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A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Inorganic Crystalline Materials".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 37103

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Dr. Artem Pronin

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Physikalisches Institut, Universität Stuttgart Pfaffenwaldring 57, 70569 Stuttgart, Germany
Interests: topological effects in condensed matter; 3D Dirac and Weyl physics; strongly correlated electron systems, superconductivity, multiferroics, ferroelectrics; dielectric relaxation; metal-insulator transitions; low-energy electrodynamics of condensed matter

Special Issue Information

Dear Colleagues,

It is my pleasure to announce this Special Issue of Crystals on topological materials. Graphene is probably the greatest inspiration in current solid-state research. Many unique properties of graphene are due to its peculiar electronic structure, characterized by the linear electronic band dispersion and the crossings of these bands near the Fermi level. This band structure leads to a charge motion that is described by the Dirac Hamiltonian for massless particles, rather than by the standard Schrödinger Hamiltonian. The search for other materials, where similar physics would be observed, has led to the theoretical predictions and experimental discovery of topological insulators as well as Dirac and Weyl semimetals. In topological insulators, the surface states provide conduction (while the bulk is insulating) and the electronic structure of these states is similar to the electronic structure of graphene. The Dirac cones in topological insulators are symmetry-protected and thus robust against perturbations. Dirac and Weyl semimetals, in turn, possess linearly dispersing bands in their bulk with the band crossing points being protected either by symmetry or topology. The family of different topological electronic phases in solids continues to grow: the theoretical predictions of nodal-line, triple-point, and type-II Weyl semimetals have recently been accompanied by different experimental verifications for these novel phases. Common to all these states is the electronic low-energy band structure, which is represented by crossing linear bands. Research on these novel phases and on related quantum phenomena, provides strong ties between solid-state and high-energy physics. On the other hand, the excitement surrounding topological materials is also fueled by appealing potential applications. Topological semimetals are known for their high mobility and large magnetoresistance that can be exploited in high-speed electronics and spintronics. Valley degrees of freedom also open up possibilities for valleytronics applications. Electronic superlenses made from topological semimetals have been suggested to collimate electrons beyond diffraction limits in scanning tunneling microscopes. The robust surface states of such compounds can be utilized in surface-related chemical processes, such as catalysis. The fundamental interest and application potential are both calling for thoughtful theoretical and experimental investigations on topological materials. In this Special Issue, we welcome contributions from both theorists and experimentalists on all relevant aspects of this novel field.

Dr. Artem Pronin
Guest Editor

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Keywords

Topological effects in condensed matter
Weyl and Dirac semimetals
Topological insulators
Skyrmions and real-space topology
Topological chiral crystals

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Published Papers (12 papers)

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Editorial

Jump to: Research

3 pages, 172 KiB

Open AccessEditorial

Advances in Topological Materials

by Artem V. Pronin

Crystals 2021, 11(6), 680; https://doi.org/10.3390/cryst11060680 - 14 Jun 2021

Viewed by 2403

Abstract

Materials with electronic bands that possess nontrivial topology have remained a focal point of condensed matter physics since 2005, when topological insulators were theoretically discovered by Kane and Mele [...] Full article

(This article belongs to the Special Issue Advances in Topological Materials)

Research

Jump to: Editorial

8 pages, 761 KiB

Open AccessArticle

Low-Energy Optical Conductivity of TaP: Comparison of Theory and Experiment

by Alexander Yaresko and Artem V. Pronin

Crystals 2021, 11(5), 567; https://doi.org/10.3390/cryst11050567 - 19 May 2021

Cited by 3 | Viewed by 2414

Abstract

The ab-plane optical conductivity of the Weyl semimetal TaP is calculated from the band structure and compared to the experimental data. The overall agreement between theory and experiment is found to be best when the Fermi level is slightly (20 to 60 meV) shifted upwards in the calculations. This confirms a small unintentional doping of TaP, reported earlier, and allows a natural explanation of the strong low-energy (50 meV) peak seen in the experimental ab-plane optical conductivity: this peak originates from transitions between the almost parallel non-degenerate electronic bands split by spin-orbit coupling. The temperature evolution of the peak can be reasonably well reproduce by calculations using an analog of the Mott formula. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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9 pages, 570 KiB

Open AccessArticle

Topological Properties in a Λ/V-Type Dice Model

by Shujie Cheng and Xianlong Gao

Crystals 2021, 11(5), 467; https://doi.org/10.3390/cryst11050467 - 22 Apr 2021

Cited by 2 | Viewed by 2204

Abstract

We studied a non-interacting

Λ

/V-type dice model composed of three triangular sublattices. By considering the isotropic nearest-neighbor hoppings and the next-nearest-neighbor hoppings with the phase, as well as the quasi-staggered on-site potential, we acquired the full phase diagrams under the [...] Read more.

We studied a non-interacting

Λ

C = \pm 1

, as well as higher ones

\pm 2, \pm 3

and a metal phase in several regimes. In addition, we also checked the bulk–edge correspondence of the system by analyzing the edge-state energy spectrum. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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8 pages, 1518 KiB

Open AccessArticle

Fractional Power-Law Intraband Optical Conductivity in the Low-Dimensional Dirac Material CaMnBi₂

by M. B. Schilling, C. X. Wang, Y. G. Shi, R. K. Kremer, M. Dressel and A. V. Pronin

Crystals 2021, 11(4), 428; https://doi.org/10.3390/cryst11040428 - 16 Apr 2021

Cited by 3 | Viewed by 2488

Abstract

We studied the broadband optical conductivity of CaMnBi₂, a material with two-dimensional Dirac electronic bands, and found that both components of the intraband conductivity follow a universal power law as a function of frequency at low temperatures. This conductivity scaling differs from the Drude(-like) behavior, generally expected for free carriers, but matches the predictions for the intraband response of an electronic system in a quantum critical region. Since no other indications of quantum criticality are reported for CaMnBi₂ so far, the cause of the observed unusual scaling remains an open question. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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9 pages, 1225 KiB

Open AccessArticle

Isotropic Nature of the Metallic Kagome Ferromagnet Fe₃Sn₂ at High Temperatures

by Rebecca L. Dally, Daniel Phelan, Nicholas Bishop, Nirmal J. Ghimire and Jeffrey W. Lynn

Crystals 2021, 11(3), 307; https://doi.org/10.3390/cryst11030307 - 20 Mar 2021

Cited by 8 | Viewed by 4483

Abstract

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe

_{3}

_{2}

is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic [...] Read more.

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe

_{3}

_{2}

is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic bubbles with an accompanying topological Hall effect. We present small-angle inelastic neutron scattering measurements that unambiguously show that Fe

_{3}

_{2}

is an isotropic ferromagnet below

T_{C} \approx 660

K to at least 480 K—the lower temperature threshold of our experimental configuration. Fe

_{3}

_{2}

is known to have competing magnetic exchange interactions, correlated electron behavior, weak magnetocrystalline anisotropy, and lattice (spatial) anisotropy; all of these features are thought to play a role in stabilizing skyrmions in centrosymmetric systems. Our results reveal that at the elevated temperatures measured, there is an absence of significant magnetocrystalline anisotropy and that the system behaves as a nearly ideal isotropic exchange interaction ferromagnet, with a spin stiffness

D (T = 480

) = 168

meV Å

^{2}

, which extrapolates to a ground state spin stiffness

D (T = 0

) = 231

meV Å

^{2}

. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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9 pages, 404 KiB

Open AccessArticle

Faraday Rotation Due to Quantum Anomalous Hall Effect in Cr-Doped (Bi,Sb)₂Te₃

by Alexey Shuvaev, Lei Pan, Peng Zhang, Kang L. Wang and Andrei Pimenov

Crystals 2021, 11(2), 154; https://doi.org/10.3390/cryst11020154 - 3 Feb 2021

Cited by 2 | Viewed by 3038

Abstract

Quantum anomalous Hall effect (QAHE) represents a quantized version of the classical anomalous Hall effect. In the latter case the magnetization takes over the role of magnetic field and induces nonzero off-diagonal elements in the conductivity matrix. In magnetic topological insulators with the band inversion the QAHE can be reached due to quantized conduction channel at the sample edge if the Fermi energy is tuned into the surface magnetic gap. In the static regime the QAHE is seen as a zero-field step in the Hall resistivity. At optical frequencies this step is transformed into a quantized value of the polarization rotation approaching the fine structure constant

α = e^{2} / 2 ε_{0} h c \approx 1 / 137

. However, due to material issues the steps reach the predicted values at millikelvin temperatures only. In this work we investigate the Faraday polarization rotation in thin films of Cr-doped topological insulator and in the sub-terahertz frequency range. Well defined polarization rotation steps can be observed in transmittance in Faraday geometry. At temperatures down to

T = 1.85

K the value of the rotation reached about 20% of the fine structure constant and disappeared completely for

T > 20

K. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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19 pages, 2770 KiB

Open AccessArticle

Effect of Deformation on Topological Properties of Cobalt Monosilicide

by Sergey Nikolaev, Dmitry Pshenay-Severin, Yuri Ivanov and Alexander Burkov

Crystals 2021, 11(2), 143; https://doi.org/10.3390/cryst11020143 - 29 Jan 2021

Cited by 4 | Viewed by 2440

Abstract

Recently, it was shown that materials with certain crystal structures can exhibit multifold band crossings with large topological charges. CoSi is one such material that belongs to non-centrosymmetric space group P2

_{1}

3 (#198) and posseses multifold band crossing points with a topological [...] Read more.

_{1}

3 (#198) and posseses multifold band crossing points with a topological charge of 4. The change of crystal symmetry, e.g., by means of external stress, can lift the degeneracy and change its topological properties. In the present work, the influence of uniaxial deformation on the band structure and topological properties of CoSi is investigated on the base of ab initio calculations. The

k \cdot p

Hamiltonian taking into account deformation is constructed on the base of symmetry consideration near the

Γ

and R points both with and without spin-orbit coupling. The transformation of multifold band crossings into nodes of other types with different topological charges, their shift both in energy and in reciprocal space and the tilt of dispersion around nodes are studied in detail depending on the direction of uniaxial deformation. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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7 pages, 955 KiB

Open AccessArticle

Optical Response of Chiral Multifold Semimetal PdGa

by Sascha Polatkan and Ece Uykur

Crystals 2021, 11(2), 80; https://doi.org/10.3390/cryst11020080 - 21 Jan 2021

Cited by 5 | Viewed by 2682

Abstract

We present a theoretical study of the band structure and optical conductivity for the chiral multifold semimetal PdGa. We identify several characteristic features in the optical conductivity and provide their origins within the band structure. As experimental optical studies for the mentioned compound have not been reported, we contrast our results with the related compounds, RhSi and CoSi. We believe that the presented hallmarks will provide guidance to future experimental works. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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13 pages, 5532 KiB

Open AccessArticle

Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB₆

by Monica Ciomaga Hatnean, Talha Ahmad, Marc Walker, Martin R. Lees and Geetha Balakrishnan

Crystals 2020, 10(9), 827; https://doi.org/10.3390/cryst10090827 - 17 Sep 2020

Cited by 4 | Viewed by 2953

Abstract

SmB

_{6}

is a mixed valence topological Kondo insulator. To investigate the effect of substituting Sm with magnetic Ce ions on the physical properties of samarium hexaboride, Ce-substituted SmB

_{6}

crystals were grown by the floating zone method for the first time as [...] Read more.

SmB

_{6}

is a mixed valence topological Kondo insulator. To investigate the effect of substituting Sm with magnetic Ce ions on the physical properties of samarium hexaboride, Ce-substituted SmB

_{6}

crystals were grown by the floating zone method for the first time as large, good quality single crystal boules. The crystal growth conditions are reported. Structural, magnetic and transport properties of single crystals of Sm

_{1 - x}

_{x}

_{6}

(

x = 0.05

, 0.10 and 0.20) were investigated using X-ray diffraction techniques, electrical resistivity and magnetisation measurements. Phase composition analysis of the powder X-ray diffraction data collected on the as-grown boules revealed that the main phase was that of the parent compound, SmB

_{6}

. Substitution of Sm ions with magnetic Ce ions does not lead to long-range magnetic ordering in the

{Sm}_{1 - x} {Ce}_{x} B_{6}

crystals. The substitution with 5% Ce and above suppresses the cross-over from bulk conductivity at high temperatures to surface-only conductivity at low temperatures. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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7 pages, 2430 KiB

Open AccessArticle

Bulk Cyclotron Resonance in the Topological Insulator Bi₂Te₃

by Dmytro L. Kamenskyi, Artem V. Pronin, Hadj M. Benia, Victor P. Martovitskii, Kirill S. Pervakov and Yurii G. Selivanov

Crystals 2020, 10(9), 722; https://doi.org/10.3390/cryst10090722 - 20 Aug 2020

Cited by 5 | Viewed by 3056

Abstract

We investigated magneto-optical response of undoped Bi₂Te₃ films in the terahertz frequency range (0.3–5.1 THz, 10–170 cm⁻¹) in magnetic fields up to 10 T. The optical transmission, measured in the Faraday geometry, is dominated by a broad Lorentzian-shaped mode, whose central frequency linearly increases with applied field. In zero field, the Lorentzian is centered at zero frequency, representing hence the free-carrier Drude response. We interpret the mode as a cyclotron resonance (CR) of free carriers in Bi₂Te₃. Because the mode’s frequency position follows a linear magnetic-field dependence and because undoped Bi₂Te₃ is known to possess appreciable number of bulk carriers, we associate the mode with a bulk CR. In addition, the cyclotron mass obtained from our measurements fits well the literature data on the bulk effective mass in Bi₂Te₃. Interestingly, the width of the CR mode demonstrates a behavior non-monotonous in field. We propose that the CR width is defined by two competing factors: impurity scattering, which rate decreases in increasing field, and electron-phonon scattering, which exhibits the opposite behavior. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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9 pages, 2956 KiB

Open AccessArticle

Ideal Photonic Weyl Nodes Stabilized by Screw Rotation Symmetry in Space Group 19

by Wenlong Gao and Yao-Ting Wang

Crystals 2020, 10(7), 605; https://doi.org/10.3390/cryst10070605 - 12 Jul 2020

Cited by 1 | Viewed by 3161

Abstract

Topological photonics have developed in recent years since the seminal discoveries of topological insulators in condensed matter physics for electrons. Among the numerous studies, photonic Weyl nodes have been studied very recently due to their intriguing surface Fermi arcs, Chiral zero modes and scattering properties. In this article, we propose a new design of an ideal photonic Weyl node metacrystal, meaning no excessive states are present at the Weyl nodes’ frequency. The Weyl node is stabilized by the screw rotation symmetry of space group 19. Group theory analysis is utilized to reveal how the Weyl nodes are spawned from line nodes in a higher symmetry metacrystal of space group 61. The minimum four Weyl nodes’ complex for time reversal invariant systems is found, which is a realistic photonic Weyl node metacrystal design compatible with standard printed circuit board techniques and is a complement to the few existing ideal photonic Weyl node designs and could be further utilized in studies of Weyl physics, for instance, Chiral zero modes and scatterings. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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7 pages, 794 KiB

Open AccessArticle

Infrared Optical Conductivity of Bulk Bi₂Te₂Se

by Elena S. Zhukova, Hongbin Zhang, Victor P. Martovitskiy, Yurii G. Selivanov, Boris P. Gorshunov and Martin Dressel

Crystals 2020, 10(7), 553; https://doi.org/10.3390/cryst10070553 - 28 Jun 2020

Cited by 3 | Viewed by 3585

Abstract

Mid- and near-infrared measurements reveal that the optical conductivity of the three-dimensional topological insulator, Bi₂Te₂Se, is dominated by bulk carriers and shows a linear-in-frequency increase at 0.5 to 0.8 eV. This linearity might be interpreted as a signature of three-dimensional (bulk) Dirac bands; however, band-structure calculations show that transitions between bands with complex dispersion contribute instead to the inter-band optical conductivity at these frequencies and, hence, the observed linearity is accidental. These results warn against the oversimplified interpretations of optical-conductivity measurements in different Dirac materials. Full article

(This article belongs to the Special Issue Advances in Topological Materials)

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