Nematic Susceptibility Research Articles

Absence of E2g Nematic Instability and Dominant A1g Response in the Kagome Metal CsV3Sb5

Ever since the discovery of the charge density wave (CDW) transition in the kagome metal CsV3Sb5, the nature of its symmetry breaking has been under intense debate. While evidence suggests that the rotational symmetry is already broken at the CDW transition temperature (TCDW), an additional electronic nematic instability well below TCDW has been reported based on the diverging elastoresistivity coefficient in the anisotropic channel (mE2g). Verifying the existence of a nematic transition below TCDW is not only critical for establishing the correct description of the CDW order parameter, but also important for understanding low-temperature superconductivity. Here, we report elastoresistivity measurements of CsV3Sb5 using three different techniques probing both isotropic and anisotropic symmetry channels. Contrary to previous reports, we find the anisotropic elastoresistivity coefficient mE2g is temperature independent, except for a step jump at TCDW. The absence of nematic fluctuations is further substantiated by measurements of the elastocaloric effect, which show no enhancement associated with nematic susceptibility. On the other hand, the symmetric elastoresistivity coefficient mA1g increases below TCDW, reaching a peak value of 90 at T*=20 K. Our results strongly indicate that the phase transition at T* is not nematic in nature and the previously reported diverging elastoresistivity is due to the contamination from the A1g channel. Published by the American Physical Society 2024

Microscopic Model for Fractional Quantum Hall Nematics.

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

The nematic susceptibility of the ferroquadrupolar metal TmAg2 measured via the elastocaloric effect

Elastocaloric measurements of the ferroquadrupolar/nematic rare-earth intermetallic TmAg2 are presented. TmAg2 undergoes a cooperative Jahn-Teller-like ferroquadrupolar phase transition at 5K, in which the Tm3+ ion’s local 4f electronic ground state doublet spontaneously splits and develops an electric quadrupole moment which breaks the rotational symmetry of the tetragonal lattice. The elastocaloric effect, which is the temperature change in the sample induced by adiabatic strains the sample experiences, is sensitive to quadrupolar fluctuations in the paranematic phase which couple to the induced strain. We show that elastocaloric measurements of this material reveal a Curie-Weiss like nematic susceptibility with a Weiss temperature of T* ≈ 2.7K, in agreement with previous elastic constant measurements. Furthermore, we establish that a magnetic field along the c-axis acts as an effective transverse field for the quadrupole moments.

Measurements of nematic susceptibility with phase sensitive nuclear magnetic resonance in pulsed strain fields.

We present nuclear magnetic resonance data in BaFe2As2 in the presence of pulsed strain fields that are interleaved in time with the radio frequency excitation pulses. In this approach, the preceding nuclear magnetization acquires a phase shift that is proportional to the strain and pulse time. The sensitivity of this approach is limited by the homogeneous decoherence time, T2, rather than the inhomogeneous linewidth. We measure the nematic susceptibility as a function of temperature and demonstrate a three orders of magnitude improvement in sensitivity. This approach will enable studies of the strain response in a broad range of materials that previously were inaccessible due to inhomogeneous broadening.

Uniaxial-strain tuning method in study of iron-based superconductors

In the study of quantum materials, introducing pressure and strain that can change lattice parameters and symmetry is an effective experimental method for manipulating the electronic properties of the system. In measurements under hydrostatic pressure or in-plane epitaxial strain, the changes in lattice parameters will lead to significant changes in the electronic structure, thereby triggering off novel quantum phenomena and phase transitions. By comparison, the in-plane uniaxial strain, which has been widely employed in recent years, not only changes lattice parameters, but also directly destroys and controls the symmetry of the system, thereby affecting the electronic ordering state and even collective excitation of the system. This article provides a comprehensive overview of the basic concepts of uniaxial strain, the development of experimental methods, and some research progress in using these methods to regulate superconductivity and electronic nematicity in iron-based superconductors. This review contains six sections. Section 1 focuses on a genetral introduction for the uniaxial strain techque and the arrangement of this paper. Section 2 is devoted to the basic concepts and formulas related to elastic moduli and the decomposition of uniaxial strain into irreducible symmetric channels under <i>D</i><sub>4<i>h</i></sub> point group. Section 3 gives iron-based superconductors (FeSCs) and discusses the uniaxial-pressure detwinning method and related research progress. Section 4 introduces the establishment of the elastoresistance as a probe of the nematic susceptibility and discusses the key researches in this direction. Section 5 describes the research progress of the effects of uniaxial strain on superconductivity and nematicity. In sections 4 and 5, key experimental techniques, such as elastoresistance, are discussed in detail. Section 6 extends the discussion to several types of quantum materials suitable for uniaxial-strain tuning method beyond the FeSCs. Finally, we provide a brief summary and outlook on the uniaxial strain tuning technique. Overall, this review article provides valuable resources for the beginners in the field of FeSC and those who are interested in using uniaxial strain to modulate the electronic properties of quantum materials. By summarizing recent advancements and experimental techniques, this review hopes to inspire further research and innovation in studying electronic materials under uniaxial strain.

Exceptional van Hove singularities in pseudogapped metals

Motivated by the pseudogap state of the cuprates, we introduce the concept of an ``exceptional'' van Hove singularity that appears when a strong electron-electron interaction splits an otherwise simply connected Fermi surface into multiply connected pieces. The singularity describes the touching of two pieces of the split Fermi surface. We show that this singularity is proximate to a second-order van Hove singularity, which can be accessed by tuning a dispersion parameter. We argue that, in a wide class of cuprates, the endpoint of the pseudogap is accessed only by triggering the exceptional van Hove singularity. The resulting Lifshitz transition is characterized by enhanced specific heat and nematic susceptibility, as seen in experiments.

Nematic fluctuations in an orbital selective superconductor Fe1+yTe1−xSex

Fe1+yTe1−xSex is characterized by its complex magnetic phase diagram and highly orbital-dependent band renormalization. Despite this, the behavior of nematicity and nematic fluctuations, especially for high tellurium concentrations, remains largely unknown. Here we present a study of both B1g and B2g nematic fluctuations in Fe1+yTe1−xSex (0 ≤ x ≤ 0.53) using the technique of elastoresistivity measurement. We discovered that the nematic fluctuations in two symmetry channels are closely linked to the corresponding spin fluctuations, confirming the intertwined nature of these two degrees of freedom. We also revealed an unusual temperature dependence of the nematic susceptibility, which we attributed to a loss of coherence of the dxy orbital. Our results highlight the importance of orbital differentiation on the nematic properties of iron-based materials.

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.

Nematicity and Glassy Behavior Probed by Nuclear Magnetic Resonance in Iron-Based Superconductors

Nuclear magnetic resonance provides a wealth of information about the magnetic and nematic degrees of freedom in the iron-based superconductors. A striking observation is that the spin lattice relaxation rate is inhomogeneous with a standard deviation that correlates with the nematic susceptibility. Moreover, the spin lattice relaxation is strongly affected by uniaxial strain, and in doped samples it depends sensitively upon the history of the applied strain. These observations suggest that quenched strain fields associated with doping atoms induce a nematic glass in the iron pnictide materials.

Optical Fingerprints of Nematicity in Iron-Based Superconductors

Nematicity, which refers to a phase of broken rotational but preserved translational symmetry, is underlined by the appearance of anisotropic properties and leaves remarkable fingerprints in all measurable physical quantities upon crossing the structural tetragonal-orthorhombic transition at Ts in several iron-based materials. Here, we review part of our own broadband optical investigations, addressing the impact of nematicity on the charge dynamics, as a function of temperature and of tunable applied stress, the latter acting as an external symmetry breaking field. We shall first focus our attention on FeSe, which undergoes a nematic (structural) transition without any subsequent onset of magnetic ordering below Ts. FeSe thus provides an opportunity to study nematicity without the limitations due to the reconstruction of the Fermi surface because of the spin-density-wave collective state in the orthorhombic phase, typical for several other iron-based superconductors. Our data reveal an astonishing anisotropy of the optical response in the mid-infrared-to-visible spectral range, which bears testimony of an important polarization of the underlying electronic structure in agreement with angle-resolved-photoemission-spectroscopy results. Our findings at high energy scales support models for the nematic phase resting on an orbital-ordering mechanism, supplemented by orbital selective band renormalization. The optical results at energies close to the Fermi level furthermore emphasize scenarios relying on scattering by anisotropic spin-fluctuations and shed new light on the origin of nematicity in FeSe. Moreover, the composition at which the associated Weiss temperature of the nematic susceptibility extrapolates to zero is found to be close to optimal doping (i.e., in coincidence with the largest superconducting transition temperature), boosting the debate to what extent nematic fluctuations contribute to the pairing-mechanism and generally affect the electronic structure of iron-based superconductors. The present review then offers a discussion of our optical data on the optimally hole-doped Ba0.6K0.4Fe2As2. We show that the stress-induced optical anisotropy in the infrared spectral range is reversible upon sweeping the applied stress and occurs only below the superconducting transition temperature. These findings demonstrate that there is a large electronic nematicity at optimal doping which extends right under the superconducting dome.

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(Fe1−xCox)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.

Elasto-Raman scattering: Arsenic optical phonon as a probe of nematicity in BaFe2As2

We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound BaFe$_2$As$_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperature, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibility close to the nematic transition $T_S$. Its temperature dependence under strong strain follows qualitatively the expected behavior of an Ising order parameter under a symmetry breaking field. Our elasto-Raman study illustrates the interest of combining selective anisotropic strain with a symmetry resolved probe like Raman scattering. Elasto-Raman scattering can be applied to a wide variety of quantum materials where uniaxial strain tunes electronic orders.

Edwards-Anderson parameter and local Ising nematicity in FeSe revealed via NMR spectral broadening

The NMR spectrum of FeSe shows a dramatic broadening on cooling towards the bulk nematic phase at $T_s=90$ K, due to the formation of a quasi-static, short-range-ordered nematic domain structure. However, a quantitative understanding of the NMR broadening and its relationship to the nematic susceptibility is still lacking. Here, we show that the temperature and pressure dependence of the broadening is in quantitative agreement with the mean-field Edwards-Anderson parameter of an Ising-nematic model in the presence of random-field disorder introduced by non-magnetic impurities. Furthermore, these results reconcile the interpretation of NMR and Raman spectroscopy data in FeSe under pressure.

Lattice-shifted nematic quantum critical point in FeSe1\u2212xSx

We report the evolution of nematic fluctuations in FeSe1−xSx single crystals as a function of Sulfur content x across the nematic quantum critical point (QCP) xc ~ 0.17 via Raman scattering. The Raman spectra in the B1g nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie–Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling, which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hund’s metals, with both itinerant carriers and local moments contributing to the nematic susceptibility.

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.

Nematic Susceptibility of the Iron-Based Superconductors Probed by Elastoresistance Measurements

Nematic Susceptibility of the Iron-Based Superconductors Probed by Elastoresistance Measurements

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.

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.

Divergent Nematic Susceptibility near the Pseudogap Critical Point in a Cuprate Superconductor

Superconductivity is a quantum phenomenon caused by bound pairs of electrons. In diverse families of strongly correlated electron systems, the electron pairs are not bound together by phonon exchange but instead by some other kind of bosonic fluctuations. In these systems, superconductivity is often found near a magnetic quantum critical point (QCP) where a magnetic phase vanishes in the zero-temperature limit. Moreover, the maximum of superconducting transition temperature Tc frequently locates near the magnetic QCP, suggesting that the proliferation of critical spin fluctuations emanating from the QCP plays an important role in Cooper pairing. In cuprate superconductors, however, the superconducting dome is usually separated from the antiferromagnetic phase and Tc attains its maximum value near the verge of enigmatic pseudogap state that appears below doping-dependent temperature T*. Thus a clue to the pairing mechanism resides in the pseudogap and associated anomalous transport properties. Recent experiments suggested a phase transition at T*, yet, most importantly, relevant fluctuations associated with the pseudogap have not been identified. Here we report on direct observations of enhanced nematic fluctuations in (Bi,Pb)2Sr2CaCu2O8+d by elastoresistance measurements, which couple to twofold in-plane electronic anisotropy, i.e. electronic nematicity. The nematic susceptibility shows Curie-Weiss-like temperature dependence above T*, and an anomaly at T* evidences a second-order transition with broken rotational symmetry. Near the pseudogap end point, where Tc is not far from its peak in the superconducting dome, nematic susceptibility becomes singular and divergent, indicating the presence of a nematic QCP. This signifies quantum critical fluctuations of a nematic order, which has emerging links to the high-Tc superconductivity and strange metallic behaviours in cuprates.

Momentum-resolved measurement of electronic nematic susceptibility in the FeSe0.9S0.1 superconductor

Unveiling the driving force for a phase transition is normally difficult when multiple degrees of freedom are strongly coupled. One example is the nematic phase transition in iron-based superconductors. Its mechanism remains controversial due to a complex intertwining among different degrees of freedom. In this paper, we report a method for measuring the nematic susceptibly of FeSe$_{0.9}$S$_{0.1}$ using angle-resolved photoemission spectroscopy (ARPES) and an $in$-$situ$ strain-tuning device. The nematic susceptibility is characterized as an energy shift of band induced by a tunable uniaxial strain. We found that the temperature-dependence of the nematic susceptibility is strongly momentum dependent. As the temperature approaches the nematic transition temperature from the high temperature side, the nematic susceptibility remains weak at the Brillouin zone center while showing divergent behavior at the Brillouin zone corner. Our results highlight the complexity of the nematic order parameter in the momentum space, which provides crucial clues to the driving mechanism of the nematic phase transition. Our experimental method which can directly probe the electronic susceptibly in the momentum space provides a new way to study the complex phase transitions in various materials.