Symmetry, Topology and Phases of Condensed Matter

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 12589

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School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Interests: condensed matter physics
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Special Issue Information

Dear Colleagues,

Condensed matter physics has made a profound impact on our lives. Breakthroughs in it have given us the quantum Hall effects, liquid crystals, Bose-Einstein condensate, superconductivity, topological materials and many more. Our understanding of matter is based on topology, symmetry and the interplay between them. They distinguish quantum phases and are used to simplify mathematics descriptions of physics problems.
 
From 1970s topology started playing a big role in condensed matter physics with the quantum Hall effect becoming the first example of a topologically nontrivial state of matter. Since the discovery of topological insulators, topological matter became one of the hottest subjects in modern physics.
 
This special issue “Symmetry, Topology and Phases of Condensed Matter” aims to cover recent developments in these areas including, but not limited to quantum Hall effects, quantum spin liquids, Majorana fermions, topological metals, semimetals, insulators, superconductors, condensation phenomena, symmetry and group theory.

Dr. Aleksey Kozikov
Guest Editor

Manuscript Submission Information

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Keywords

  • Crystallographic and time-reversal symmetry
  • Incommensurate systems and quasi-crystals
  • Group theory, electron and phonon dispersion relations, theory and applications of representations
  • Topological states of matter
  • Quantum Hall effects
  • Condensation and superfluidity
  • Dirac and Weyl semimetals, superconductors, quantum materials, Nanostructures
  • Skyrmions, Majorana fermions, Abelian and non-Abelian anyons
  • Electronic structure, Strong correlations;Transport and optical phenomena, X-ray scattering, numerical simulations, non-perturbative and field theory, statistical, many-body physics

Published Papers (7 papers)

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Research

15 pages, 5230 KiB  
Article
The Continuous Measure of Symmetry as a Dynamic Variable: A New Glance at the Three-Body Problem
by Mark Frenkel, Shraga Shoval and Edward Bormashenko
Symmetry 2023, 15(12), 2153; https://doi.org/10.3390/sym15122153 - 04 Dec 2023
Viewed by 1089
Abstract
The time evolution of the continuous measure of symmetry for a system built of three bodies interacting via the potential U(r)~1r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of [...] Read more.
The time evolution of the continuous measure of symmetry for a system built of three bodies interacting via the potential U(r)~1r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of a pure gravitational interaction, the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes eventually to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the repulsive Coulomb interaction, the time evolution of the CMS is quite different. The CMS calculated for all of the studied initial configurations of the point charges, and all of their charge-to-mass ratios, always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies. The influence of Stokes-like friction on the change in symmetry of three-body gravitating systems is elucidated; the Stokes-like friction slows the decrease in the CMS and increases the stability of the Lagrange triangle. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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13 pages, 721 KiB  
Article
Dissipative Quantum Criticality as a Source of Strange Metal Behavior
by Marco Grilli, Carlo Di Castro, Giovanni Mirarchi, Götz Seibold and Sergio Caprara
Symmetry 2023, 15(3), 569; https://doi.org/10.3390/sym15030569 - 21 Feb 2023
Cited by 3 | Viewed by 1129
Abstract
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, [...] Read more.
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/Tlog(1/T), down to low temperatures. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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11 pages, 1745 KiB  
Article
Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
by Simone Traverso, Niccolò Traverso Ziani and Maura Sassetti
Symmetry 2022, 14(8), 1736; https://doi.org/10.3390/sym14081736 - 19 Aug 2022
Cited by 1 | Viewed by 1337
Abstract
The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with [...] Read more.
The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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11 pages, 3023 KiB  
Article
Informational Measure of Symmetry vs. Voronoi Entropy and Continuous Measure of Entropy of the Penrose Tiling. Part II of the “Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling”
by Edward Bormashenko, Irina Legchenkova, Mark Frenkel, Nir Shvalb and Shraga Shoval
Symmetry 2021, 13(11), 2146; https://doi.org/10.3390/sym13112146 - 10 Nov 2021
Cited by 6 | Viewed by 1446
Abstract
The notion of the informational measure of symmetry is introduced according to: Hsym(G)=i=1kP(Gi)lnP(Gi), where [...] Read more.
The notion of the informational measure of symmetry is introduced according to: Hsym(G)=i=1kP(Gi)lnP(Gi), where P(Gi) is the probability of appearance of the symmetry operation Gi within the given 2D pattern. Hsym(G) is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as Hsym(D3)= 1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. The informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. The informational measure of symmetry does not correlate with either the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns. Quantification of the “ordering” in 2D patterns performed solely with the Voronoi entropy is misleading and erroneous. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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26 pages, 1289 KiB  
Article
Polynomial Invariant of Molecular Circuit Topology
by Alireza Mashaghi and Roland van der Veen
Symmetry 2021, 13(9), 1751; https://doi.org/10.3390/sym13091751 - 19 Sep 2021
Cited by 1 | Viewed by 1588
Abstract
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain [...] Read more.
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain entanglements and local or global structural symmetries stabilised by formation contacts between different parts of the chain. Circuit topology captures the arrangements of intra-chain contacts within a given folded linear chain and allows for the classification and comparison of chains. Contacts keep chain segments in physical proximity and can be either mechanically hard attachments or soft entanglements that constrain a physical chain. Contrary to knot theory, which offers many established knot invariants, circuit invariants are just being developed. Here, we present polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts. A computer implementation and table of chains with up to three contacts is also provided. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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13 pages, 5120 KiB  
Article
Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams
by Edward Bormashenko, Irina Legchenkova, Mark Frenkel, Nir Shvalb and Shraga Shoval
Symmetry 2021, 13(9), 1659; https://doi.org/10.3390/sym13091659 - 08 Sep 2021
Cited by 8 | Viewed by 2832
Abstract
A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of [...] Read more.
A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diagrams emerging from the centers of the edges of the Penrose rhombs, considered nuclei, deny the hypothesis that the continuous measure of symmetry and the Voronoi entropy are always correlated. The Voronoi entropy of this kind of tiling built of asymmetric convex quadrangles equals zero, whereas the continuous measure of symmetry of this pattern is high. Voronoi diagrams generate new types of Penrose tiling, which are different from the classical Penrose tessellation. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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11 pages, 508 KiB  
Article
Prediction of Hysteresis Loop of Barium Hexaferrite Nanoparticles Based on Neuroevolutionary Models
by Lina Alhmoud, Abdul Raouf Al Dairy, Hossam Faris and Ibrahim Aljarah
Symmetry 2021, 13(6), 1079; https://doi.org/10.3390/sym13061079 - 16 Jun 2021
Cited by 1 | Viewed by 1822
Abstract
Neuroevolutionary models are used to predict magnetic hysteresis for barium hexaferrites (to predict magnetic hysteresis for barium hexaferrites). Magnetic hysteresis for a specific set of samples of barium hexaferrite doped with titanium were measured experimentally at room temperature and reported before. Neural networks [...] Read more.
Neuroevolutionary models are used to predict magnetic hysteresis for barium hexaferrites (to predict magnetic hysteresis for barium hexaferrites). Magnetic hysteresis for a specific set of samples of barium hexaferrite doped with titanium were measured experimentally at room temperature and reported before. Neural networks are trained using these experimental data in order to generate magnetization and predict magnetic hysteresis for various concentrations of titanum. We present the prediction for various methods of neural calculations and the deviations from actual data results were negligible. Finally, the predictions of magnetic hysteresis are summerized for the titanume concentration between 0.0 and 1.0. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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