Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2

Quantum-well states at the surface of a heavy-fermion superconductor

Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1-4). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands2,5-10. Their energy-level separation is typically hundreds of meV (refs. 3,6,11). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states12,13. Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu2Si2, which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.

Elucidating the role of precursors in synthesizing single crystalline lithium niobate nanomaterials: a study of effects of lithium precursors on nanoparticle quality

A number of solution-based procedures have been realized for the synthesis of lithium niobate (LiNbO3) nanoparticles (NPs). Relatively little is, however, known about the influences of the selection of lithium (Li) precursors on the resulting dimensions, shapes, crystallinity, and purity of the products. A comparative study is provided herein on the role of different Li precursors during the synthesis of LiNbO3 NPs. To the best of our knowledge, this study provides the first systematic comparison of the effects of various Li reagents on the preparation of LiNbO3 NPs through solvothermal processes. This solution-phase approach was tuned by the inclusion of Li precursors that either lacked carbon based anions (e.g., F-, Cl-, Br-, I-, OH-, NO3-, or SO42-) or contained carbon-based anions (e.g., C2H5O-, C2H3OO-, C5H7OO-, or CO32-). All other variables were held constant during the synthesis, such as reaction temperature, solvent, niobium precursor, and surfactants. The results of these studies suggest that the type of Li precursor selected plays an important role in nanoparticle formation, such as through controlling the uniformity, crystallinity, and aggregation of LiNbO3 NPs. The average diameter of the resulting NPs can also vary from ∼30 to ∼830 nm as a function of the Li reagent used in the synthesis. The selection of Li precursors also influences the phase purity of the products. This comparative study on the preparation of crystalline LiNbO3 NPs represents a critical step forward to understand the influences and roles of precursors in the design of synthetic processes for the preparation of a variety of alkali metal niobates (e.g., including NaNbO3 and KNbO3) and crystalline metal oxide-based NPs containing other transition metals (e.g., titanium, tantalum).

Electronic Nematicity in URu_{2}Si_{2} Revisited

The nature of the hidden-order (HO) state in URu_{2}Si_{2} remains one of the major unsolved issues in heavy-fermion physics. Recently, torque magnetometry, x-ray diffraction, and elastoresistivity data have suggested that the HO phase transition at T_{HO}≈ 17.5  K is driven by electronic nematic effects. Here, we search for thermodynamic signatures of this purported structural instability using anisotropic thermal expansion, Young's modulus, elastoresistivity, and specific-heat measurements. In contrast to the published results, we find no evidence of a rotational symmetry breaking in any of our data. Interestingly, our elastoresistivity measurements, which are in full agreement with published results, exhibit a Curie-Weiss divergence, which we however attribute to a volume and not to a symmetry-breaking effect. Finally, clear evidence for thermal fluctuations is observed in our heat-capacity data, from which we estimate the HO correlation length.

Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu2Si2

This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu₂Si₂ when tuned with pressure, magnetic field, and substitutions for all three elements. Such 'perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. Here we attempt to update the present situation of URu₂Si₂ importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we review the pressure dependence of URu₂Si₂ and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other 5f elements for U, and 3d, 4d, and 5d elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.

One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning

The unusual correlated state that emerges in URu2Si2 below T HO = 17.5 K is known as "hidden order" because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are "hidden." We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T HO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

Charge-Stripe Order and Superconductivity in Ir1-xPtxTe2

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir_1−xPt_xTe₂, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition x_c ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir_0.95Pt_0.05Te₂ is preempted — and hence triggered — by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Direct bulk-sensitive probe of 5f symmetry in URu2Si2

The second-order phase transition into a hidden order phase in URu₂Si₂ goes along with an order parameter that is still a mystery, despite 30 years of research. However, it is understood that the symmetry of the order parameter must be related to the symmetry of the low-lying local electronic [Formula: see text]-states. Here, we present results of a spectroscopic technique, namely core-level nonresonant inelastic X-ray scattering (NIXS). This method allows for the measurement of local high-multipole excitations and is bulk-sensitive. The observed anisotropy of the scattering function unambiguously shows that the 5[Formula: see text] ground-state wave function is composed mainly of the [Formula: see text] with majority [Formula: see text] = [Formula: see text] + [Formula: see text] and/or [Formula: see text] singlet states. The incomplete dichroism indicates the possibility that quantum states of other irreducible representation are mixed into the ground state.

Field-induced spin-density wave beyond hidden order in URu2Si2

URu₂Si₂ is one of the most enigmatic strongly correlated electron systems and offers a fertile testing ground for new concepts in condensed matter science. In spite of >30 years of intense research, no consensus on the order parameter of its low-temperature hidden-order phase exists. A strong magnetic field transforms the hidden order into magnetically ordered phases, whose order parameter has also been defying experimental observation. Here, thanks to neutron diffraction under pulsed magnetic fields up to 40 T, we identify the field-induced phases of URu₂Si₂ as a spin-density-wave state. The transition to the spin-density wave represents a unique touchstone for understanding the hidden-order phase. An intimate relationship between this magnetic structure, the magnetic fluctuations and the Fermi surface is emphasized, calling for dedicated band-structure calculations.

The strongly-correlated electron system URu₂Si₂ possesses a hidden-order phase whose order parameter remains unidentified. Here, the authors demonstrate the development of spin-density-wave phases in URu₂Si₂ under high magnetic fields, providing a potential in-road to understanding this system.

Thermodynamic Measurement of Angular Anisotropy at the Hidden Order Transition of URu_{2}Si_{2}

The heavy fermion compound URu_{2}Si_{2} continues to attract great interest due to the unidentified hidden order it develops below 17.5 K. The unique Ising character of the spin fluctuations and low-temperature quasiparticles is well established. We present detailed measurements of the angular anisotropy of the nonlinear magnetization that reveal a cos^{4}θ Ising anisotropy both at and above the ordering transition. With Landau theory, we show this implies a strongly Ising character of the itinerant hidden order parameter.

Unfolding the physics of URu2Si2 through silicon to phosphorus substitution

The heavy fermion intermetallic compound URu₂Si₂ exhibits a hidden-order phase below the temperature of 17.5 K, which supports both anomalous metallic behavior and unconventional superconductivity. While these individual phenomena have been investigated in detail, it remains unclear how they are related to each other and to what extent uranium f-electron valence fluctuations influence each one. Here we use ligand site substituted URu₂Si_2-xP_x to establish their evolution under electronic tuning. We find that while hidden order is monotonically suppressed and destroyed for x≤0.035, the superconducting strength evolves non-monotonically with a maximum near x≈0.01 and that superconductivity is destroyed near x≈0.028. This behavior reveals that hidden order depends strongly on tuning outside of the U f-electron shells. It also suggests that while hidden order provides an environment for superconductivity and anomalous metallic behavior, it's fluctuations may not be solely responsible for their progression.

The heavy fermion compound URu₂Si₂ displays a hidden order phase and superconductivity at low temperatures. Here, the authors perform substitution studies—partially replacing silicon with phosphorus—and study the effects on hidden order and superconductivity.

Evidence for a nematic component to the hidden-order parameter in URu2Si2 from differential elastoresistance measurements

For materials that harbour a continuous phase transition, the susceptibility of the material to various fields can be used to understand the nature of the fluctuating order and hence the nature of the ordered state. Here we use anisotropic biaxial strain to probe the nematic susceptibility of URu2Si2, a heavy fermion material for which the nature of the low temperature 'hidden order' state has defied comprehensive understanding for over 30 years. Our measurements reveal that the fluctuating order has a nematic component, confirming reports of twofold anisotropy in the broken symmetry state and strongly constraining theoretical models of the hidden-order phase.

Symmetry of the excitations in the hidden order state of URu2Si2

We perform polarized electronic Raman scattering on URu2Si2 single crystals at low temperature down to 8 K in the hidden-order state and under a magnetic field up to 10 T. The hidden-order state is characterized by a sharp excitation at 1.7 meV and a gap in the electronic continuum below 6.8 meV. Both Raman signatures are of pure A2g symmetry. By comparing the behavior of the Raman sharp excitation and the neutron resonance at Q0=(0,0,1), we provide new evidence, constrained by selection rules of the two probes, that the hidden-order state breaks the translational symmetry along the c axis such that Γ and Z points fold on top of each other. The observation of these distinct Raman features with a peculiar A2g symmetry as a signature of the hidden-order phase places strong constraints on current theories of the hidden-order in URu2Si2.