Multicomponent superconducting order parameter in UTe2

An unconventional superconducting state was recently discovered in UTe2, where 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, suggest that a unique set of symmetries, magnetic properties, and topology underlie the superconducting state. Here, we report observations of a non-zero polar Kerr effect and of two transitions in the specific heat upon entering the superconducting state, which together suggest that the superconductivity in UTe2 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 UTe2.

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

The unusual correlated state that emerges in URu2Si2 below THO = 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 THO. 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.

Methods of catastrophe theory in the phenomenology of phase transitions

The monograph is devoted to describing the methods of catastrophe theory and building on the basis of these methods, phenomenological models of phase transitions in solids. Methods of constructing structurally stable normal forms of functions, including functions that are imposed on the symmetry conditions. The classification of phenomenological models of phase transitions for two interacting one-component order parameter, two-component and three-component order parameters the number of control parameters varied in the experiment. Theoretical dependence of the anomalies of the physical properties of the models are compared with experimental data in ferroelectrics, magnetic materials, solid solutions of rare earth metals, multiferroics and other solids that are experiencing phase transitions. For professionals in the field of solid state physics and phase transitions.

THE PRINCIPLE OF LOCAL ROTATIONAL INVARIANCE AND THE COEXISTENCE OF MAGNETISM, CHARGE AND SUPERCONDUCTIVITY

We propose a macroscopic description of the superconducting state in presence of an applied external magnetic field in terms of first order differential equations. They describe a corrugated two-component order parameter intertwined with a spin-charged background, caused by spin correlations and charged dislocations. The first order differential equations are a consequence of a Weitzenböck–Liechnorowitz identity which renders a SUL(2) ⊗ UL(1) invariant ground state, based on (L) local rotational and electromagnetic gauge symmetry. The proposal is based on a long ago developed formalism by Élie Cartan to investigate curved spaces, viewed as a collection of small Euclidean granules that are translated and rotated with respect to each other. Élie Cartan's formalism unveils the principle of local rotational invariance as a gauge symmetry because the global SU(2) invariance of the order parameter is turned local by the interlacement of spin and charge to pairing.

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn–Teller transitions in ABX 3 perovskites. I. Theory

Space groups, order-parameter and strain/order-parameter coupling relationships in ABX 3 perovskite structures which combine cooperative Jahn–Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn–Teller ordering schemes are associated with the irreducible representations {M}_2^+ and {R}_3^ + of the space group Pm\overline 3m. A third, less-common ordering scheme is associated with \Gamma _3^ +. These combine with tilting instabilities associated with {M}_3^ + and {R}_4^ + to generate a predicted suite of Jahn–Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn–Teller instabilities or of Jahn–Teller ordering on octahedral tilting.