Scaling theory of the mott transition and breakdown of the Grüneisen scaling near a finite-temperature critical end point

Cellular Griffiths-like phase

Protein compartmentalization in the frame of a liquid-liquid phase separation is a key mechanism to optimize spatiotemporal control of biological systems. Such a compartmentalization process reduces the intrinsic noise in protein concentration due to stochasticity in gene expression. Employing Flory-Huggins solution theory, Avramov/Casalini's model, and the Grüneisen parameter, we unprecedentedly propose a cellular Griffiths-like phase (CGLP), which can impact its functionality and self-organization. The here-proposed CGLP is key ranging from the understanding of primary organisms' evolution to the treatment of diseases. Our findings pave the way for an alternative Biophysics approach to investigate coacervation processes.

Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19

We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.

Unveiling the Physics of the Mutual Interactions in Paramagnets

In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field (Bloc). Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields (B). Nevertheless, as both the temperature (T) → 0 K and B → 0 T, such many-body contributions become ubiquitous. Here, employing the magnetic Grüneisen parameter (Γmag) and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-T and vanishing B. Our key results are: i) absence of a genuine zero-field quantum phase transition due to the presence of Bloc; ii) connection between the canonical definition of temperature and Γmag; and iii) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions.

Enhanced Grüneisen Parameter in Supercooled Water

We use the recently-proposed compressible cell Ising-like model to estimate the ratio between thermal expansivity and specific heat (the Grüneisen parameter Γs) in supercooled water. Near the critical pressure and temperature, Γs becomes significantly sensitive to thermal fluctuations of the order-parameter, a characteristic behavior of pressure-induced critical points. Such enhancement of Γs indicates that two energy scales are governing the system, namely the coexistence of high- and low-density liquids, which become indistinguishable at the critical point in the supercooled phase. The temperature dependence of the compressibility, sound velocity and pseudo-Grüneisen parameter Γw are also reported. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Man's Land regime, and indicates possible applications of this model to other systems. In particular, an application of the model to the qualitative behavior of the Ising-like nematic phase in Fe-based superconductors is also presented.

Low-Frequency Dynamics of Strongly Correlated Electrons in (BEDT-TTF)2X Studied by Fluctuation Spectroscopy

Fluctuation spectroscopy measurements of quasi-two-dimensional organic charge-transfer salts (BEDT-TTF) 2 X are reviewed. In the past decade, the method has served as a new approach for studying the low-frequency dynamics of strongly correlated charge carriers in these materials. We review some basic aspects of electronic fluctuations in solids, and give an overview of selected problems where the analysis of 1 / f -type fluctuations and the corresponding slow dynamics provide a better understanding of the underlying physics. These examples are related to (1) an inhomogeneous current distribution due to phase separation and/or a percolative transition; (2) slow dynamics due to a glassy freezing either of structural degrees of freedom coupling to the electronic properties or (3) of the electrons themselves, e.g., when residing on a highly-frustrated crystal lattice, where slow and heterogeneous dynamics are key experimental properties for the vitrification process of a supercooled charge-liquid. Another example is (4), the near divergence and critical slowing down of charge carrier fluctuations at the finite-temperature critical endpoint of the Mott metal-insulator transition. Here also indications for a glassy freezing and temporal and spatial correlated dynamics are found. Mapping out the region of ergodicity breaking and understanding the influence of disorder on the temporal and spatial correlated fluctuations will be an important realm of future studies, as well as the fluctuation properties deep in the Mott or charge-ordered insulating states providing a connection to relaxor or ordered ferroelectric states studied by dielectric spectroscopy.

Slow dynamics of electrons at a metal-Mott insulator boundary in an organic system with disorder

The Mott transition-a metal-insulator transition caused by repulsive Coulomb interactions between electrons-is a central issue in condensed matter physics because it is the mother earth of various attractive phenomena. Outstanding examples are high-Tc (critical temperature) cuprates and manganites exhibiting colossal magnetoresistance. Furthermore, spin liquid states, which are quantum-fluctuation-driven disordered ground states in antiferromagnets, have recently been found in magnetic systems very near the Mott transition. To date, intensive studies on the Mott transition have been conducted and appear to have established a nearly complete framework for understanding the Mott transition. We found an unknown type of Mott transition in an organic spin liquid material with a slightly disordered lattice. Around the Mott transition region of this material under pressure, nuclear magnetic resonance experiments capture the emergence of slow electronic fluctuations of the order of kilohertz or lower, which is not expected in the conventional Mott transition that appears as a clear first-order transition at low temperatures. We suggest that they are due to the unconventional metal-insulator fluctuations emerging around the disordered Mott transition in analogy to the slowly fluctuating spin phase, or Griffiths phase, realized in Ising spin systems with disordered lattices.

Breakdown of Hooke's law of elasticity at the Mott critical endpoint in an organic conductor

The Mott metal-insulator transition, a paradigm of strong electron-electron correlations, has been considered as a source of intriguing phenomena. Despite its importance for a wide range of materials, fundamental aspects of the transition, such as its universal properties, are still under debate. We report detailed measurements of relative length changes ΔL/L as a function of continuously controlled helium-gas pressure P for the organic conductor κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl across the pressure-induced Mott transition. We observe strongly nonlinear variations of ΔL/L with pressure around the Mott critical endpoint, highlighting a breakdown of Hooke's law of elasticity. We assign these nonlinear strain-stress relations to an intimate, nonperturbative coupling of the critical electronic system to the lattice degrees of freedom. Our results are fully consistent with mean-field criticality, predicted for electrons in a compressible lattice with finite shear moduli. We argue that the Mott transition for all systems that are amenable to pressure tuning shows the universal properties of an isostructural solid-solid transition.

Mott Quantum Criticality in the Anisotropic 2D Hubbard Model

We present evidence for Mott quantum criticality in an anisotropic two-dimensional system of coupled Hubbard chains at half-filling. In this scenario emerging from variational cluster approximation and cluster dynamical mean-field theory, the interchain hopping t_{⊥} acts as a control parameter driving the second-order critical end point T_{c} of the metal-insulator transition down to zero at t_{⊥}^{c}/t≃0.2. Below t_{⊥}^{c}, the volume of the hole and electron Fermi pockets of a compensated metal vanishes continuously at the Mott transition. Above t_{⊥}^{c}, the volume reduction of the pockets is cut off by a first-order transition. We discuss the relevance of our findings to a putative quantum critical point in layered organic conductors, whose location remains elusive so far.

Critical slowing down of the charge carrier dynamics at the Mott metal-insulator transition

We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical end point, we observe a divergent increase of the resistance fluctuations accompanied by a drastic shift of spectral weight to low frequencies, demonstrating the critical slowing down of the order parameter (doublon density) fluctuations. The slow dynamics is accompanied by non-Gaussian fluctuations, indicative of correlated charge carrier dynamics. A possible explanation is a glassy freezing of the electronic system as a precursor of the Mott MIT.

Universality class of the mott transition

Pressure dependence of the conductivity and thermoelectric power is measured through the Mott transition in the layer organic conductor EtMe_{3}P[Pd(dmit)_{2}]_{2}. The critical behavior of the thermoelectric effect provides a clear and objective determination of the Mott-Hubbard transition during the isothermal pressure sweep. Above the critical end point, the metal-insulator crossing, determined by the thermoelectric effect minimum value, is not found to coincide with the maximum of the derivative of the conductivity as a function of pressure. We show that the critical exponents of the Mott-Hubbard transition fall within the Ising universality class regardless of the dimensionality of the system.

Probing the Mott physics in κ-(BEDT-TTF)₂X salts via thermal expansion

In the field of interacting electron systems the Mott metal-to-insulator (MI) transition represents one of the pivotal issues. The role played by lattice degrees of freedom for the Mott MI transition and the Mott criticality in a variety of materials are current topics under debate. In this context, molecular conductors of the κ-(BEDT-TTF)2X type constitute a class of materials for unraveling several aspects of the Mott physics. In this review, we present a synopsis of literature results with focus on recent expansivity measurements probing the Mott MI transition in this class of materials. Progress in the description of the Mott critical behavior is also addressed.

Charge-ordering transition in (TMTTF)2X explored via dilatometry

Charge-ordering phenomena have been highly topical over the past few years. A phase transition towards a charge-ordered state has been observed experimentally in several classes of materials. Among them, many studies have been devoted to the family of quasi-one-dimensional organic charge-transfer salts (TMTTF)2X, where (TMTTF) stands for tetramethyltetrathiafulvalene and X for a monovalent anion (X = PF6, AsF6 and SbF6). However, the relationship between the electron localization phenomena and the role of the lattice distortion in stabilizing the charge-ordering pattern is poorly documented in the literature. Here we present a brief overview of selected literature results, with emphasis placed on recent thermal expansion experiments probing the charge-ordering transition of these salts.

Mott metal-insulator transition on compressible lattices

The critical properties of the finite temperature Mott end point are drastically altered by a coupling to crystal elasticity, i.e., whenever it is amenable to pressure tuning. Similar as for critical piezoelectric ferroelectrics, the Ising criticality of the electronic system is preempted by an isostructural instability, and long-range shear forces suppress microscopic fluctuations. As a result, the end point is governed by Landau criticality. Its hallmark is, thus, a breakdown of Hooke's law of elasticity with a nonlinear strain-stress relation characterized by a mean-field exponent. Based on a quantitative estimate, we predict critical elasticity to dominate the temperature range ΔT*/T(c)≃8%, close to the Mott end point of κ-(BEDT-TTF)(2)X.

High-resolution thermal expansion measurements under helium-gas pressure

We report on the realization of a capacitive dilatometer, designed for high-resolution measurements of length changes of a material for temperatures 1.4 K ≤ T ≤ 300 K and hydrostatic pressure P ≤ 250 MPa. Helium ((4)He) is used as a pressure-transmitting medium, ensuring hydrostatic-pressure conditions. Special emphasis has been given to guarantee, to a good approximation, constant-pressure conditions during temperature sweeps. The performance of the dilatometer is demonstrated by measurements of the coefficient of thermal expansion at pressures P ~/= 0.1 MPa (ambient pressure) and 104 MPa on a single crystal of azurite, Cu(3)(CO(3))(2)(OH)(2), a quasi-one-dimensional spin S = 1/2 Heisenberg antiferromagnet. The results indicate a strong effect of pressure on the magnetic interactions in this system.

Diffusionless γ⇄α phase transition in polycrystalline and single-crystal cerium

The cerium γ⇄α transition was investigated using high-pressure, high-temperature angle-dispersive x-ray diffraction measurements on both poly- and single-crystalline samples, explicitly addressing symmetry change and transformation paths. The isomorphic hypothesis of the transition is confirmed, with a transition line ending at a solid-solid critical point. The critical exponent is determined, showing a universal behavior that can be pictured as a liquid-gas transition. We further report an isomorphic transition between two single crystals (with more than 14% of volume difference), an unparalleled observation in solid-state matter interpreted in terms of dislocation-induced diffusionless first-order phase transformation.