Fluctuations Of Order Parameter Research Articles

Optical investigations of fluctuation of order parameter in THz range in SrxBa1-xNb2O6 crystals with different chemical compositions

Low-frequency spectra are investigated in a series of strontium barium niobate crystals SrxBa1-xNb2O6 with chemical compositions x = 0.33, 0.5, 0.61, and 0.75 in a back-scattering (ZZ) geometry and a wide temperature range including ferroelectric and paraelectric phases. It is shown that for all crystals studied, a central peak (CP) is clearly manifested in the vicinity of phase transition temperature. The temperature dependences of the CP parameters were obtained in all investigated crystals. It is shown that the central peak in all crystals studied is described by a number of relaxation times, which is typical for relaxors.

Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual

Superconductivity results from an instability of the Fermi surface -- contour of \textit{poles} of the single particle propagator -- to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model \textit{Luttinger} surface, or contour of \textit{zeros} of the Green function. At zero temperature ($\beta \rightarrow \infty$) and a critical interaction strength ($u_{c\infty}$) characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law $\frac{1}{\sqrt{\omega}}$ type, van-Hove singularity (vHS) indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit ($\beta u \gg 1$), the leading order fluctuation free energy terms in the normal state of this NFL-SC transition resemble the equivalent $\left(O(1)\right)$ terms of the Sachdev-Ye-Kitaev (SYK) model. This free energy contribution takes a simple form $-\beta F = \beta u_{c\infty} - \gamma~\text{ln}\left(\beta u_{c \infty}\right)$ where $\gamma$ is a constant equal to $\frac{1}{2}$. Weak impurity scattering ($\tau \gg \beta^{-1}$) leaves the low-energy spectral density unaffected, but leads to an interaction-driven enhancement of superconductivity. Our results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy-models exhibiting gravity duals.

Self-similar dynamics of order parameter fluctuations in pump-probe experiments

Upon excitation by a laser pulse, broken-symmetry phases of a wide variety of solids demonstrate similar order parameter dynamics characterized by a dramatic slowing down of relaxation for stronger pump fluences. Motivated by this recurrent phenomenology, we develop a simple non-perturbative effective model of dynamics of collective bosonic excitations in pump-probe experiments. We find that as the system recovers after photoexcitation, it shows universal prethermalized dynamics manifesting a power-law, as opposed to exponential, relaxation, explaining the slowing down of the recovery process. For strong quenches, long-wavelength over-populated transverse modes dominate the long-time dynamics; their distribution function exhibits universal scaling in time and space, whose universal exponents can be computed analytically. Our model offers a unifying description of order parameter fluctuations in a regime far from equilibrium, and our predictions can be tested with available time-resolved techniques.

Transient Trapping into Metastable States in Systems with Competing Orders

The quench dynamics of a system involving two competing orders is investigated using a Ginzburg-Landau theory with relaxational dynamics. We consider the scenario where a pump rapidly heats the system to a high temperature, after which the system cools down to its equilibrium temperature. We study the evolution of the order parameter amplitude and fluctuations in the resulting time dependent free energy landscape. Exponentially growing thermal fluctuations dominate the dynamics. The system typically evolves into the phase associated with the faster-relaxing order parameter, even if it is not the global free energy minimum. This theory offers a natural explanation for the widespread experimental observation that metastable states may be induced by laser induced collapse of a dominant equilibrium order parameter.

Fluid critical behavior at liquid–gas phase transition: Analytic method for microscopic description

The behavior of fluids in the vicinity of the liquid–gas critical point is studied within the cell fluid model framework. The analytic method for deriving the equation of state of a cell fluid model in the low-temperature region (T < Tc) is developed using the renormalization group transformation within the collective variables approach. Mathematical description within the grand canonical ensemble is illustrated by an example of the Morse interaction potential possessing the Fourier transform. A specific feature of the proposed method lies in the possibility to use exclusively microscopic characteristics of a fluid (parameters of the interaction potential) for calculating macroscopic quantities (pressure and other thermodynamic quantities) without involving the hard-spheres reference system. The grand partition function, thermodynamic potential, and equation of state of the model near the critical point are derived taking into account the non-Gaussian (quartic) distribution of order parameter fluctuations. A nonlinear equation, which links the density and the chemical potential, is presented and solved. Graphs of the dependence of the density on the chemical potential are plotted for various values of the relative temperature. The numerical estimates of the critical-point parameters for potassium, obtained in addition to the estimates for sodium, are given. The calculated critical-point parameters for liquid alkali metals (sodium and potassium) are in accord with experimental data. The coexistence curve for sodium is plotted and compared with other authors' data in the immediate vicinity of Tc, where theoretical and experimental researches are difficult to carry out. The differences between the obtained results and the earlier published results for T > Tc are discussed.

Landau ordering phase transitions beyond the Landau paradigm

Continuous phase transitions associated with the onset of a spontaneously broken symmetry are thought to be successfully described by the Landau-Ginzburg-Wilson-Fisher theory of fluctuating order parameters. In this work we show that such transitions can admit new universality classes which cannot be understood in terms of a theory of order parameter fluctuations. We explicitly demonstrate continuous time reversal symmetry breaking quantum phase transitions of $3+1$-D bosonic systems described by critical theories expressed in terms of a deconfined gauge theory with massless Dirac fermions instead of the fluctuating Ising order parameter. We dub such phase transitions "Landau transitions beyond Landau description" (LBL). A key feature of our examples is that the stability of the LBL fixed points requires a crucial global symmetry, which is non-anomalous, unbroken, and renders no symmetry protected topological phase throughout the phase diagram. Despite this, there are elementary critical fluctuations of the phase transition that transform projectively under this symmetry group. We also construct examples of other novel quantum critical phenomena, notably a continuous Landau-forbidden deconfined critical point between two Landau-allowed phases in $3+1$-D.

Higgs Mode in Superconductors

When the continuous symmetry of a physical system is spontaneously broken, two types of collective modes typically emerge: the amplitude and the phase modes of the order-parameter fluctuation. For superconductors, the amplitude mode is referred to most recently as the Higgs mode as it is a condensed-matter analog of a Higgs boson in particle physics. Higgs mode is a scalar excitation of the order parameter, distinct from charge or spin fluctuations, and thus does not couple to electromagnetic fields linearly. This is why the Higgs mode in superconductors has evaded experimental observations for over a half century after the initial theoretical prediction, except for a charge-density-wave coexisting system. With the advance of nonlinear and time-resolved terahertz spectroscopy techniques, however, it has become possible to study the Higgs mode through the nonlinear light–Higgs coupling. In this review, we overview recent progress in the study of the Higgs mode in superconductors.

Electromagnetic response of superconductors in the presence of multiple collective modes

We revisit the importance of collective-mode fluctuations and gauge invariance in the electromagnetic response of superconducting systems. In particular, we show that order-parameter fluctuations, gapless or not, have no contribution to the Meissner effect in both $s$- and $p$-wave superconductors. More generally, we extend this result to uniform and nonuniform superfluids with no external wavevector scale. To facilitate this analysis, we formulate a path-integral-based matrix methodology for computing the electromagnetic response of fermionic fluids in the presence of concomitantly fluctuating collective modes. Closed-form expressions for the electromagnetic response in different scenarios are provided, including the case of fluctuations of electronic density and the phase and amplitude of the order parameter. All microscopic symmetries and invariances are manifestly satisfied in our formalism, and it can be straightforwardly extended to other scenarios.

Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth Order and Looks Like Second Order

We report that the thermally induced Mott transition in vanadium sesquioxide shows critical slowing down and enhanced variance ("critical opalescence") of the order parameter fluctuations measured through low-frequency resistance-noise spectroscopy. Coupled with the observed increase of the phase-ordering time, these features suggest that the strong abrupt transition is controlled by a critical-like singularity in the hysteretic metastable phase. The singularity is identified with the spinodal point and is a likely consequence of the strain-induced long-range interaction.

Soft modes in HoFe2.5Ga0.5(BO3)4 solid solution

The condensation of two soft modes has been found when studying the Raman spectra of the solid solution HoFe2.5Ga0.5(BO3)4 in the temperature range from 7 to 350 K. The first high-temperature soft mode is associated with the structural phase transition from the R32 phase to the P3121 phase. The second soft mode is related to the reveal of the phonon-magnon interaction during magnetic ordering in the crystal. The temperatures of the structural phase transition T1 = 266 K and the magnetic phase transition T2 = 28 K are established. Experimentally interaction between the structural phase transition order parameter fluctuations and the magnetic order parameter fluctuations was found.

Energy domain versus time domain precursor fluctuations above the Verwey transition in magnetite

We study the dynamics and interactions of the critical fluctuations of the Verwey transition in magnetite (${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$) in the pretransition region by means of inelastic neutron scattering experiments on a natural single crystal. We find that a ${\mathrm{\ensuremath{\Delta}}}_{5}$ mode interacts strongly with a central peak of order parameter fluctuations, whose width is determined by the order parameter coherence time. This is compared with pump-probe experiments, which we formerly explained in terms of fluctuation-assisted stimulated Raman scattering. Our estimates of the order parameter correlation time from experiments in the energy domain (inelastic neutron scattering experiments) and in the time domain (pump-probe experiments) coincide, thus giving further credit to our previous interpretation of pump-probe experiments and confirming that the Verwey transition is of the order-disorder type, without phonon softening.

Role of hydrodynamics in liquid–liquid transition of a single-component substance

Liquid-liquid transition (LLT) is an unconventional transition between two liquid states in a single-component system. This phenomenon has recently attracted considerable attention not only because of its counterintuitive nature but also since it is crucial for our fundamental understanding of the liquid state. However, its physical understanding has remained elusive, particularly of the critical dynamics and phase-ordering kinetics. So far, the hydrodynamic degree of freedom, which is the most intrinsic kinetic feature of liquids, has been neglected in its theoretical description. Here we develop a Ginzburg-Landau-type kinetic theory of LLT taking it into account, based on a two-order parameter model. We examine slow critical fluctuations of the nonconserved order parameter coupled to the hydrodynamic degree of freedom in equilibrium. We also study the nonequilibrium process of LLT. We show both analytically and numerically that domain growth becomes faster (slower), depending upon the density decrease (increase) upon the transition, as a consequence of hydrodynamic flow induced by the density change. The coupling between nonconserved order parameter and hydrodynamic interaction results in anomalous domain growth in both nucleation-growth-type and spinodal-decomposition-type LLT. Our study highlights the characteristic features of hydrodynamic fluctuations and phase ordering during LLT under complex interplay among conserved and nonconserved order parameters and the hydrodynamic transport intrinsic to the liquid state.

Self-Consistent Consideration of Fluctuations in Singlet Superconducting Phases with s and d Symmetry

We analyze the behavior of thermal fluctuations of the superconducting order parameter with extended s-wave and $${{d}_{{{{x}^{2}} - {{y}^{2}}}}}$$-wave symmetry. For this purpose, we develop a method of self-consistent consideration of the order parameter fluctuations and charge carrier scatterers by fluctuations of coupled electron pairs using the theory of functional integration. The study is performed based on the quasi-two-dimensional one-band model with attraction between electrons located at neighboring sites. We obtain the distribution functions of the phase fluctuation probabilities depending on temperature, charge carrier concentrations, and model parameters. It is shown that the phase of the order parameter in the superconducting region is coherent, and the density of states has a dip at the Fermi level. In approaching the incoherent region of the phase diagram, the dip in the density of states disappears simultaneously with the loss of phase coherence. At the same time, the order parameter amplitude averaged over fluctuations remains finite at any temperature and concentration of charge carriers. Our results show that the pseudogap state cannot be explained in the frames of this scenario.

Detrended fluctuation analysis of seismicity and order parameter fluctuations before the M7.1 Ridgecrest earthquake

Detrended fluctuation analysis (DFA) has been recently applied for the investigation of temporal correlations between the earthquake magnitudes before major earthquakes. Here, we employ DFA together with natural time analysis in order to identify precursory phenomena to the M7.1 Ridgecrest earthquake on July 6, 2019. The analysis reveals that a minimum of the variability of the order parameter of seismicity in natural time is observed almost a month before the occurrence of this earthquake. This minimum was observed when DFA indicated the development of the presence of long-range correlations which turned to an almost random behavior before the strong earthquake. Upon starting the study of seismicity in natural time from the minimization of the variability on June 5, 2019, we conclude that criticality has been reached at 22:41 UTC on July 2, 2019, almost 3 days before the earthquake occurrence. The application of an algorithm based on the coherent noise model would have led to a warning 3 min before the occurrence of the M7.1 Ridgecrest earthquake.

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid–liquid transition

Crystallization is one of the most familiar and fundamental phase transition phenomena. There is a possibility that crystallization may be enhanced by critical-like fluctuations associated with another nearby phase transition if the order parameter of the former is coupled to that of the latter; however, the mechanism of such order parameter coupling and its generality remain elusive due to the lack of experimental studies. Here we report experimental evidence for a nontrivial coupling between crystallization and liquid-liquid transition (LLT) for a molecular liquid, triphenyl phosphite. We find that the crystal nucleation frequency is drastically enhanced by short-time preannealing near but above the spinodal temperature of LLT. By successfully separating the thermodynamic and kinetic factors governing crystal nucleation, we show that this enhancement is induced by the lowering of the crystal-liquid interfacial energy due to the presence of critical-like order parameter fluctuations. This finding may be regarded as a fingerprint of the presence of LLT below the melting point. Thus, it may allow us not only to control the crystal nucleation frequency by LLT but also to unveil LLT hidden behind crystallization. This enhancement of nucleation frequency by critical-like fluctuations of another ordering phenomenon may be general to a variety of combinations of phase transitions. It would provide a way to control a crystal grain structure, which is a crucial control factor of mechanical and thermal properties of crystalline materials.

Stickiness in the order parameter time-series as a signature of criticality

We show that, in continuous phase transitions, the order parameter fluctuations in time, are characterized by a resonant phenomenon, occurring whenever a physical system enters in a critical region. It is realized in the mean waiting time 〈λ〉 of the order parameter time-series, in the immediate neighbourhood of its equilibrium (mean) value. By varying the control parameter within the critical region, 〈λ〉 becomes maximum at the critical point. To illustrate this resonant behaviour, we first use simulated data of the 3D ferromagnetic Ising model. Subsequently, we demonstrate the universality of this phenomenon in experimental voltage drop across the resistor data of a driven resistor–inductor–diode circuit for different driving frequencies. The latter has been recently shown (Potirakis et al., 2017) to act as the order parameter of a continuous transition from normal rectifier phase, in the low frequency regime, to a full-wave conducting, capacitor-like phase at high frequencies. Using a simple phenomenological ansatz for the waiting time distribution within the critical region, we gain some insight to the emergence of the critical resonance, achieving at the same time a semi-quantitative description.

Multiple intertwined pairing states and temperature-sensitive gap anisotropy for superconductivity at a nematic quantum-critical point

The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropic s-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap Delta (theta ,{omega }_{m}) and show that its angular dependence strongly varies below {T}_{{rm{c}}}. We show that this variation is a signature of QC pairing and comes about because there are multiple s-wave pairing instabilities with closely spaced transition temperatures {T}_{{rm{c}},n}. Taken alone, each instability would produce a gap Delta (theta ,{omega }_{m}) that changes sign 8n times along the Fermi surface. We show that the equilibrium gap Delta (theta ,{omega }_{m}) is a superposition of multiple components that are nonlinearly induced below the actual {T}_{{rm{c}}}={T}_{{rm{c}},0}, and get resonantly enhanced at T={T}_{{rm{c}},n} < {T}_{{rm{c}}}. This gives rise to strong temperature variation of the angular dependence of Delta (theta ,{omega }_{m}). This variation progressively disappears away from a QC point.

Spin transport in an electrically driven magnon gas near Bose-Einstein condensation: Hartree-Fock-Keldysh theory

An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation. We find that the steady state magnon distribution function generally has a non-thermal form that cannot be described by a single effective chemical potential and effective temperature. We also show that the BEC instability in the electrically-driven magnon system is signaled by a sign change in the imaginary part of the poles for long-wavelength magnon modes and by the divergence of the nonequilibrium magnon distribution function. In the presence of two bath temperatures, we find that the correlation length of the superfluid order parameter fluctuations exhibits nontrivial finite temperature crossover behaviors that are richer than the standard crossover behaviors obtained for the vacuum-superfluid transition in an equilibrium dilute Bose gas. We study the consequences of these thermal crossovers on the magnon spin conductivity and obtain an inverse square-root divergence in the spin conductivity in the vicinity of the electrically-induced BEC instability. A spintronics device capable of testing our spin transport predictions is discussed.

Correlations between elastic, calorimetric, and polar properties of ferroelectric PbSc0.5Ta0.5O3 (PST)

Calorimetric, elastic, and polar properties of ferrolectric lead scandium tantalate PbSc0.5Ta0.5O3 with 65% cation order have been investigated in the vicinity of the paraelectric-ferroelectric transition at Ttrans=295 K. Comparison of temperature dependencies of the excess specific heat and elastic properties indicates that both anomalies stem from thermal fluctuations of order parameters in three dimensions. These fluctuations are consistent with the tweed microstructure. This transition is driven by several coupled thermodynamic order parameters, as evidenced by a strongly nonlinear scaling of the excess entropy with the squared ferroelectric polarization.

Proximity effect in a superconductor-quasicrystal hybrid ring

We compute the real-space profile of the superconducting order parameter (OP) in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter $\phi$, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on $\phi$ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly $larger$ than in a normal periodic conductor for special values of $\phi$.