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.

Iron pnictides and chalcogenides: a new paradigm for superconductivity.

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Role of Equilibrium Fluctuations in Light-Induced Order.

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

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.

Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor.

Spatial disorder has been shown to drive two-dimensional (2D) superconductors to an insulating phase through a superconductor-insulator transition (SIT). Numerical calculations predict that with increasing disorder, emergent electronic granularity is expected in these materials-a phenomenon where superconducting (SC) domains on the scale of the material's coherence length are embedded in an insulating matrix and coherently coupled by Josephson tunneling. Here, we present spatially resolved scanning tunneling spectroscopy (STS) measurements of the three-dimensional (3D) superconductor BaPb1-x Bi x O3 (BPBO), which surprisingly demonstrate three key signatures of emergent electronic granularity, having only been previously conjectured and observed in 2D thin-film systems. These signatures include the observation of emergent SC domains on the scale of the coherence length, finite energy gap over all space, and strong enhancement of spatial anticorrelation between pairing amplitude and gap magnitude as the SIT is approached. These observations are suggestive of 2D SC behavior embedded within a conventional 3D s-wave host, an intriguing but still unexplained interdimensional phenomenon, which has been hinted at by previous experiments in which critical scaling exponents in the vicinity of a putative 3D quantum phase transition are consistent only with dimensionality d = 2.

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.

Expanding the momentum field of view in angle-resolved photoemission systems with hemispherical analyzers.

In photoelectron spectroscopy, the measured electron momentum range is intrinsically related to the excitation photon energy. Low photon energies <10 eV are commonly encountered in laser-based photoemission and lead to a momentum range that is smaller than the Brillouin zones of most materials. This can become a limiting factor when studying condensed matter with laser-based photoemission. An additional restriction is introduced by widely used hemispherical analyzers that record only electrons photoemitted in a solid angle set by the aperture size at the analyzer entrance. Here, we present an upgrade to increase the effective solid angle that is measured with a hemispherical analyzer. We achieve this by accelerating the photoelectrons toward the analyzer with an electric field that is generated by a bias voltage on the sample. Our experimental geometry is comparable to a parallel plate capacitor, and therefore, we approximate the electric field to be uniform along the photoelectron trajectory. With this assumption, we developed an analytic, parameter-free model that relates the measured angles to the electron momenta in the solid and verify its validity by comparing with experimental results on the charge density wave material TbTe3. By providing a larger field of view in momentum space, our approach using a bias potential considerably expands the flexibility of laser-based photoemission setups.

High resolution time- and angle-resolved photoemission spectroscopy with 11 eV laser pulses.

Performing time- and angle-resolved photoemission (tr-ARPES) spectroscopy at high momenta necessitates extreme ultraviolet laser pulses, which are typically produced via high harmonic generation (HHG). Despite recent advances, HHG-based setups still require large pulse energies (from hundreds of µJ to mJ) and their energy resolution is limited to tens of meV. Here, we present a novel 11 eV tr-ARPES setup that generates a flux of 5 × 1010 photons/s and achieves an unprecedented energy resolution of 16 meV. It can be operated at high repetition rates (up to 250 kHz) while using input pulse energies down to 3 µJ. We demonstrate these unique capabilities by simultaneously capturing the energy and momentum resolved dynamics in two well-separated momentum space regions of a charge density wave material ErTe3. This novel setup offers the opportunity to study the non-equilibrium band structure of solids with exceptional energy and time resolutions at high repetition rates.

Dynamical Slowing-Down in an Ultrafast Photoinduced Phase Transition.

Complex systems, which consist of a large number of interacting constituents, often exhibit universal behavior near a phase transition. A slowdown of certain dynamical observables is one such recurring feature found in a vast array of contexts. This phenomenon, known as critical slowing-down, is well studied mostly in thermodynamic phase transitions. However, it is less understood in highly nonequilibrium settings, where the time it takes to traverse the phase boundary becomes comparable to the timescale of dynamical fluctuations. Using transient optical spectroscopy and femtosecond electron diffraction, we studied a photoinduced transition of a model charge-density-wave (CDW) compound LaTe_{3}. We observed that it takes the longest time to suppress the order parameter at the threshold photoexcitation density, where the CDW transiently vanishes. This finding can be captured by generalizing the time-dependent Landau theory to a system far from equilibrium. The experimental observation and theoretical understanding of dynamical slowing-down may offer insight into other general principles behind nonequilibrium phase transitions in many-body systems.

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.

Measurement of elastoresistivity at finite frequency by amplitude demodulation.

Elastoresistivity, the relation between resistivity and strain, can elucidate the subtle properties of the electronic structure of a material and is an increasingly important tool for the study of strongly correlated materials. To date, elastoresistivity measurements have predominantly been performed with quasi-static (DC) strain. In this work, we demonstrate a method using AC strain in elastoresistivity measurements. A sample experiencing AC strain has a time-dependent resistivity, which modulates the voltage produced by an AC current; this effect produces time-dependent variations in resistivity that are directly proportional to the elastoresistivity, and which can be measured more quickly, with less strain on the sample, and with less stringent requirements for temperature stability than the previous DC technique. Example measurements between 10 Hz and 3 kHz are performed on a material with a large, well-characterized and temperature dependent elastoresistivity: the representative iron-based superconductor Ba(Fe0.975Co0.025)2As2. These measurements yield a frequency independent elastoresistivity and reproduce results from previous DC elastoresistivity methods to within experimental accuracy. We emphasize that the dynamic (AC) elastoresistivity is a distinct material-specific property that has not previously been considered.

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.

Tuning Perpendicular Magnetic Anisotropy by Oxygen Octahedral Rotations in (La_{1-x}Sr_{x}MnO_{3})/(SrIrO_{3}) Superlattices.

Perpendicular magnetic anisotropy (PMA) plays a critical role in the development of spintronics, thereby demanding new strategies to control PMA. Here we demonstrate a conceptually new type of interface induced PMA that is controlled by oxygen octahedral rotation. In superlattices comprised of La_{1-x}Sr_{x}MnO_{3} and SrIrO_{3}, we find that all superlattices (0≤x≤1) exhibit ferromagnetism despite the fact that La_{1-x}Sr_{x}MnO_{3} is antiferromagnetic for x>0.5. PMA as high as 4×10^{6} erg/cm^{3} is observed by increasing x and attributed to a decrease of oxygen octahedral rotation at interfaces. We also demonstrate that oxygen octahedral deformation cannot explain the trend in PMA. These results reveal a new degree of freedom to control PMA, enabling discovery of emergent magnetic textures and topological phenomena.

HfSe2 and ZrSe2: Two-dimensional semiconductors with native high-κ oxides.

The success of silicon as a dominant semiconductor technology has been enabled by its moderate band gap (1.1 eV), permitting low-voltage operation at reduced leakage current, and the existence of SiO2 as a high-quality "native" insulator. In contrast, other mainstream semiconductors lack stable oxides and must rely on deposited insulators, presenting numerous compatibility challenges. We demonstrate that layered two-dimensional (2D) semiconductors HfSe2 and ZrSe2 have band gaps of 0.9 to 1.2 eV (bulk to monolayer) and technologically desirable "high-κ" native dielectrics HfO2 and ZrO2, respectively. We use spectroscopic and computational studies to elucidate their electronic band structure and then fabricate air-stable transistors down to three-layer thickness with careful processing and dielectric encapsulation. Electronic measurements reveal promising performance (on/off ratio > 106; on current, ~30 µA/µm), with native oxides reducing the effects of interfacial traps. These are the first 2D materials to demonstrate technologically relevant properties of silicon, in addition to unique compatibility with high-κ dielectrics, and scaling benefits from their atomically thin nature.

High Current Density and Low Thermal Conductivity of Atomically Thin Semimetallic WTe2.

Two-dimensional (2D) semimetals beyond graphene have been relatively unexplored in the atomically thin limit. Here, we introduce a facile growth mechanism for semimetallic WTe2 crystals and then fabricate few-layer test structures while carefully avoiding degradation from exposure to air. Low-field electrical measurements of 80 nm to 2 µm long devices allow us to separate intrinsic and contact resistance, revealing metallic response in the thinnest encapsulated and stable WTe2 devices studied to date (3-20 layers thick). High-field electrical measurements and electrothermal modeling demonstrate that ultrathin WTe2 can carry remarkably high current density (approaching 50 MA/cm(2), higher than most common interconnect metals) despite a very low thermal conductivity (of the order ∼3 Wm(-1) K(-1)). These results suggest several pathways for air-stable technological viability of this layered semimetal.

Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors.

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations (phonons in the case of conventional s-wave superconductors). Other collective modes that can play the same role, especially spin fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements from five optimally doped iron-based superconductors to show that divergent nematic susceptibility appears to be a generic feature in the optimal doping regime of these materials. This observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds and possibly beyond.

Effect of disorder on the resistivity anisotropy near the electronic nematic phase transition in pure and electron-doped BaFe(2)As(2).

We show that the strain-induced resistivity anisotropy in the tetragonal state of the representative underdoped Fe arsenides BaFe_{2}As_{2}, Ba(Fe_{1-x}Co_{x})_{2}As_{2} and Ba(Fe_{1-x}Ni_{x})_{2}As_{2} is independent of disorder over a wide range of defect and impurity concentrations. This result demonstrates that the anisotropy in the in-plane resistivity in the paramagnetic orthorhombic state of this material is not due to elastic scattering from anisotropic defects. Conversely, our result can be most easily understood if the resistivity anisotropy arises primarily from an intrinsic anisotropy in the electronic structure.

Direct measurement of current-phase relations in superconductor/topological insulator/superconductor junctions.

Proximity to a superconductor is predicted to induce exotic quantum phases in topological insulators. Here, scanning superconducting quantum interference device (SQUID) microscopy reveals that aluminum superconducting rings with topologically insulating Bi2Se3 junctions exhibit a conventional, nearly sinusoidal 2π-periodic current-phase relations. Pearl vortices occur in longer junctions, indicating suppressed superconductivity in aluminum, probably due to a proximity effect. Our observations establish scanning SQUID as a general tool for characterizing proximity effects and for measuring current-phase relations in new materials systems.

Alternative route to charge density wave formation in multiband systems.

Charge and spin density waves, periodic modulations of the electron, and magnetization densities, respectively, are among the most abundant and nontrivial low-temperature ordered phases in condensed matter. The ordering direction is widely believed to result from the Fermi surface topology. However, several recent studies indicate that this common view needs to be supplemented. Here, we show how an enhanced electron-lattice interaction can contribute to or even determine the selection of the ordering vector in the model charge density wave system ErTe(3). Our joint experimental and theoretical study allows us to establish a relation between the selection rules of the electronic light scattering spectra and the enhanced electron-phonon coupling in the vicinity of band degeneracy points. This alternative proposal for charge density wave formation may be of general relevance for driving phase transitions into other broken-symmetry ground states, particularly in multiband systems, such as the iron-based superconductors.

Divergent nematic susceptibility in an iron arsenide superconductor.

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe(1-x)Co(x))(2)As(2) distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.