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Higgs and Goldstone modes, well known in high energy physics, have been realized in a number of condensed matter physics contexts, including superconductivity, magnetism and structural phase transitions. Here, we show that the Leggett mode, a collective mode observed in multi-band su perconductors, also has an analog in crystallographic phase transitions. Such structural Leggett modes can occur in the phase channel as in the original work of Leggett, Prog. Theor. Phys 36,901 (1966). That is, they are antiphase Goldstone modes (anti-phasons). In addition, a new collective mode can also occur in the amplitude channel, an out-of phase (antiphase) Higgs mode, that should be observable in multi-band superconductors as well. We illustrate the existence and properties of these structural Leggett modes using the example of the pyrochlore relaxor ferroelectric, Cd$_2$Nb$_2$O$_7$.
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Traditionally, phase transitions are explored using a combination of macroscopic functional characterization and scattering techniques, providing insight into average properties and symmetries of the lattice but local atomic level mechanisms during phase transitions generally remain unknown. Here we explore the mechanisms of a phase transition between the trigonal prismatic and distorted octahedral phases of layered chalogenides in the MoS2 ReS2 system from the observations of local degrees of freedom, namely atomic positions by Scanning Transmission Electron Microscopy (STEM). We employ local crystallographic analysis based on machine learning of atomic environments to build a picture of the transition from the atomic level up and determine local and global variables controlling the local symmetry breaking. In particular, we argue that the dependence of the average symmetry breaking distortion amplitude on global and local concentration can be used to separate local chemical and global electronic effects on transition. This approach allows exploring atomic mechanisms beyond the traditional macroscopic descriptions, utilizing the imaging of compositional fluctuations in solids to explore phase transitions over a range of realized and observed local stoichiometries and atomic configurations.
Gen Shirane began studying ferroelectrics while he was still based in Japan in the early 1950s. It was therefore natural that when he arrived at Brookhaven and began specialising in neutron scattering that he would devote much of his energy and expertise studying structural phase transitions. We review the ground breaking experiments that showed the behaviour of antiferroelectrics and ferroelectrics were reasonably described in terms of the soft mode concept of structural phase transitions. This work lead directly to Gen being awarded the Buckley prize and, jointly with John Axe, awarded the Warren prize. We then describe his work on incommensurate phase transitions and in particular how the giant Kohn anomalies are responsible for the structural instabilities in one-dimensional metals. Finally Gen carefully investigated the central peak and the two-length scale phenomena that occur at most if not all transitions. Due to Gens elegant experimental work we know a great deal about both of these effects but in neither case is theory able to explain all of his results
We report on the observation of rich variety of crystallographic phase formation in RexMo1-xS2 alloy for x < 0.5. For x < 0.23, no low dimensional super-structural modulation is observed and inter-cation hybridization remains discrete forming dimers to tetramers with increasing Re concentration. For x > 0.23, super-strutural modulaton is observed. Depending on the Re concentrations (x = 0.23, 0.32, 0.38 and 0.45) and its distributions, various types of cation hybridization results in rich variety of low dimensional super-structural modulation as directly revealed by high resolution transmission electron microscopy. These layered alloy system may be useful for various energy and novel device applications.
Topological insulators and topological superconductors display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the von Neumann entropy, entanglement spectrum, fidelity, and fidelity spectrum may be used to detect and distinguish topological phases and their transitions. As an example we consider a two-dimensional $p$-wave superconductor, with Rashba spin-orbit coupling and a Zeeman term. The nature of the phases and their changes are clarified by the eigenvectors of the $k$-space reduced density matrix. We show that in the topologically nontrivial phases the highest weight eigenvector is fully aligned with the triplet pairing state. A signature of the various phase transitions between two points on the parameter space is encoded in the $k$-space fidelity operator.
AgClO4 has been studied under compression by x-ray diffraction and density functional theory calculations. Experimental evidence of a structural phase transition from the tetragonal structure of AgClO4 to an orthorhombic barite-type structure has been found at 5.1 GPa. The transition is supported by total-energy calculations. In addition, a second transition to a monoclinic structure is theoretically proposed to take place beyond 17 GPa. The equation of state of the different phases is reported as well as the calculated Raman-active phonons and their pressure evolution. Finally, we provide a description of all the structures of AgClO4 and discuss their relationships. The structures are also compared with those of AgCl in order to explain the structural sequence determined for AgClO4.
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