Parity-time phase transition in photonic crystals with $$C_{6v}$$ symmetry

Abstract We investigate the parity-time (PT) phase transition in photonic crystals with $$C_{6v}$$ C 6 v symmetry, with balanced gain and loss on dielectric rods in the triangular lattice. A two-level non-Hermitian model that incorporates the gain and loss in the tight-binding approximation was employed to describe the dispersion of the PT symmetric system. In the unbroken PT phase, the double Dirac cone feature associated with the $$C_{6v}$$ C 6 v symmetry is preserved, with a frequency shift of second order due to the presence of gain and loss. The helical edge states with real eigenfrequencies can exist in the common band gap for two topologically distinct lattices. In the broken PT phase, the non-Hermitian perturbation deforms the dispersion by merging the frequency bands into complex conjugate pairs and forming the exceptional contours that feature the PT phase transition. In this situation, the band gap closes and the edge states are mixed with the bulk states.

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Edge-state influence on high-order harmonic generation in topological nanoribbons

The European Physical Journal D ◽

10.1140/epjd/s10053-021-00201-9 ◽

2021 ◽

Vol 75 (6) ◽

Author(s):

Christoph Jürß ◽

Dieter Bauer

Keyword(s):

Phase Transition ◽

Band Gap ◽

Harmonic Generation ◽

Tight Binding ◽

High Order ◽

Edge States ◽

Binding Parameters ◽

High Order Harmonic Generation ◽

Tight Binding Approximation ◽

High Order Harmonic

Abstract The high-order harmonic generation in finite topological nanoribbons is investigated using a tight-binding approximation. The narrow, two-dimensional ribbons consist of hexagonal structures. A topological phase transition is defined by a sudden change of the topological invariant. In the bulk, this kind of phase transition might occur if an existing band gap closes and reopens again. Through the bulk-boundary correspondence, this is related to the emergence of topologically protected edge states in the respective finite systems. For the finite ribbons studied in this work, the variation of the tight-binding parameters leads to the emergence of two edge states after the closing of the band gap. The energies of those edge states as functions of the tight-binding parameters display crossings and avoided crossings, which influence the high-harmonic spectra. Graphic Abstract

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Energy Gaps in BN/GNRs Planar Heterostructure

Materials ◽

10.3390/ma14175079 ◽

2021 ◽

Vol 14 (17) ◽

pp. 5079

Author(s):

Jinyue Guan ◽

Lei Xu

Keyword(s):

Phase Transition ◽

Boron Nitride ◽

Band Gap ◽

Lattice Mismatch ◽

Tight Binding ◽

Graphene Nanoribbon ◽

Band Gaps ◽

Energy Gaps ◽

Local Potentials

Using the tight-binding approach, we study the band gaps of boron nitride (BN)/ graphene nanoribbon (GNR) planar heterostructures, with GNRs embedded in a BN sheet. The width of BN has little effect on the band gap of a heterostructure. The band gap oscillates and decreases from 2.44 eV to 0.26 eV, as the width of armchair GNRs, nA, increases from 1 to 20, while the band gap gradually decreases from 3.13 eV to 0.09 eV, as the width of zigzag GNRs, nZ, increases from 1 to 80. For the planar heterojunctions with either armchair-shaped or zigzag-shaped edges, the band gaps can be manipulated by local potentials, leading to a phase transition from semiconductor to metal. In addition, the influence of lattice mismatch on the band gap is also investigated.

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Phase Transition in Photonic Crystals Doped with Nanoparticles

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.31.242 ◽

2007 ◽

Vol 31 ◽

pp. 242-245 ◽

Cited By ~ 1

Author(s):

Mahi R. Singh

Keyword(s):

Phase Transition ◽

Photonic Crystals ◽

Numerical Simulations ◽

Band Gap ◽

Photonic Band Gap ◽

Dipole Interaction ◽

The Real ◽

Photonic Band

We have study the phenomenon on of phase transition in photonic band gap (PBG) materials doped with four-level nanoparticles in the presence of the dipole-dipole interaction. Numerical simulations for the real susceptibility have been performed for an isotropic PBG material. It is found that the real susceptibility has a singularity for a certain value of the nanostructure concentration. This is a signature of the phase transition in the system.

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Electronic Structure and Surface Properties of SrBi2Ta2O9 and Related Oxides

MRS Proceedings ◽

10.1557/proc-493-249 ◽

1997 ◽

Vol 493 ◽

Cited By ~ 3

Author(s):

J Robertson ◽

C W Chen

Keyword(s):

Electronic Structure ◽

Band Gap ◽

Conduction Band ◽

Tight Binding ◽

Schottky Barriers ◽

Band Edge ◽

Conduction Band Edge ◽

Edge States ◽

Tight Binding Method ◽

S States

ABSTRACTThe electronic structure of SrBi2Ta2O9 and related oxides such as SrBi2Nb2O9, Bi2WO6 and Bi3Ti4O12 have been calculated by the tight-binding method. In each case, the band gap is about 4.1 eV and the band edge states occur on the Bi-O layers and consist of mixed O p/Bi s states at the top of the valence band and Bi p states at the bottom of the conduction band. The main difference between the compounds is that Nb 5d and Ti 4d states in the Nb and Ti compounds lie lower than the Ta 6d states in the conduction band. The surface pinning levels are found to pin Schottky barriers 0.8 eV below the conduction band edge.

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Tight–Binding Analysis of Electronic Structure of Germanene Sheet and Nanoribbons Including Stone-Wales Defect

10.21203/rs.3.rs-462442/v1 ◽

2021 ◽

Author(s):

Komeil Rahmani ◽

Saeed Mohammadi

Keyword(s):

Band Structure ◽

Band Gap ◽

Energy Band ◽

Dirac Point ◽

Tight Binding ◽

Topological Defects ◽

Energy Band Structure ◽

Fermi Velocity ◽

Tight Binding Approximation ◽

Wales Defect

Abstract In this paper, we investigate the electronic characteristics of germanene using the tight binding approximation. Germanene as the germanium-based analogue of graphene has attracted much research interest in recent years. Our analysis is focused on the pristine sheet of germanene as well as defective monolayer. The Stone-Wales defect, which is one of the most common topological defects in such structures, is considered in this work. Not only the infinite sheet of germanene but also the germanene nanoribbons in different orientations are analyzed. The obtained results show that applying the Stone–Wales defect into the germanene monolayer changes the energy band structure; the E-k curves around the Dirac point are no longer linear, a band gap is opened, and the Fermi velocity is reduced to half of that of defect-free germanene. In the case of nanoribbon structures, the armchair germanene nanoribbons with nanoribbon widths of 3p and 3p+1 reveal the semiconductor behaviour. However, armchair germanene nanoribbon with width of 3p+2 is semi-metal. After applying the Stone–Wales defect, the band gap of armchair germanene nanoribbons with widths of 3p and 3p+1 is reduced and it is increased for the width of 3p+2. Furthermore, there is no band gap in the energy band structure of zigzag germanene nanoribbon and the metallic behaviour is obvious.

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THE BAND-GAP AND TRUE BAND-GAP IN NOMINALLY METALLIC CARBON NANOTUBES: THE TIGHT-BINDING STUDY ON CORRUGATION EFFECT

International Journal of Modern Physics B ◽

10.1142/s0217979214500180 ◽

2014 ◽

Vol 28 (08) ◽

pp. 1450018

Author(s):

HONGXIA LU ◽

JIANBAO WU ◽

JIZHEN WANG ◽

SHAOCONG SHI ◽

WEIYI ZHANG

Keyword(s):

Carbon Nanotubes ◽

Total Energy ◽

Band Gap ◽

Tight Binding ◽

Small Radius ◽

Single Wall Carbon Nanotubes ◽

Curvature Effect ◽

Tight Binding Approximation ◽

Energy Calculations ◽

Small Band

In this paper, the band-gap and true band-gap are analyzed for the corrugated structures of various types of single wall carbon nanotubes (SWCNTs) within the tight binding approximation. We show that corrugation, combined with curvature effect, yields naturally the true small band-gap in all SWCNTs with small radius. The more stable corrugated structures of SWCNTs are backed by the abinitio total energy calculations for nominally metallic armchair SWCNTs.

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SPIN-ORBIT COUPLING IN GRAPHENE UNDER UNIAXIAL STRAIN: TIGHT-BINDING APPROACH AND FIRST-PRINCIPLES CALCULATIONS

Modern Physics Letters B ◽

10.1142/s0217984911026097 ◽

2011 ◽

Vol 25 (11) ◽

pp. 823-830 ◽

Cited By ~ 3

Author(s):

BAIHUA GONG ◽

XIN-HUI ZHANG ◽

ER-HU ZHANG ◽

SHENG-LI ZHANG

Keyword(s):

Band Gap ◽

First Principles ◽

Tight Binding ◽

Uniaxial Strain ◽

Orbit Coupling ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

First Principles Calculations ◽

Binding Model ◽

Tight Binding Approximation

Tuning the spin-orbit coupling (SOC) in graphene is highly desired for its application in spintronics. In this paper, we calculated the band gap induced by SOC in graphene under uniaxial strain from a tight-binding model, and found that the band gap has a monotonic increasing dependence on the strain in the range of -20% to 15%. Our results suggest that strain can be used as a reversible and controllable way to tune the SOC in graphene. First-principles calculations were performed, confirming the results of tight-binding approximation.

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Electromagnetic propagation characteristics of one-dimensional photonic crystals with metal layers in quasi-parity-time (PT)-symmetric system

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0104 ◽

2020 ◽

Vol 75 (7) ◽

pp. 665-670

Author(s):

Guanxia Yu ◽

Yihang Lv ◽

Xiaomeng Zhang ◽

Ruoyu Cao

Keyword(s):

Band Gap ◽

Loss Factor ◽

Electromagnetic Waves ◽

Matrix Theory ◽

Symmetric System ◽

Propagation Characteristics ◽

Electromagnetic Propagation ◽

Transmission Coefficients ◽

Gain And Loss ◽

Incident Waves

AbstractIn this study, the propagation characteristics of electromagnetic waves in a parity-time (PT)-symmetrical 1D photonic crystal comprising dispersed silver layers are investigated. Based on the transmission matrix theory, the total reflection and transmission coefficients of the structure are obtained. It was found that, due to the PT-symmetrical structure, the reflections of the left and right incident waves are nonreciprocal. Numerical simulations indicated that the width of the band gap decreases with the increase in the gain and loss factor ρ in the PT medium, and the band gap ultimately disappears when ρ reaches a critical value, i. e., ${\rho }_{PT}$. With the increase in $\rho { >}{\rho }_{PT}$, anomalous transmittance and reflection occur within the original bang gap. As the gain and loss factor ρ continue to increase, the abnormal transmittance and reflectivity exhibit a trend of oscillatory decline, and perfect transmission can be achieved at larger values of ρ.

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ELECTRONIC STRUCTURE OF GRAPHENE NANORIBBONS SUBJECTED TO TWIST AND NONUNIFORM STRAIN

International Journal of High Speed Electronics and Systems ◽

10.1142/s0129156411006489 ◽

2011 ◽

Vol 20 (01) ◽

pp. 153-160 ◽

Cited By ~ 1

Author(s):

A. DOBRINSKY ◽

A. SADRZADEH ◽

B. I. YAKOBSON ◽

J. XU

Keyword(s):

Band Gap ◽

Density Functional ◽

Graphene Nanoribbons ◽

Tight Binding ◽

Tight Binding Approximation ◽

Functional Theory ◽

Gap Opening ◽

Gap Creation ◽

Band Gap Modulation ◽

Twisted Graphene

Graphene nanoribbons exhibit band gap modulation when subjected to strain. While band gap creation has been theoretically investigated for uniaxial strains, other deformations such as nanoribbon twist have not been considered. Our main objective in this paper is to explore band gap opening in twisted graphene nanoribbons that have metallic properties under tight-binding approximation. While simple considerations based on the Hückel model allow to conclude that zigzag graphene nanoribbons exhibit no band gap when subjected to twist, the Hückel model overall may be inaccurate for band gap prediction in metallic nanoribbons. We utilize Density Functional Theory Tight-Binding Approximation together with a requirement that energy of twisted nanoribbons is minimized to evaluate band gap of metalic armchair nanoribbons. Besides considering twisting deformations, we also explore the possibility of creating band gap when graphene nanoribbons are subject to inhomogeneous deformation such as sinusoidal deformations.

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Tight-Binding Calculation of the Electronic Structure of Semiconductor Nanocrystals

MRS Proceedings ◽

10.1557/proc-272-217 ◽

1992 ◽

Vol 272 ◽

Cited By ~ 1

Author(s):

P. E. Lippens ◽

M. Lannoo

Keyword(s):

Experimental Data ◽

Electronic Structure ◽

Band Gap ◽

Density Of States ◽

Semiconductor Nanocrystals ◽

Tight Binding ◽

Band Gap Energy ◽

Tight Binding Approximation ◽

Gap Energy

ABSTRACTWe show that an empirical tight-binding approximation can be used for the determination of some electronic properties of semiconductor nanocrystals. Two different calculations based on this approximation are presented. The first calculation concerns the band-gap energy and the second one the density of states. The results are given for different II-VI compounds and compared to available experimental data.

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