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Symmetry
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Symmetries of Electronic Order
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Symmetries of Electronic Order

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (30 November 2012) | Viewed by 40269

Special Issue Editor

Dr. Sergey Borisenko

E-Mail Website
Guest Editor
Institute for Solid State Research, IFW-Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
Interests: unconventional superconductivity; strongly correlated electron systems; angle-resolved photoemission spectroscopy (ARPES)
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As we know, the symmetry of the electronic charge distribution in solids closely follows that of the crystal lattice. Depending on temperature or other factors this symmetry can be broken as a result of self-organisation of the valence electrons. Examples include superconductivity, density waves, orbital ordering, quantum magnetism or colossal magneto-resistance. A central challenge in modern condensed matter physics is to understand such many-body systems and identify the strong interactions which lead to these ordering phenomena.

The most concise and informative characteristic of the electronic order and its symmetry is the Fermi surface, a surface in reciprocal space confining the occupied electronic states. The notion of the Fermi surface developed in quantum physics made it possible to explain many physical properties of metals: their ability to conduct electric current and heat, their ductility, shininess etc. Detailed understanding of the Fermi surface and supporting low-energy electronic structure of the systems exhibiting different ordering phenomena will certainly help to unravel the underlying mechanisms of quantum electronic order and show the roots to synthesis of functional materials with desired physical properties.

Novel experimental methods, such as angle-resolved photoemission spectroscopy, offer a direct access to the Fermi surface and low-energy electronic structure of solids. On the other hand, the Fermi surface and electronic dispersion can also be calculated from the first principles. Using both tools, it became possible to characterize what is required most for complete understanding of particular type of the quantum electronic order - the symmetry and strength of the interactions which finally define the physical properties in those systems.

Contributions are invited on both experimental and theoretical studies of low-energy electronic structure of solids with emphasis on the Fermi surface. Possible classes of materials include, but not limited to:

  • superconductors,
  • spin density waves compounds,
  • charge density waves compounds,
  • orbitally ordered systems,
  • topological insulators,
  • carbon-based materials,
  • nano-structures

Dr. Sergey Borisenko
Guest Editor

Keywords

  • fermi surface
  • photoemission spectroscopy
  • spectral function
  • ab-initio calculations
  • electronic structure

Published Papers (5 papers)

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2284 KiB  
Article
Fermi Surface Reconstruction due to Hidden Rotating Antiferromagnetism in N and P-Type High-TC Cuprates
by Mohamed Azzouz
Symmetry 2013, 5(2), 215-232; https://doi.org/10.3390/sym5020215 - 07 May 2013
Cited by 3 | Viewed by 7771
Abstract
The Fermi surface calculated within the rotating antiferromagnetism theory undergoes a topological change when doping changes from p-type to n-type, in qualitative agreement with experimental data for n-type cuprate Nd2−xCexCuO4 and p-type La2−xSrxCuO4. Also, the reconstruction of the Fermi surface, observed experimentally close [...] Read more.
The Fermi surface calculated within the rotating antiferromagnetism theory undergoes a topological change when doping changes from p-type to n-type, in qualitative agreement with experimental data for n-type cuprate Nd2−xCexCuO4 and p-type La2−xSrxCuO4. Also, the reconstruction of the Fermi surface, observed experimentally close to optimal doping in p-type cuprates, and slightly higher than optimal doping in the overdoped regime for this n-type high-TC cuprate, is well accounted for in this theory. This reconstruction is a consequence of the quantum criticality caused by the disappearance of rotating antiferromagnetism. The present results are in qualitative agreement with recently observed quantum oscillations in some high-TC cuprates. This paper presents new results about the application of the rotating antiferromagnetism theory to the study of the electronic structure for n-type materials. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
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2311 KiB  
Article
One-Sign Order Parameter in Iron Based Superconductor
by Sergey V. Borisenko, Volodymyr B. Zabolotnyy, Alexnader A. Kordyuk, Danil V. Evtushinsky, Timur K. Kim, Igor V. Morozov, Rolf Follath and Bernd Büchner
Symmetry 2012, 4(1), 251-264; https://doi.org/10.3390/sym4010251 - 21 Mar 2012
Cited by 108 | Viewed by 15309
Abstract
The onset of superconductivity at the transition temperature is marked by the onset of order, which is characterized by an energy gap. Most models of the iron-based superconductors find a sign-changing (s±) order parameter [1–6], with the physical implication that pairing is driven [...] Read more.
The onset of superconductivity at the transition temperature is marked by the onset of order, which is characterized by an energy gap. Most models of the iron-based superconductors find a sign-changing (s±) order parameter [1–6], with the physical implication that pairing is driven by spin fluctuations. Recent work, however, has indicated that LiFeAs has a simple isotropic order parameter [7–9] and spin fluctuations are not necessary [7,10], contrary to the models [1–6]. The strength of the spin fluctuations has been controversial [11,12], meaning that the mechanism of superconductivity cannot as yet be determined. We report the momentum dependence of the superconducting energy gap, where we find an anisotropy that rules out coupling through spin fluctuations and the sign change. The results instead suggest that orbital fluctuations assisted by phonons [13,14] are the best explanation for superconductivity. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
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582 KiB  
Article
An Application of the Extended Global SO(3) × SO(3) × U(1) Symmetry of the Hubbard Model on a Square Lattice: The Spinon, η-Spinon, and c Fermion Description
by Jose M. P. Carmelo and Maria J. Sampaio
Symmetry 2011, 3(4), 780-827; https://doi.org/10.3390/sym3040780 - 12 Dec 2011
Viewed by 4421
Abstract
In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, [...] Read more.
In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N2a 1 sites consistent with its extended global symmetry. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global symmetry. Such objects emerge from a suitable electron-rotated-electron unitary transformation. An application to the spin spectrum of the parent compound La2CuO4 is shortly reviewed. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
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2379 KiB  
Article
d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry
by Toshikazu Ekino, Alexander M. Gabovich, Mai Suan Li, Marek Pękała, Henryk Szymczak and Alexander I. Voitenko
Symmetry 2011, 3(4), 699-749; https://doi.org/10.3390/sym3040699 - 20 Oct 2011
Cited by 21 | Viewed by 7828
Abstract
A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the [...] Read more.
A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
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414 KiB  
Article
Symmetry Aspects of the Band Structure and Motion Equations Applied in Calculating the Cyclotron Frequency of Electrons in Metals
by Stanislaw Olszewski and Tomasz Roliński
Symmetry 2011, 3(3), 541-563; https://doi.org/10.3390/sym3030541 - 10 Aug 2011
Cited by 1 | Viewed by 4279
Abstract
Cyclotron frequency of a crystal electron is, in general, not an easily accessible parameter. Nevertheless, its calculation can be simplified when the symmetry properties of the band structure and those of the motion equations in the magnetic field are simultaneously taken into account. [...] Read more.
Cyclotron frequency of a crystal electron is, in general, not an easily accessible parameter. Nevertheless, its calculation can be simplified when the symmetry properties of the band structure and those of the motion equations in the magnetic field are simultaneously taken into account. In effect, a combined symmetry of the electron Hamiltonian and that of the Lorentz equation provide us with a non-linear oscillator problem of high symmetry. In the next step, the kinetic energy of the oscillator can be separated from the whole of electron energy and applied in a new kind of calculation of the cyclotron frequency which is much more simple than before. In consequence, a detailed approach to the electron circulation, also in more complex band structures, becomes a relatively easy task. For different crystal lattices of cubic symmetry taken as examples the cyclotron frequency of the present and a former method are compared numerically giving the same results. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
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