Density-matrix methods and time dependence of order parameter in superconductors.
Time dependent differential equation for order parameter in superconductors near critical temperature derived from density matrix equations
Di Castro, C.↗
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Surface energy from order parameter profile: At the QCD phase transition
The order parameter profile between coexisting confined and plasma regions at the quantum chromodynamic (QCD) phase transition is constructed. The dimensionless combination of the surface energy (Sigma) and the correlation length (Zeta) is estimated to be Sigma Zeta 3 approximately equals 0.8.
Frei, Z.↗
Anisotropic field-induced changes in the superconducting order parameter of UTe 2
UTe 2 is a newly discovered unconventional superconductor, where electron Cooper pairs combine into a spin-triplet ground state. We study the specific heat C( H,T ) of a high-quality UTe 2 single crystal, with a single anomaly at a high superconducting transition temperature T c = 2.1 K and a low residual Sommerfeld coefficient γ 0 . Applying magnetic fields up to 12 T along the crystallographic axes a, b , and c , we observe highly anisotropic behavior in γ 0 ( H ). Below 4 T, γ 0 ( H ) ≈ γ 0 + λi √H (i = a, b, c) , which is expected for an unconventional superconductor with nodes on the Fermi surface away from the direction of the magnetic field. At 4 T ( a and b axes) and 5.5 T ( c axis), distinctive changes in the behavior of γ 0 (H) suggest that a stable low-field ground state begins to evolve above 4 T. The data analysis indicates that the nodes are located near the a–b plane, with possible order parameters d B2u + iεd B1u or d B2u + iεd Au . Our findings support B 2u as the primary superconducting order parameter in UTe 2 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Mechanical analysis of heterogeneous materials with higher-order parameters
Abstract Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.
42 ENGINEERING↗
Establishing the consequences of intertwined order parameters in spatially modulated superconductors. Final Report
This the Final Report for the grant DE-SC0012368. The purpose of this project was to establish the generality and full implications of phasesensitive coupling between charge and superconducting order parameters in materials exhibiting charge inhomogeneity. Specifically, our targeted goal was to first confirm experimentally a number of unique phenomena predicted by Berg et al for the cuprate material La 2-x Ba x CuO 4 (LBCO), commonly believed to contain such coupling and then extend the work to include several other superconducting families. More generally, our expanded research program sought to identify material families with co-existing charge and superconducting orders, and to understand the nature of the coupling between the order parameters. In the long term, we hope these are the first steps in identifying symmetry-based unifying principles, which might provide the foundation for a universal phenomenological theory, appropriate to describe to multiple families containing unconventional superconductivity.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Evidence for a robust sign-changing s-wave order parameter in monolayer films of superconducting Fe (Se,Te)/Bi 2 Te 3
The Fe-based superconductor Fe (Se,Te) combines non-trivial topology with unconventional superconductivity and may be an ideal platform to realize exotic states such as high-order topological corner modes and Majorana modes. Thin films of Fe (Se,Te) are particularly important for device fabrication and phase sensitive transport measurements. While bulk Fe (Se,Te) has been extensively studied, the nature of the superconducting order parameter in the monolayer limit has not yet been explored. In this work, we study monolayer films of Fe (Se,Te) on Bi 2 Te 3 with scanning tunneling spectroscopy. Monolayer Fe (Se,Te)/Bi 2 Te 3 heterostructures host a multigap superconducting state that strongly resembles the bulk. Analysis of the phase-referenced quasiparticle interference signal reveals a sign-changing s-wave order parameter similar to the bulk as well as a unique pattern of sign changes which have not been observed in the bulk. Our work establishes monolayer Fe (Se,Te)/Bi 2 Te 3 as a robust multi-band unconventional superconductor and sets the stage for explorations of non-trivial topology in this highly-tunable system.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Effects of local order parameter dependent transport coefficient in diblock copolymers under applied electric fields
In this work, we present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics, and, in this work, it is applied to study the effects of electric fields on thin films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of the transport coefficient on the local order parameter is used to relate it with the diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. In addition, transient behavior is found to be affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric field induced alignment of lamellae domains due to the field are found to be in qualitative agreement with experiments. This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin films containing diblock copolymers in the presence of applied electric fields.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗
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↗
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↗
Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
We develop recursion relations, in particle number, for all (unprojected) Jain composite fermion (CF) wave functions. These recursions generalize a similar recursion originally written down by Read for Laughlin states, in mixed first-second quantized notation. In contrast, our approach is purely second-quantized, giving rise to an algebraic, “pure guiding center” definition of CF states that de-emphasizes first quantized many-body wave functions. Key to the construction is a second-quantized representation of the flux attachment operator that maps any given fermion state to its CF counterpart. An algebra of generators of edge excitations is identified. In particular, in those cases where a well-studied parent Hamiltonian exists, its properties can be entirely understood in the present framework, and the identification of edge state generators can be understood as an instance of “microscopic bosonization.” Here, the intimate connection of Read's original recursion with “nonlocal order parameters” generalizes to the present situation, and we are able to give explicit second-quantized formulas for nonlocal order parameters associated with CF states.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Exploring order parameters and dynamic processes in disordered systems via variational autoencoders
The local order parameter in a disordered system is explored with convolutional neural networks and variational autoencoder.
36 MATERIALS SCIENCE↗
Study of the cowley and the christy-hall theories of order parameters.
Cowley and Christy-Hall theories of binary alloys and Warren-Cowley order parameters relationship to joint probabilities and Flinn function autocorrelations
INTERNAL ENERGY↗
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↗
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↗
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.↗
Disorder-Driven Transition from s ± to s + + Superconducting Order Parameter in Proton Irradiated Ba ( Fe 1 - x Rh x ) 2 As 2 Single Crystals
Here, microwave measurements of the London penetration depth and critical temperature T c were used to show evidence of a disordered-driven transition from s ± to s ++ order parameter symmetry in optimally doped Ba(Fe 1–x Rh x ) 2 As 2 single crystals, where disorder was induced by means of 3.5 MeV proton irradiation. Signatures of such a transition, as theoretically predicted, are found as a drop in the low-temperature values of the London penetration depth and a virtually disorder-independent superconducting T c . We show how these experimental observations can be described by multiband Eliashberg calculations in which the effect of disorder is accounted for in a suitable way. To this aim, an effective two-band approach is adopted, allowing us to treat disorder in a range between the Born approximation and the unitary limit.
36 MATERIALS SCIENCE↗
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↗