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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multicomponent superconducting order parameter in UTe 2

An unconventional superconducting state was recently discovered in uranium ditelluride (UTe 2 ), in which spin-triplet superconductivity emerges from the paramagnetic normal state of a heavy-fermion material. The coexistence of magnetic fluctuations and superconductivity, together with the crystal structure of this material, suggests that a distinctive set of symmetries, magnetic properties, and topology underlie the superconducting state. Here, we report observations of a nonzero polar Kerr effect and of two transitions in the specific heat upon entering the superconducting state, which together suggest that the superconductivity in UTe 2 is characterized by a two-component order parameter that breaks time-reversal symmetry. These data place constraints on the symmetries of the order parameter and inform the discussion on the presence of topological superconductivity in UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Coupled order parameters and photoinduced domain walls in the charge density wave of (TaSe 4 ) 2 I

The charge density wave in (TaSe 4 ) 2 I has drawn much attention recently as a controversial candidate for an axion insulator where the CDW breaks the chiral symmetry of the Weyl semimetal. Here we use ultrafast x-ray scattering to study the collective modes of this CDW. By measuring several diffraction peaks we find that the order parameter involves coupled optical and acoustic modes. For strong near-infrared excitation, the dynamics of the x-ray diffraction show evidence of photoinduced inversion of both components of the CDW order parameter, and associated domain walls. These results demonstrate the potential of ultrafast methods to induce topological defects through highly nonequilibrium dynamics. In (TaSe 4 ) 2 I these defects should lead to exotic electronic states due to the nontrivial topology of the band structure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Possible unconventional order parameter in single crystals of SrPt 3 P superconductor

Here, anisotropic properties of single crystals of SrPt 3 P were studied using London penetration depth and electrical resistivity measurements. The upper critical field, $H_{c2}(T)$, was determined from four-probe electrical resistivity measurements for three orthogonal directions of a magnetic field with respect to the crystal. The London penetration depth, $λ(T)$, was determined from the magnetic susceptibility of the Meissner–London state measured using a tunnel-diode resonator technique. Whereas $H_{c2}(T)$ and the normal-state $ρ(T)$ are practically identical for all three magnetic field orientations, the London penetration depth shows significant unidirectional anisotropy. The low-temperature $λ(T)$ is exponentially attenuated when a small excitation radiofrequency magnetic field, $H_{rf}$, is applied along the c"-direction, in which case screening currents flow in the a"b"-plane, while for the other two orientations, $H_{rf}$∥ a" and $H_{rf}$ ∥ b", the London penetration depth shows a much stronger, $λ(T)$ ~ T 2 , variation. Such unusual and contrasting behavior of the two anisotropies, $γ_{H}$(T) = $H_{c2}$/$H_{c2,c}$ = $ξ_{ab}$/$ξ_{c}$ and $γ_{λ}$(T) = $λ_{c}$\$λ_{ab'}$, imposes significant constraints on the possible order parameter. Although our measurements are insufficient to derive conclusively the superconducting gap anisotropy, the order parameter with two point nodes and a modulation in the perpendicular direction is qualitatively consistent with the experimental observations.

anisotropic superconducting gap↗
DOE OSTI2021

On the Order Parameter of the Continuous Phase Transition in the Classical and Quantum Mechanical Limits

The mean field theory is revisited in the classical and quantum mechanical limits. Taking into account the boundary conditions at the phase transition and the third law of the thermodynamics the physical properties of the ordered and disordered phases were reported. The equation for the order parameter predicts the occurrence of a saturation of Ψ 2 = 1 near Θ S , the temperature below the quantum mechanical ground state is reached. The theoretical predictions are also compared with high resolution thermal expansion data of SrTiO 3 monocrystalline samples and other some previous results. An excellent agreement has been found suggesting a universal behavior of the theoretical model to describe continuous structural phase transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Short-range order parameter expansions for simple configurational energetics

Local chemical environments of multicomponent crystals are parametrized according to basis vectors of their irreducible invariant subspaces. These short-range order parameters enable Taylor expansions of configurational properties that easily incorporate additional couplings. As one example, expansions including long-range composition can describe the energies of many alloys more accurately than conventional cluster expansions while using far fewer neighbors and basis functions.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).

Izmailov, Alexander F.↗
NASA NTRS1993

Theory of Metastable State Relaxation for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.

Izmailov, Alexander↗
DOE OSTI2023

Order Parameter Engineering for Random Systems

The chemical short-range order (CSRO) in crystalline materials influences the properties, and its effect is significant in the context of multicomponent materials. Here, we propose a scheme for the CSRO parameter or Δ-parameter in terms of the number of like and unlike bonds in the multicomponent systems. The OPERA or Order Parameter Engineering for RAndom Systems scheme for semi-canonical and canonical ensembles is proposed. The proposed framework of Δ-parameter with OPERA framework can generate the single-phase supercell with desired CSRO without explicit energy calculations and provides a computationally efficient scheme for exploration of the CSRO. We demonstrate the applicability of the Δ-parameter as a scalar quantity for describing the CSRO in multicomponent alloys and oxides (FCC-CoCrNi, BCC-MoNbTaW, and (CoCuMgNiZn)O).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Dynamic scaling of order parameter fluctuations in model B

Brookhaven National Laboratory has performed a dedicated set of experiments, called the Beam Energy Scan (BES), with the goal of location a possible critical point in the phase diagram of nuclear matter, This point is analogous to the endpoint of the liquid-gas phase transition in water, where the liquid phase corresponds to a phase of hadrons, and the gas phase to a plasma of quarks and gluons. In order to describe the data generated by these experiments we have studied numerical simulations of the stochastic diffusion equation with a conserved charge. Here, we focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z ≃ 3.972(2), which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Mapping the nonequilibrium order parameter of a quasi-two dimensional charge density wave system

The driving force of a charge density wave (CDW) transition in quasi-two dimensional systems is still debated, while being crucial in understanding electronic correlation in such materials. Here we use femtosecond time- and angle-resolved photoemission spectroscopy combined with computational methods to investigate the coherent lattice dynamics of a prototypical CDW system. The photo-induced temporal evolution of the periodic lattice distortion associated with the amplitude mode reveals the dynamics of the free energy functional governing the order parameter. Our approach establishes that optically-induced screening rather than CDW melting at the electronic level leads to a transiently modified potential which explains the anharmonic behaviour of the amplitude mode and discloses the structural origin of the symmetry-breaking phase transition.

electronic properties and materials↗
DOE OSTI2021

Quantitative and interpretable order parameters for phase transitions from persistent homology

Here, we apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define “persistence” critical exponents and study how they are related to those critical exponents usually considered.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effects of the Order Parameter Anisotropy on the Vortex Lattice in UPt3

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt 3 for the applied magnetic field along the crystalline c -axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal plane that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt ±15° vortex lattice rotation was previously reported by Huxley et al. , Nature 406 , 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al. , Nature Physics 16 , 531-535 (2020), can be attributed directly to the symmetry breaking field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Using resonant energy X-ray diffraction to extract chemical order parameters in ternary semiconductors

II–IV–V 2 materials, ternary analogs to III–V materials, are emerging for their potential applications in devices such as LEDs and solar cells. Controlling cation ordering in II–IV–V 2 materials offers the potential to tune properties at nearly fixed compositions and lattice parameters. While tuning properties at a fixed lattice constant through ordering has the potential to be a powerful tool used in device fabrication, cation ordering also creates challenges with characterization and quantification of ordering. In this work, we investigate two different methods to quantify cation ordering in ZnGeP 2 thin films: a stretching parameter calculated from lattice constants , and an order parameter determined from the cation site occupancies ( S ). We use high resolution X-ray diffraction (HRXRD) to determine and resonant energy X-ray diffraction (REXD) to extract S . REXD is critical to distinguish between elements with similar Z -number ( e.g. Zn and Ge). We found that samples with a corresponding to the ordered chalcopyrite structure had only partially ordered S values. The optical absorption onset for these films occurred at lower energy than expected for fully ordered ZnGeP 2 , indicating that S is a more accurate descriptor of cation order than the stretching parameter. Since disorder is complex and can occur on many length scales, metrics for quantifying disorder should be chosen that most accurately reflect the physical properties of interest.

36 MATERIALS SCIENCE↗