Special Issue "Topological Crystalline Insulators: Current Progress and Prospects"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystal Engineering".

Deadline for manuscript submissions: closed (1 December 2016)

Special Issue Editor

Guest Editor
Dr. Satoshi Sasaki

School of Physics and Astronomy, University of Leeds, Leeds, UK
Website | E-Mail
Interests: exotic superconductors; Dirac, Weyl, and Majorana fermions in topological materials; electronic and transport properties; magnetoelectric effects; phase transition; growth of single crystals, thin films, and crystalline nanostructures of topological materials; macroscopic quantum phenomena; surface and interface; nanofabrications

Special Issue Information

Dear Colleagues,

The discovery of topological insulators with time-reversal symmetry has reignited interest in symmetry and topology of band structures in solid-state physics and chemistry. Interestingly, it has been theoretically demonstrated that different classes of symmetry in materials can protect relevant topological phases of matter. For example, topological superconducting phases that can harbor Majorana fermions can be protected by particle-hole symmetry.

Crystalline systems can adopt a huge variety of symmetries, including reflection (mirror) and rotation operations in point group symmetry, and symmorphic/nonsymmorphic operations in space group symmetry. Therefore, crystals have enormous potential for the existence of novel topological phases.

Topological crystalline insulators (TCIs) that exhibit these rich topological phases of matter have been attracting much interest in material research and their realization in real materials is interesting and challenging. Hence, it is worth summarizing current progress in the study of topological crystalline insulators and discussing what can be the milestones and prospects of these materials. By organizing this Special Issue, we aim to contribute to the topological community and those who will start the study in this field.

If you, as an investigator in this field, approve of our intention, we are happy to invite you to contribute to this Special Issue. Under “keywords” you can find various types of work related to the study of TCIs that would qualify as topics. Please note that this list is not inclusive.

Dr. Satoshi Sasaki
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Growth of bulk crystals, thin films, and crystalline nanostructures
  • Material classifications with respect to symmetry-protected topological phases of matter in different dimensions
  • Electronic band structures, electronic properties, transport properties
  • Surface and interface
  • Superconductivities
  • Dirac fermions and/or Majorana fermions
  • Crystal defects and/or impurity effects

Published Papers (5 papers)

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Research

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Open AccessArticle Topology and Holonomy in Discrete-time Quantum Walks
Crystals 2017, 7(5), 122; doi:10.3390/cryst7050122
Received: 24 January 2017 / Revised: 28 March 2017 / Accepted: 18 April 2017 / Published: 28 April 2017
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Abstract
We present a research article which formulates the milestones for the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space. Unlike other similar
[...] Read more.
We present a research article which formulates the milestones for the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space. Unlike other similar systems recently studied in detail in the literature, this system does not present continous 1D topological boundaries, it only presents a discrete number of Dirac points where the quasi-energy gap closes. At these discrete points, the topological winding number is not defined. Therefore, such discrete points represent topological boundaries of dimension zero, and they endow the system with a non-trivial topology. We illustrate the non-trivial character of the system by calculating the Zak phase. We discuss the prospects of this system, we propose a suitable experimental scheme to implement these ideas, and we present preliminary experimental data. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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Open AccessArticle Unexpected Au Alloying in Tailoring In-Doped SnTe Nanostructures with Gold Nanoparticles
Crystals 2017, 7(3), 78; doi:10.3390/cryst7030078
Received: 27 December 2016 / Revised: 28 February 2017 / Accepted: 1 March 2017 / Published: 6 March 2017
Cited by 1 | PDF Full-text (985 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Materials with strong spin-orbit interaction and superconductivity are candidates for topological superconductors that may host Majorana fermions (MFs) at the edges/surfaces/vortex cores. Bulk-superconducting carrier-doped topological crystalline insulator, indium-doped tin telluride (In-SnTe) is one of the promising materials. Robust superconductivity of In-SnTe nanostructures has
[...] Read more.
Materials with strong spin-orbit interaction and superconductivity are candidates for topological superconductors that may host Majorana fermions (MFs) at the edges/surfaces/vortex cores. Bulk-superconducting carrier-doped topological crystalline insulator, indium-doped tin telluride (In-SnTe) is one of the promising materials. Robust superconductivity of In-SnTe nanostructures has been demonstrated recently. Intriguingly, not only 3-dimensional (3D) nanostructures but also ultra-thin quasi-2D and quasi-1D systems can be grown by the vapor transport method. In particular, nanostructures with a controlled dimension will give us a chance to understand the dimensionality and the quantum confinement effects on the superconductivity of the In-SnTe and may help us work on braiding MFs in various dimensional systems for future topological quantum computation technology. With this in mind, we employed gold nanoparticles (GNPs) with well-identified sizes to tailor In-SnTe nanostructures grown by vapor transport. However, we could not see clear evidence that the presence of the GNPs is necessary or sufficient to control the size of the nanostructures. Nevertheless, it should be noted that a weak correlation between the diameter of GNPs and the dimensions of the smallest nanostructures has been found so far. To our surprise, the ones grown under the vapor–liquid–solid mechanism, with the use of the GNPs, contained gold that is widely and inhomogeneously distributed over the whole body. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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Open AccessArticle Anisotropic Magnetic Responses of Topological Crystalline Superconductors
Crystals 2017, 7(2), 58; doi:10.3390/cryst7020058
Received: 29 November 2016 / Accepted: 6 February 2017 / Published: 17 February 2017
Cited by 2 | PDF Full-text (3813 KB) | HTML Full-text | XML Full-text
Abstract
Majorana Kramers pairs emerged on surfaces of time-reversal-invariant topological crystalline superconductors show the Ising anisotropy to an applied magnetic field. We clarify that crystalline symmetry uniquely determines the direction of the Majorana Ising spin for given irreduciblerepresentationsofpairpotential,derivingconstraintstotopologicalinvariants. In addition, necessary conditions for nontrivial
[...] Read more.
Majorana Kramers pairs emerged on surfaces of time-reversal-invariant topological crystalline superconductors show the Ising anisotropy to an applied magnetic field. We clarify that crystalline symmetry uniquely determines the direction of the Majorana Ising spin for given irreduciblerepresentationsofpairpotential,derivingconstraintstotopologicalinvariants. In addition, necessary conditions for nontrivial topological invariants protected by the n-fold rotational symmetry are shown. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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Open AccessArticle Indium Substitution Effect on the Topological Crystalline Insulator Family (Pb1−xSnx)1−yInyTe: Topological and Superconducting Properties
Crystals 2017, 7(2), 55; doi:10.3390/cryst7020055
Received: 1 December 2016 / Revised: 30 January 2017 / Accepted: 11 February 2017 / Published: 16 February 2017
Cited by 1 | PDF Full-text (3306 KB) | HTML Full-text | XML Full-text
Abstract
Topological crystalline insulators (TCIs) have been of great interest in the area of condensed matter physics. We investigated the effect of indium substitution on the crystal structure and transport properties in the TCI system (Pb1−xSnx)1−yIn
[...] Read more.
Topological crystalline insulators (TCIs) have been of great interest in the area of condensed matter physics. We investigated the effect of indium substitution on the crystal structure and transport properties in the TCI system (Pb1−xSnx)1−yInyTe. For samples with a tin concentration x 50 % , the low-temperature resisitivities show a dramatic variation as a function of indium concentration: with up to ∼2% indium doping, the samples show weak-metallic behavior similar to their parent compounds; with ∼6% indium doping, samples have true bulk-insulating resistivity and present evidence for nontrivial topological surface states; with higher indium doping levels, superconductivity was observed, with a transition temperature, T c , positively correlated to the indium concentration and reaching as high as 4.7 K. We address this issue from the view of bulk electronic structure modified by the indium-induced impurity level that pins the Fermi level. The current work summarizes the indium substitution effect on (Pb,Sn)Te, and discusses the topological and superconducting aspects, which can be provide guidance for future studies on this and related systems. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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Review

Jump to: Research

Open AccessReview Dirac Landau Level Spectroscopy in Pb1−xSnxSe and Pb1−xSnxTe across the Topological Phase Transition: A Review
Crystals 2017, 7(1), 29; doi:10.3390/cryst7010029
Received: 15 December 2016 / Revised: 7 January 2017 / Accepted: 7 January 2017 / Published: 20 January 2017
Cited by 1 | PDF Full-text (2347 KB) | HTML Full-text | XML Full-text
Abstract
Topological crystalline insulators (TCIs) are topological materials that have Dirac surface states occurring at crystalline symmetric points in the Brillouin zone. This topological state has been experimentally shown to occur in the lead–tin salts Pb1−xSnxSe and Pb1−xSn
[...] Read more.
Topological crystalline insulators (TCIs) are topological materials that have Dirac surface states occurring at crystalline symmetric points in the Brillouin zone. This topological state has been experimentally shown to occur in the lead–tin salts Pb1−xSnxSe and Pb1−xSnxTe. More recent works also took interest in studying the topological phase transition from trivial to non-trivial topology that occurs in such materials as a function of increasing Sn content. A peculiar property of these materials is the fact that their bulk bands disperse following a massive Dirac dispersion that is linear at low energies above the energy gap. This makes Pb1−xSnxSe and Pb1−xSnxTe ideal platforms to simultaneously study 3D and 2D Dirac physics. In this review, we will go over infrared magneto-optical studies of the Landau level dispersion of Pb1−xSnxSe and Pb1−xSnxTe for both the bulk and surface bands and summarize work that has been done on this matter. We will review recent work on probing the topological phase transition in TCI. We will finally present our views on prospects and open questions that have yet to be addressed in magneto-optical spectroscopy studies on Pb1-xSnxSe and Pb1−xSnxTe. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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