Browsing by Subject "Topological insulators"
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Item Open Access Extensions of one-dimensional topological insulator models and their properties(Bilkent University, 2021-04) Pulcu, YetkinWe mainly study the SSH model, a one dimensional topological insulator. As a start, we give a brief introduction about the model and theoretically showed that it should have at least 2 distinct states using Jackiw-Rebbi model. Instead of us-ing only the periodic boundary conditions, we also use open boundary conditions which revealed the zero energy edge states. Introducing the spectral symmetries, we show how a given system can be characterized using the periodic table of topo-logical insulators [1] and depending on the symmetries we discuss which invariant can be used to determine different topological states. Using an enlarged system for a certain symmetry class Z, we show that polarization or Berry phase fails to distinguish different topological states. Subsequently, we implement a similar idea that Haldane used [2], breaking the time-reversal symmetry via introducing the complex next nearest neighbor hopping and find that the system is charac-terized by Z2 invariant. Moving away from the ”textbook” way of writing the Bloch states, we introduce the distance dependent SSH model where the distance between A and B sublattice is p/q with p and q are being co-primes. We find that the polarization can be found using the inversion symmetry of the wannier centers, which characterize the topological index. Plotting the curve in the pa-rameter space, we come to conclusion that Brillouin zone must be extended q times in order for the system to conserve its periodicity, which brings the knot behaviour of the curves that can be used to distinguish the topological state. At last, we make the SSH model spinful by introducing the time-reversal symmetry protecting Rashba spin-orbit coupling. Due to the Kramers’ theorem, degenerate states occur and non-Abelian Berry connection must be constructed to analyze the system. We find that Kato propagator is suitable and gauge invariant way of doing this and computed the time-reversal polarization of the system.Item Open Access First-principles study on structural, vibrational, elastic, piezoelectric, and electronic properties of the Janus BiXY (X= S, Se, Te and Y = F, Cl, Br, I) monolayers(American Physical Society, 2021-03-09) Varjovi, Mirali Jahangirzadeh; Durgun, EnginBroken inversion symmetry in atomic structure can lead to the emergence of specific functionalities at the nanoscale. Therefore, realizing 2D materials in Janus form is a growing field, which offers unique features and opportunities. In this paper, we investigate the structural, vibrational, elastic, piezoelectric, and electronic properties of Janus BiXY (X=S, Se, Te and Y=F, Cl, Br, I) monolayers based on first-principle methods. The structural optimization and vibrational frequency analysis reveal that all of the proposed structures are dynamically stable. Additionally, ab initio molecular dynamics simulations verify the thermal stability of these structures even at elevated temperatures. The mechanical response of the Janus BiXY crystals in the elastic regime is investigated in terms of in-plane stiffness and the Poisson ratio, and the obtained results ascertain their mechanical flexibility. The piezoelectric stress and strain coefficient analysis demonstrates the appearance of strong out-of-plane piezoelectricity, which is comparable with the Janus transition metal dichalcogenide monolayers. The calculated electronic band structures reveal that except for BiTeF, all Janus BiXY monolayers are indirect band gap semiconductors, and their energy band gaps span from the infrared to the visible part of the optical spectrum. Subsequently, large Rashba spin splitting is observed in electronic band structures when the spin-orbit coupling is included. The obtained results point out Janus 2D BiXY structures as promising materials for a wide range of applications in nanoscale piezoelectric and spintronics fields.Item Open Access Generalized Aubry-Andre-Harper model with modulated hopping and p-wave pairing(American Physical Society, 2019) Yahyavi, Mohammad; Hetenyi, Balazs; Tanatar, BilalWe study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.Item Open Access Optical properties and electronic band structure of topological insulators on A2 5B36 compound based(IEEE, 2012) Koc H.; Mamedov, Amirullah M.; Özbay, EkmelWe have performed a first principles study of structural, electronic, and optical properties of rhombohedral Sb 2Te 3 and Bi 2Te 3 compounds using the density functional theory within the local density approximation. The lattice parameters, bulk modulus, and its pressure derivatives of these compounds have been obtained. The linear photon-energy dependent dielectric functions and some optical properties such as the energy-loss function, the effective number of valance electrons and the effective optical dielectric constant are calculated and presented in the study © 2012 IEEE.Item Open Access Reentrant localization transition in a quasiperiodic chain(American Physical Society, 2021-03-09) Roy, S.; Mishra T., T.; Tanatar, Bilal; Basu S., S.Systems with quasiperiodic disorder are known to exhibit a localization transition in low dimensions. After a critical strength of disorder, all the states of the system become localized, thereby ceasing the particle motion in the system. However, in our analysis, we show that in a one-dimensional dimerized lattice with staggered quasiperiodic disorder, after the localization transition, some of the localized eigenstates become extended for a range of intermediate disorder strengths. Eventually, the system undergoes a second localization transition at a higher disorder strength, leading to all states being localized. We also show that the two localization transitions are associated with the mobility regions hosting the single-particle mobility edges. We establish this reentrant localization transition by analyzing the eigenspectra, participation ratios, and the density of states of the system.Item Open Access Structural, elastic, and electronic properties of topological insulators: Sb2Te3 and Bi2Te3(IEEE, 2013) Koc H.; Mamedov, Amirullah M.; Özbay, EkmelWe have performed a first principles study of structural, elastic, and electronic properties of rhombohedral Sb2Te3 and Bi 2Te3 compounds using the density functional theory within the local density approximation. The lattice parameters of considered compounds have been calculated. The second-order elastic constants have been calculated, and the other related quantities such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocities, and Debye temperature have also been estimated in the present work. The calculated electronic band structure shows that Sb2Te3 and Bi2Te 3 compounds have a direct forbidden band gap. Our structural estimation and some other results are in agreement with the available experimental and theoretical data. © 2013 IEEE.Item Open Access A study of the modern theory of polarization on extensions of one dimensional topological insulators and disordered systems(Bilkent University, 2021-12) Parlak, SelçukWe work on identifying topological and quantum phase transition via the modern theory of polarization. We go through the problem of electrostatics definition of absolute polarization via a discrete chain of anions and cations. We move from this discrete approach to a continuous one and prove the emergence of the Berry phase under adiabatic evolution. Introducing the Resta's position operator, we show the correspondence to the definition of polarization and go through the polarization distribution of the system. Using these concepts we studied band structures, topological invariants, and symmetries in the Su-Schrie er-Heeger model. With these basics, we analyzed the emergence of torus knots and its identification of topological transition on the distance-dependent SSH model. We go through the formal definitions of knot theory and how to identify them to establish a new system using Klein bottle knots. Following the distance vector structure in the distance-dependent SSH model, we try to establish a real-life system using Klein bottle parametrizations; Pinched torus, figure 8, and the bottle shape. In all of the parametrizations, the interpretation of the real-life system had hoppings on empty sites. Klein bottle knots are tried to observe via parametrizations of the Klein bottle. In all cases, due to the four-dimensional nature of the Klein bottle, we encountered intersecting curves on 3-dimensional interpretations of the Klein bottle. To understand the system better, we go through the Berry phase and dispersion relation of the system. After not encountering anything significant, we try to acquire a knot structure on fundamental polygons. We obtain a Hopf link and unlink with a possible intersection point. The intersection becomes hard to judge due to computational approximation on determining the knot diagrams. Due to the complexity of the project, we go through the Anderson model to study the modern theory of polarization. A background on Anderson localization with a computational method: Transfer matrix method is given. We state Mott's relation of conductivity and discuss the concept of mobility edge. We show the localization theory of Resta by introducing the complex number z. With this, we prove that the jzj becomes 1 when the states are localized and 0 when we have extended states. We also go through the scaling theory of localization. To understand the scaling theory, we introduce the concept of the renormalization group and discuss how this idea is used in the gang of four paper. We go through the assumptions and results of the gang of four by observing that the scaling exponent of conductance exhibits a critical value only in the three dimensions. Using Resta's quantity, we try to establish the gang of four results by examining the size scaling of the variance of polarization of the system and introducing a renormalization flow with Resta's quantity. We observe the low-temperature limit by examining a single state in the ground state. With this, we recover the results of the gang of four. Based on the discussion of Mott's on mobility edge, we further examine the high-temperature limit, where the system is in the average of all states. We identify the transition point via two fixed points(repulsive and attractive) on flow diagrams and size scaling exponent in all dimensions. We recover the behavior of the gang of four in one and three dimensions by examination of the fixed points, and we state the ambiguity of two-dimensional solutions due to the convergence problem of the fixed points. We further solidify the analogy of conductance and Resta's number by observing the Binder cumulant and analogical mobility edge of the system. We found the same repulsive fixed point on Binder cumulant and analogical behavior on the mobility edge argument.Item Open Access Topological insulator based locally resonant phononic crystals: wave propagation and acoustic band gaps(Taylor and Francis Inc., 2016) Oltulu, O.; Simsek S.; Mamedov, A. M.; Özbay, EkmelABSTRACT: In the present work the acoustic band structure of a two-dimensional phononic crystal (PC) containing an organic ferroelectric (PVDF- polyvinylidene fluoride) and topological insulator (Bi2Te3) were investigated by the plane-wave-expansion (PWE) method. Two-dimensional PC with square lattices composed of Bi2Te3 cylindrical rods embedded in the PVDF matrix are studied to find the existence of stop bands for the waves of certain energy. Phononic band diagram ω = ω(k) for a 2D PC along the Г-X-M-Г path in the square Brillouin zone show four stop bands in the frequency range 0.01–8.0 kHz.Item Open Access Topological Insulators: Electronic Band Structure and Spectroscopy(Institute of Physics Publishing, 2017) Palaz S.; Koc, H.; Mamedov, Aamirullah M.; Özbay, EkmelIn this study, we present the results of our ab initio calculation of the elastic constants, density of states, charge density, and Born effective charge tensors for ferroelectric (rhombohedral) and paraelectric phases (cubic) of the narrow band ferroelectrics (GeTe, SnTe) pseudopotentials. The related quantities such as bulk modulus and shear modulus using obtained elastic constants have also been estimated in the present work. The total and partial densities of states corresponding to the band structure of Sn(Ge)Te(S,Se) were calculated. We also calculated the Born effective charge tensor of an atom (for instance, Ge, Sn, Te, etc.), which is defined as the induced polarization of the solid along the main direction by a unit displacement in the perpendicular direction of the sublattice of an atom at the vanishing electric field. © Published under licence by IOP Publishing Ltd.Item Open Access Variational study of the interacting, spinless Su-Schrieffer-Heeger model(Institute of Physics Publishing, 2018) Yahyavi, Mohammad; Saleem, Luqman; Hetényi, BalazsWe study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution 'walks across' smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.