direct relation between enhanced pairing and nematic fluctuations in this model system, as well as the interplay with a unidirectional charge-density-wave order comparable to that found in the cuprates, offers a means to investigate the role of nematicity in strengthening superconductivity.

Possible quantum critical behavior revealed by the critical current density of hole doped high-Tc cuprates in comparison to heavy fermion superconductors

The superconducting critical current density, Jc, in hole doped cuprates show strong dependence on the doped hole content, p, within the copper oxide plane(s). The doping dependent Jc mainly exhibits the variation of the intrinsic depairing critical current density as p is varied. Jc(p) tends to peak at p ~ 0.185 in copper oxide superconductors. This particular value of the hole content, often termed as the critical hole concentration, has several features putative to a quantum critical point (QCP). Very recently, the pressure dependences of the superconducting transition temperature (Tc) and the critical current (Ic) in pure CeRhIn5 and Sn doped CeRhIn5 heavy fermion compounds have been reported (Nature Communications (2018) 9:44, https://doi.org/10.1038/s41467-018-02899-5 ). The critical pressure demarcates an antiferromagnetic quantum critical point where both Tc and Ic are maximized. We have compared and contrasted this behavior with those found for Y1-xCaxBa2Cu3O7-δ in this brief communication. The resemblance of the systematic behavior of the critical current with pressure and hole content between heavy fermion systems and hole doped cuprates is significant. This adds to the circumstantial evidence that quantum critical physics probably plays a notable role behind the unconventional normal and superconducting state properties of copper oxide superconductors.

Ultrafast nematic-orbital excitation in FeSe

The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In iron-pnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have as-yet-unconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time-, energy-, momentum- and orbital-resolved photo-emission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strong-excitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavily-damped oscillation. This short-life nematicity oscillation is seemingly related to the imbalance of Fe 3d_xz and d_yz orbitals. These phenomena show critical behavior as a function of pump fluence. Our real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice.

Several experiments have shown evidence for unusual nematic electronic behaviour in unconventional superconductors. Here the authors use pump-probe spectroscopy to observe out-of-equilibrium behaviour of coupled nematic-orbital excitations in iron selenide.

Divergence of the quadrupole-strain susceptibility of the electronic nematic system YbRu2Ge2

A wide range of strongly correlated quantum materials, including some high-temperature superconductors, exhibit “electronic nematic” phases, in which the electronic properties spontaneously break the rotational symmetry of the crystal. However, the role that the corresponding nematic fluctuations play in these complicated systems is unclear, motivating the search for simpler model systems. Here, we identify a particular 4f intermetallic material which exhibits ferroquadrupole order, YbRu2Ge2, as just such a model system. We also provide a robust and accurate method to probe the divergence of an important associated quantity, the quadrupole-strain susceptibility. The temperature dependence of this quantity provides insight into the nature of the interactions that lead to ferroquadrupole order, in this case, magnetoelastic coupling.

Ferroquadrupole order associated with local 4f atomic orbitals of rare-earth ions is a realization of electronic nematic order. However, there are relatively few examples of intermetallic materials which exhibit continuous ferroquadrupole phase transitions, motivating the search for additional materials that fall into this category. Furthermore, it is not clear a priori whether experimental approaches based on transport measurements which have been successfully used to probe the nematic susceptibility in materials such as the Fe-based superconductors will be as effective in the case of 4f intermetallic materials, for which the important electronic degrees of freedom are local rather than itinerant and are consequently less strongly coupled to the charge-carrying quasiparticles near the Fermi energy. In the present work, we demonstrate that the intermetallic compound YbRu2Ge2 exhibits a tetragonal-to-orthorhombic phase transition consistent with ferroquadrupole order of the Yb ions and go on to show that elastoresistivity measurements can indeed provide a clear window on the diverging nematic susceptibility in this system. This material provides an arena in which to study the causes and consequences of electronic nematicity.

Interplay between nematic fluctuation and superconductivity in a two-orbital Hubbard model: a quantum Monte Carlo study

To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model at intermedium correlation regimes by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ([Formula: see text]). Simultaneously, it was found that the on-site nematic interaction suppresses the [Formula: see text] antiferromagnetic order and long-range electron pairing correlations for dominant pairing channels. Our findings suggest that on-site nematic fluctuation seems to compete with superconductivity in iron-based superconductors.

Electron Mass Enhancement near a Nematic Quantum Critical Point in NaFe_{1-x}Co_{x}As

A magnetic order can be completely suppressed at zero temperature (T), by doping carriers or applying pressure, at a quantum critical point, around which physical properties change drastically. However, the situation is unclear for an electronic nematic order that breaks rotation symmetry. Here, we report nuclear magnetic resonance studies on NaFe_{1-x}Co_{x}As where magnetic and nematic transitions are well separated. The nuclear magnetic resonance spectrum is sensitive to inhomogeneous magnetic fields in the vortex state, which is related to London penetration depth λ_{L} that measures the electron mass m^{*}. We discovered two peaks in the doping dependence of λ_{L}^{2}(T∼0), one at x_{M}=0.027 where the spin-lattice relaxation rate shows quantum critical behavior, and another at x_{c}=0.032 around which the nematic transition temperature extrapolates to zero and the electrical resistivity shows a T-linear variation. Our results indicate that a nematic quantum critical point lies beneath the superconducting dome at x_{c} where m^{*} is enhanced. The impact of the nematic fluctuations on superconductivity is discussed.

Hedgehog Spin-Vortex Crystal Antiferromagnetic Quantum Criticality in CaK(Fe_{1-x}Ni_{x})_{4}As_{4} Revealed by NMR

Two ordering states, antiferromagnetism and nematicity, have been observed in most iron-based superconductors (SCs). In contrast to those SCs, the newly discovered SC CaK(Fe_{1-x}Ni_{x})_{4}As_{4} exhibits an antiferromagnetic (AFM) state, called hedgehog spin-vortex crystal (SVC) structure, without nematic order, providing the opportunity for the investigation into the relationship between spin fluctuations and SC without any effects of nematic fluctuations. Our ^{75}As nuclear magnetic resonance studies on CaK(Fe_{1-x}Ni_{x})_{4}As_{4} (0≤x≤0.049) revealed that CaKFe_{4}As_{4} is located close to a hidden hedgehog SVC AFM quantum-critical point (QCP). The magnetic QCP without nematicity in CaK(Fe_{1-x}Ni_{x})_{4}As_{4} highlights the close connection of spin fluctuations and superconductivity in iron-based SCs. The advantage of stoichiometric composition also makes CaKFe_{4}As_{4} an ideal platform for further detailed investigation of the relationship between magnetic QCP and superconductivity in iron-based SCs without disorder effects.

Collapse of Critical Nematic Fluctuations in FeSe under Pressure

We report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8 GPa where the superconducting transition temperature T_{c} reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6 GPa, indicating they play a marginal role in the fourfold enhancement of T_{c} at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2 GPa, in agreement with lattice dynamical and electronic structure calculations using local density approximation combined with dynamical mean field theory. Our results reveal two different regimes of nematicity in the phase diagram of FeSe under pressure: a d-wave Pomeranchuk instability of the Fermi surface at low pressure and a magnetic driven orthorhombic distortion at higher pressure.

Local orthorhombic lattice distortions in the paramagnetic tetragonal phase of superconducting NaFe1-xNixAs

Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe1-xNixAs, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural transition temperature Ts in underdoped samples and extend well into the overdoped regime that exhibits neither magnetic nor structural phase transitions. These unexpected local orthorhombic distortions display Curie-Weiss temperature dependence and become suppressed below the superconducting transition temperature Tc, suggesting that they result from the large nematic susceptibility near optimal superconductivity. Our results account for observations of rotational symmetry breaking above Ts, and attest to the presence of significant nematic fluctuations near optimal superconductivity.

Imaging Anomalous Nematic Order and Strain in Optimally Doped BaFe_{2}(As,P)_{2}

We present the strain and temperature dependence of an anomalous nematic phase in optimally doped BaFe_{2}(As,P)_{2}. Polarized ultrafast optical measurements reveal broken fourfold rotational symmetry in a temperature range above T_{c} in which bulk probes do not detect a phase transition. Using ultrafast microscopy, we find that the magnitude and sign of this nematicity vary on a 50-100  μm length scale, and the temperature at which it onsets ranges from 40 K near a domain boundary to 60 K deep within a domain. Scanning Laue microdiffraction maps of local strain at room temperature indicate that the nematic order appears most strongly in regions of weak, isotropic strain. These results indicate that nematic order arises in a genuine phase transition rather than by enhancement of local anisotropy by a strong nematic susceptibility. We interpret our results in the context of a proposed surface nematic phase.

Electron-electron interactions and the paired-to-nematic quantum phase transition in the second Landau level

In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron-electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron-electron interactions play a critical role in driving the paired-to-nematic transition.

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

Transverse fields to tune an Ising-nematic quantum phase transition

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

Topological Phase Transitions in Multicomponent Superconductors

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent U(1)×U(1) symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibits small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd_{2}Re_{2}O_{7} and half-Heusler materials is discussed.

Maximizing T c by tuning nematicity and magnetism in FeSe1-x S x superconductors

A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature (T c). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving non-magnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe have considerable overlap, how each order affects superconductivity remains perplexing. Here we construct the three-dimensional electronic phase diagram, temperature (T) against pressure (P) and isovalent S-substitution (x), for FeSe1-x S x . By simultaneously tuning chemical and physical pressures, against which the chalcogen height shows a contrasting variation, we achieve a complete separation of nematic and antiferromagnetic phases. In between, an extended non-magnetic tetragonal phase emerges, where T c shows a striking enhancement. The completed phase diagram uncovers that high-T c superconductivity lies near both ends of the dome-shaped antiferromagnetic phase, whereas T c remains low near the nematic critical point.

Unified Phase Diagram for Iron-Based Superconductors

High-temperature superconductivity is closely adjacent to a long-range antiferromagnet, which is called a parent compound. In cuprates, all parent compounds are alike and carrier doping leads to superconductivity, so a unified phase diagram can be drawn. However, the properties of parent compounds for iron-based superconductors show significant diversity and both carrier and isovalent dopings can cause superconductivity, which casts doubt on the idea that there exists a unified phase diagram for them. Here we show that the ordered moments in a variety of iron pnictides are inversely proportional to the effective Curie constants of their nematic susceptibility. This unexpected scaling behavior suggests that the magnetic ground states of iron pnictides can be achieved by tuning the strength of nematic fluctuations. Therefore, a unified phase diagram can be established where superconductivity emerges from a hypothetical parent compound with a large ordered moment but weak nematic fluctuations, which suggests that iron-based superconductors are strongly correlated electron systems.

Dichotomy between in-plane magnetic susceptibility and resistivity anisotropies in extremely strained BaFe2As2

High-temperature superconductivity in the Fe-based materials emerges when the antiferromagnetism of the parent compounds is suppressed by either doping or pressure. Closely connected to the antiferromagnetic state are entangled orbital, lattice, and nematic degrees of freedom, and one of the major goals in this field has been to determine the hierarchy of these interactions. Here we present the direct measurements and the calculations of the in-plane uniform magnetic susceptibility anisotropy of BaFe₂As₂, which help in determining the above hierarchy. The magnetization measurements are made possible by utilizing a simple method for applying a large symmetry-breaking strain, based on differential thermal expansion. In strong contrast to the large resistivity anisotropy above the antiferromagnetic transition at T _N, the anisotropy of the in-plane magnetic susceptibility develops largely below T _N. Our results imply that lattice and orbital degrees of freedom play a subdominant role in these materials.Interplay between lattice, orbital, magnetic and nematic degrees of freedom is crucial for the superconductivity in Fe-based materials. Here, the authors demonstrate the subdominant roles of pure lattice distortions and/or orbital ordering in BaFe₂As₂ by characterizing the in-plane magnetic susceptibility anisotropy.

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

Nanoscale electrodynamics of strongly correlated quantum materials

Electronic, magnetic, and structural phase inhomogeneities are ubiquitous in strongly correlated quantum materials. The characteristic length scales of the phase inhomogeneities can range from atomic to mesoscopic, depending on their microscopic origins as well as various sample dependent factors. Therefore, progress with the understanding of correlated phenomena critically depends on the experimental techniques suitable to provide appropriate spatial resolution. This requirement is difficult to meet for some of the most informative methods in condensed matter physics, including infrared and optical spectroscopy. Yet, recent developments in near-field optics and imaging enabled a detailed characterization of the electromagnetic response with a spatial resolution down to 10 nm. Thus it is now feasible to exploit at the nanoscale well-established capabilities of optical methods for characterization of electronic processes and lattice dynamics in diverse classes of correlated quantum systems. This review offers a concise description of the state-of-the-art near-field techniques applied to prototypical correlated quantum materials. We also discuss complementary microscopic and spectroscopic methods which reveal important mesoscopic dynamics of quantum materials at different energy scales.

Effect of Nematic Order on the Low-Energy Spin Fluctuations in Detwinned BaFe_{1.935}Ni_{0.065}As_{2}

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

Superconductivity in FeSe Thin Films Driven by the Interplay between Nematic Fluctuations and Spin-Orbit Coupling

The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both s-wave and d-wave symmetries are equally favored, and T_{c} is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry breaking at the film interface lifts this harmful degeneracy and selects the s-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated Li_{1-x}(OH)_{x}FeSe.

Remarkable Stability of Charge Density Wave Order in La_{1.875}Ba_{0.125}CuO_{4}

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾  h. We discuss the implications of these results for some of the competing theories.

Superconductivity near a Quantum-Critical Point: The Special Role of the First Matsubara Frequency

Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting T_{c} is nonzero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ω_{m}=±πT. We obtain the analytic formula for T_{c}, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.

Nematic Quantum Critical Fluctuations in BaFe_{2-x}Ni_{x}As_{2}

We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe_{2-x}Ni_{x}As_{2} by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction, as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions, or more exotically, a higher symmetry may be present around optimal doping.

Nematic quantum critical point without magnetism in FeSe1-xSx superconductors

In most unconventional superconductors, the importance of antiferromagnetic fluctuations is widely acknowledged. In addition, cuprate and iron-pnictide high-temperature superconductors often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. In these materials, however, such nematic correlations are intertwined with antiferromagnetic or charge orders, preventing the identification of the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systematic elastoresistance measurements in FeSe1-xSx superconductors, which, unlike other iron-based families, exhibit an electronic nematic order without accompanying antiferromagnetic order. We find that the nematic transition temperature decreases with sulfur content x; whereas, the nematic fluctuations are strongly enhanced. Near [Formula: see text], the nematic susceptibility diverges toward absolute zero, revealing a nematic quantum critical point. The obtained phase diagram for the nematic and superconducting states highlights FeSe1-xSx as a unique nonmagnetic system suitable for studying the impact of nematicity on superconductivity.