Electronic Nematic Order Research Articles

Superconductivity and nematic order in a new titanium-based kagome metal CsTi3Bi5 without charge density wave order

The cascade of correlated topological quantum states in the newly discovered vanadium-based kagome superconductors, AV3Sb5 (A = K, Rb, and Cs), with a Z2 topological band structure has sparked immense interest. Here, we report the discovery of superconductivity and electronic nematic order in high-quality single-crystals of a new titanium-based kagome metal, CsTi3Bi5, that preserves the translation symmetry, in stark contrast to the charge density wave superconductor AV3Sb5. Transport and magnetic susceptibility measurements show superconductivity with an onset superconducting transition temperature Tc of approximately 4.8 K. Using the scanning tunneling microscopy/spectroscopy and Josephson scanning tunneling spectroscopy, we demonstrate that the single crystals of CsTi3Bi5 exhibit two distinct superconducting gaps. Furthermore, the superconducting gaps break the six-fold crystal rotational symmetry down to two-fold. At low energies, we find that the quasiparticle interference patterns exhibit rotational-symmetry-breaking C2 patterns, revealing a nematic ordered normal state with the same nematic direction as in the superconducting state. Our findings uncover a novel superconducting state in CsTi3Bi5 and provide new insights for the intrinsic electron liquid crystal phases in kagome superconductors.

Machine learning the microscopic form of nematic order in twisted double-bilayer graphene

Modern scanning probe techniques, such as scanning tunneling microscopy, provide access to a large amount of data encoding the underlying physics of quantum matter. In this work, we show how convolutional neural networks can be used to learn effective theoretical models from scanning tunneling microscopy data on correlated moiré superlattices. Moiré systems are particularly well suited for this task as their increased lattice constant provides access to intra-unit-cell physics, while their tunability allows for the collection of high-dimensional data sets from a single sample. Using electronic nematic order in twisted double-bilayer graphene as an example, we show that incorporating correlations between the local density of states at different energies allows convolutional neural networks not only to learn the microscopic nematic order parameter, but also to distinguish it from heterostrain. These results demonstrate that neural networks are a powerful method for investigating the microscopic details of correlated phenomena in moiré systems and beyond.

Electronic nematic order in the normal state of strontium ruthenate

Electronic nematic order in the normal state of strontium ruthenate

Distinct behavior of electronic structure under uniaxial strain in BaFe2As2

We report a study of the electronic structure of BaFe2As2 under uniaxial strains using angle-resolved photoemission spectroscopy and transport measurements. Two electron bands at the MY point, with an energy splitting of 50 meV in the strain-free sample, shift downward and merge into each other under a large uniaxial strain, while three hole bands at the Γ point shift downward together. However, we also observed an enhancement of the resistance anisotropy under uniaxial strains by electrical transport measurements, implying that the applied strains strengthen the electronic nematic order in BaFe2As2. These observations suggest that the splitting of these two electron bands at the MY point is not caused by the nematic order in BaFe2As2.

Simultaneous formation of two-fold rotation symmetry with charge order in the kagome superconductor CsV3Sb5 by optical polarization rotation measurement

We report the observation of two-fold rotation symmetry in charge density wave (CDW) state in the newly discovered Kagome superconductor CsV$_3$Sb$_5$. Below its CDW transition temperature ($T_{CDW}$), the polarization rotation of the reflected laser beam promptly emerges and increases close to about 1 mrad, and the rotation angle shows two-fold rotation symmetry. With femtosecond laser pulse pumping, the rotation angle can be easily suppressed and then recovers in several picoseconds accompanied with coherent oscillations. Significantly, the oscillations in the signal also experience a 180 degree periodic change. Our investigation provides clear optical evidence for the formation of nematic order with two-fold rotation symmetry just below $T_{CDW}$. The results imply a immediate development of nematicity and possible time-reversal symmetry breaking in CDW state of CsV$_3$Sb$_5$.

Absence of precursor incommensurate charge order in electronic nematic Ba0.35Sr0.65Ni2As2

Recent discoveries of charge order and electronic nematic order in the iron-based superconductors and cuprates have pointed towards the possibility of nematic and charge fluctuations playing a role in the enhancement of superconductivity. The Ba1-xSrxNi2As2 system, closely related in structure to the BaFe2As2 system, has recently been shown to exhibit both types of ordering without the presence of any magnetic order. We report single crystal X-ray diffraction, resistance transport measurements, and magnetization of \BaSrLate, providing evidence that the previously reported incommensurate charge order with wavevector $(0,0.28,0)_{tet}$ in the tetragonal state of \BaNi~vanishes by this concentration of Sr substitution together with nematic order. Our measurements suggest that the nematic and incommensurate charge orders are closely tied in the tetragonal state, and show that the $(0,0.33,0)_{tri}$ charge ordering in the triclinic phase of BaNi2As2 evolves to become $(0,0.5,0)_{tri}$ charge ordering at $x$=0.65 before vanishing at $x$=0.71.

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] Tex. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Theoretical Insights into Electronic Nematic Order, Bond-Charge Orders, and Plasmons in Cuprate Superconductors

In this article, we focus on the charge degree of freedom in cuprate superconductors and review theoretical insights into the electronic nematic order, bond-charge orders, and plasmons. The low-energy charge dynamics is controlled by the spin-spin interaction J, which generates various bond-charge ordering tendencies including the electronic nematic order. The nematic order is driven by a d-wave Pomeranchuk instability and is pronounced in the underdoped region as well as around van Hove filling in the hole-doped case; the nematic tendency is weak in the electron-doped region. Nematicity consistent with the d-wave Pomeranchuk instability was reported for hole-doped cuprates in various experiments. Although the t-J and Hubbard models correctly predicted the proximity to the nematic instability in cuprates far before the experimental indications were obtained, full understanding of the charge ordering tendencies in hole-doped cuprates still requires further theoretical studies. In electron-doped cuprates, on the other hand, the d-wave bond-charge excitations around momentum q=(0.5pi,0) explain the resonant x-ray scattering data very well. Plasmon excitations are also present and the agreement between the large-N theory of the t-J model and resonant inelastic x-ray scattering measurements is nearly quantitative in both hole- and electron-doped cuprates. Theoretically the charge dynamics in cuprates is summarized as a dual structure in energy space: the low-energy region scaled by J, where the nematic and various bond-charge orders are relevant, and the high-energy region typically larger than J, where plasmons are predominant.

Magnetic-Field-Induced Spin Nematicity in FeSe1 – x S x and FeSe1 – y Te y Superconductor SystemsSupported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0300300 and 2017YFA0303003), the National Natural Science Foundation of China (Grant Nos. 12061131005, 11834016, and 11888101), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB25000000), and the

The angular-dependent magnetoresistance (AMR) of the ab plane is measured on the single crystals of iron-chalcogenide FeSe1–x S x (x = 0, 0.07, 0.13 and 1) and FeSe1–y Te y (y = 0.06, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature T sn. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe1–x S x and FeSe1–y Te y systems, no matter whether the sample shows an electronic nematic order at T s ≲ T sn, or an antiferromagnetic order at T N < T sn, or neither order. Importantly, we find that the induced spin nematicity shows a very different response to sulfur substitution from the spontaneous electronic nematicity: The spin-nematic T sn is not suppressed but even enhanced by the substitution, whereas the electronic-nematic T s is rapidly suppressed, in the FeSe1–x S x system. Furthermore, we find that the superconductivity is significantly suppressed with the enhancement of the induced spin nematicity in both FeSe1–x S x and FeSe1–y Te y samples.

Decoupling of lattice and orbital degrees of freedom in an iron-pnictide superconductor

The interplay of structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity, defined as the breaking of four-fold symmetry triggered by electronic degrees of freedom, is competing with superconductivity, the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction (XRD), we reveal a new structural orthorhombic phase with an exceptionally high onset temperature ($T_\mathrm{ort} \sim 250$ K), which coexists with superconductivity ($T_\mathrm{c} = 25$ K), in an electron-doped iron-pnictide superconductor far from the underdoped region. Furthermore, our angle-resolved photoemission spectroscopy (ARPES) measurements demonstrate the absence of electronic nematic order as the driving mechanism, in contrast to other underdoped iron pnictides where nematicity is commonly found. Our results establish a new, high temperature phase in the phase diagram of iron-pnictide superconductors and impose strong constraints for the modeling of their superconducting pairing mechanism.

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data (arXiv:2009.11645) to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. We compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

Tendencies of enhanced electronic nematicity in the Hubbard model and a comparison with Raman scattering on high-temperature superconductors

The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbard model to experimental results from Raman spectroscopy in $\text{La}_{2-x}\text{Sr}_{x}\text{CuO}_{4}$, which show a prominent increase in the $B_{1g}$ response around 10% hole doping as the temperature decreases, indicative of a rise in nematic fluctuations at low energy. Our results support a picture of nematic fluctuations with $B_{1g}$ symmetry occurring in underdoped cuprates, which may arise from melted stripes at elevated temperatures.

Multiband effect in elastoresistance of Fe(Se,Te)

We have investigated the elastoresistance of two Tex () compounds that have a close chemical composition but differ significantly in electronic properties. The first compound has a negative temperature coefficient of resistance and does not show any phase transitions other than a superconducting one. The elastoresistance of this compound approximately follows the law which is a special case of the Curie-Weiss law, which is usually observed for Fe(Se,S) with metallic conductivity. The second compound has a metallic type of conductivity and, in addition to the superconducting transition, there is also a phase transition at a temperature of about 30 K. The elastoresistance of the second compound is sign-reversing and can be approximated with the sum of two Curie-Weiss–type terms with opposite signs and different critical temperatures. We attribute this behavior to the competition of contributions to the elastoresistance from different band valleys. These competing contributions may appear since the composition of our compound is close to the critical point at which the low-temperature ground state in the 11 series of iron-based superconductors changes from electronic nematic order to magnetic order.

Nematic spin liquid phase in a frustrated spin-1 system on the square lattice

Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-$1$ model on the square lattice with the nearest-neighbor bilinear ($J_1$) and biquadratic ($K_1$) interactions. We provide strong evidence for a nematic spin liquid phase in a range of $K_1/J_1$ near the SU(3)-symmetric point ($J_1 = K_1$), based on the linear flavor-wave theory and extensive density matrix renormalization group calculation. This phase displays no spin dipolar or quadrupolar order, preserves translational symmetry but spontaneously breaks $C_4$ lattice rotational symmetry, and possesses fluctuations peaked at the wavevector $(\pi, 2\pi/3)$. The spin excitation gap drops rapidly with system size and appears to be gapless, and the nematic order is attributed to the dominant $(\pi, 2\pi/3)$ fluctuations. Our results provide a novel mechanism for electronic nematic order and, more generally, open up a new avenue to explore frustration-induced exotic ground states.

Resistivity near a nematic quantum critical point: Impact of acoustic phonons

We revisit the issue of the resistivity of a two-dimensional electronic system tuned to a nematic quantum critical point (QCP), focusing on the non-trivial impact of the coupling to the acoustic phonons. Due to the unavoidable linear coupling between the electronic nematic order parameter and the lattice strain fields, long-range nematic interactions mediated by the phonons emerge in the problem. By solving the semi-classical Boltzmann equation in the presence of scattering by impurities and nematic fluctuations, we determine the temperature-dependence of the resistivity as the nematic QCP is approached. One of the main effects of the nemato-elastic coupling is to smooth the electronic non-equilibrium distribution function, making it approach the simple cosine angular dependence even when the impurity scattering is not too strong. We find that at temperatures lower than a temperature scale set by the nemato-elastic coupling, the resistivity shows the $T^2$ behavior characteristic of a Fermi liquid. This is in contrast to the $T^{4/3}$ low-temperature behavior expected for a lattice-free nematic quantum critical point. More importantly, we show that the effective resistivity exponent $\alpha_\text{eff}(T)$ in $\rho(T)-\rho_0\sim T^{\alpha_\text{eff}(T)}$ displays a pronounced temperature dependence, implying that a nematic QCP cannot generally be characterized by a simple resistivity exponent. We discuss the implications of our results to the interpretation of experimental data, particularly in the nematic superconductor FeSe$_{1-x}$S$_x$.

Thermoelectric signature of the nematic phase in hole-doped iron-based superconductors

Studies of the copper-based superconductors demonstrate how their phase diagram becomes more complex as experimental probes improve, able to distinguish among subtly different electronic phases. One of those phases, nematicity, has become the matter of great interest also in the iron-based superconductors, where it is detected deep in the tetragonal state. Here we present the evolution of the in-plane Nernst effect anisotropy in the strain detwinned Ca(Fe1-xCox)2As2 single crystals, whose behaviour can be explained within the approach developed to describe the nematic order parameter in liquid crystals [1,2]. Furthermore, the employed method turns out to be universally applicable to data from other superconductors: Ba(Fe1-xCox)2As2 [3] as well as YBa2Cu3Oy [4]. We conclude the observed broken rotational symmetry of the electronic system is a consequence of the emerging thermodynamic electronic nematic order at a temperature much higher than onset of the magnetic and structural transitions.

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 3dxz and dyz 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.

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

Ferroquadrupole order associated with local [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.

Pressure-induced rotational symmetry breaking in URu2Si2

Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu$_2$Si$_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here we present a high-resolution x-ray diffraction study of the URu$_2$Si$_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_c\approx3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{HO}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{OR}\sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.

Symmetric and antisymmetric strain as continuous tuning parameters for electronic nematic order

We report the separate response of the critical temperature of the nematic phase transition ${T}_{\mathrm{S}}$ to symmetric and antisymmetric strains for the prototypical underdoped iron pnictide $\mathrm{Ba}{({\mathrm{Fe}}_{0.975}{\mathrm{Co}}_{0.025})}_{2}{\mathrm{As}}_{2}$. This decomposition is achieved by comparing the response of ${T}_{\mathrm{S}}$ to in-plane uniaxial stress and hydrostatic pressure. In addition to quantifying the two distinct linear responses to symmetric strains, we find a quadratic variation of ${T}_{\mathrm{S}}$ as a response to antisymmetric strains ${\ensuremath{\varepsilon}}_{{\mathrm{B}}_{1\mathrm{g}}}=\frac{1}{2}({\ensuremath{\varepsilon}}_{\mathrm{xx}}\ensuremath{-}{\ensuremath{\varepsilon}}_{\mathrm{yy}})$, exceeding the nonlinear response to symmetric strains by at least two orders of magnitude. These observations establish orthogonal antisymmetric strain as a powerful tuning parameter for nematic order.