Dr. Bogdan OSTAHIE

We theoretically study the 2D Su-Schrieffer-Heeger model in the context of Floquet topological insulators (FTIs). FTIs are systems which undergo topological phase transitions, governed by Chern numbers, as a result of time reversal symmetry (TRS) breaking by a time periodic process. In our proposed model, the condition of TRS breaking is achieved by circularly polarized light irradiation. We analytically show that TRS breaking is forbidden in the absence of second order neighbors hopping. In the absence of light irradiation, we identify a symmetry-protected degeneracy and prove the appearance of a flat band along a specific direction in the momentum space. Furthermore, we employ a novel method to show that the four unit cell atoms, in the absence of irradiation, can be interpreted as conserved spin states. With the breaking of TRS via light irradiation, these spin states are no longer conserved, leading to the emergence of chiral edge states. We also show how the interplay between the TRS breaking and dimerization leads to some complex topological phase transitions. The validity of our findings is substantiated through Chern numbers, spectral properties, localization of chiral edge states and simulations of quantum Hall transport. Our model is suitable not only for condensed matter (materials), but also for cold gases trapped in optical lattices or topolectrical circuits.

We investigate the energy spectrum and transport properties of a diatomic square lattice model that manifest antichiral characteristics. The emergence of antichiral edge states is primarily governed by the relative sign of the next-nearest-neighbor hopping parameters on the two sublattices. However, in finite systems, the atomic structure at the boundaries plays a crucial role in determining whether the system exhibits chiral/antichiral behavior. Using both analytical and numerical methods, we reveal the presence of antichiral edge states in ribbon geometries and emphasize the importance of atomic connectivity at the edges. Extending our analysis, we simulate various finite size geometries to identify which configuration supports antichiral behavior. The transport properties are studied in the Landauer-B & uuml;ttiker approach for a Hall device with four leads. We study the transmittance coefficients, transverse (Hall), and longitudinal resistance by comparing the antichiral versus chiral situations. In particular, the antichiral case shows a vanishing Hall effect and negative longitudinal resistance. The presence of the bulk currents is proved by calculating explicitly the currents on the plaquette and the local density of states in the system with leads. Additionally, we investigate the influence of Anderson disorder on the transmittance coefficients to highlight the reduced robustness of antichiral systems.

We investigate the second-order Floquet topological (SOFT) phase transitions, from the perspective of spatial symmetries. In this respect, we consider a generic honeycomb lattice Floquet topological insulator (FTI), realized by circularly polarized light irradiation, in the presence of spin-orbit coupling (Kane-Mele model). We find that our studied FTI presents chiral symmetry on a preferential direction in Fourier space, the same property that protects the topological phases in the Su-Schrieffer-Heeger (SSH) model. Thus we were allowed to characterize the SOFT phases in terms of mirror-graded winding numbers (Zak phase). Moreover, our model exhibits C2 and C3 symmetry in Fourier space, a property which lead us to investigate two finite structures having the aforementioned symmetries, namely, rhombic and triangular shapes. Indeed, we find that both of them undergo SOFT phase transitions, characterized by the appearance of 0D corner states symmetrically localized over the whole sheet. Finally, we investigate the C2 and C3 symmetry breaking. Interestingly, we reveal that the corner states are not destroyed, but localize at preferential corners instead, giving rise to a corner polarization.

We investigate the transport and energy spectrum properties of a three-dimensional high-order topological structure formed by stacking two-dimensional square diatomic Chern insulator lattices. Electron-hole symmetry and the energy spectrum degeneracy at individual points in the semimetallic phase are proven to be due to chiral and antiunitary symmetries in the periodic system. Additionally, we explore the influence of boundary conditions in a slab system with varying surface atom connectivity, and we demonstrate analytically the presence of zero-energy surface states in specific configurations. Moreover, we describe the emergence of two chiral hinge states driven by a perpendicular phase in the nanowire geometry. Next, the quantum Hall resistance is computed in the cross-configuration of a four-lead device. In this paper, we demonstrate that the trajectories of hinge states, determined by the number of layers in parallelepiped finite structure, give rise to fractional Hall plateaus.

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting N particles with multiple flavors in the interacting SU(N) Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the N-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.

We theoretically investigate the spectral and quantum transport properties of two-dimensional heterostructures build up of different topological materials. Surprising behavior arises due to particular tuning of the edge states, provided by internal symmetries or an external magnetic field, in the different constituents of the heterostructure. Specifically, we use the Chern-type topological insulator and the Weyl semimetals with one or two interfaces interposed between these systems. The energy spectrum may contain gaps which exhibit edge states of alternating chirality or, on the contrary, of a given chirality everywhere in the spectrum. Then, the calculation predicts that the quantum Hall effect may lack the negative plateaus or show asymmetric plateaus in the lower and upper part of the spectrum. Also, the channel distribution on the finite size system with interfaces and attached leads may give rise to fractional values of the quantum Hall resistance. The calculations are based on a diatomic lattice model, with hopping to the nearest-and next-nearest-neighbors, exposed to an internal periodic flux (of Haldane-type), and also to an external magnetic field.

We investigate topological and disorder effects in non-Hermitian systems with chiral symmetry. The system under consideration consists in a finite Su-Schrieffer-Heeger chain to which two semi-infinite leads are attached. The system lacks the parity-time and time-reversal symmetries and is appropriate for the study of quantum transport properties. The complex energy spectrum is analyzed in terms of the chain-lead coupling and chiral disorder strength, and shows substantial differences between chains with even and odd number of sites. The mid-gap edge states acquire a finite lifetime and are both of topological origin or generated by a strong coupling to the leads. The disorder induces coalescence of the topological eigenvalues, associated with exceptional points and vanishing of the eigenfunction rigidity. The electron transmission coefficient is approached in the Landauer formalism, and an analytical expression for the transmission in the range of topological states is obtained. Notably, the chiral disorder in this non-Hermitian system induces unitary conductance enhancement in the topological phase. (C) 2020 Elsevier B.V. All rights reserved.

We investigate the spectral and transport properties of a diatomic square lattice with hopping to the next-nearest-neighbors and broken time-reversal symmetry, which behaves as a Chern insulator. In a finite-size approach, the attention is paid to the formation of chiral edge states in the topological insulating phase, but also in the semimetallic one. The edge states are revealed in the ribbon and plaquette geometries by analytical and numerical methods, significant differences being produced by the specific atomic connectivity at the boundary. The Hall resistance R-H is calculated in the plaquette geometry using the Landauer-Mittiker approach. The chiral edge states located in the unique gap of the energy spectrum manifest themselves by quantized values R-H = +/- h/e(2) specific to the Chern insulator. The semimetallic system containing chiral edge states embedded in the quasicontinuum of bulk states shows a disorder-driven AQHE as a consequence of the Anderson localization process.

Herein, the spectral and transport properties in the finite phosphorene lattice are investigated using the tight-binding model in the presence of Anderson disorder potential. The focus is on the zig-zag edge states localization, provided by the numerically calculated inverse participation number. At low disorder, the zig-zag states undergo a localization process, keeping their 1D character, while further increasing the disorder leads to delocalization due to hybridization with the extended 2D states. The disorder-induced changes in the electronic conductance, from one zig-zag edge to the other, are also discussed.

Spectral and transport properties of electrons in confined phosphorene systems are investigated in a five hopping parameter tight-binding model, using analytical and numerical techniques. The main emphasis is on the properties of the topological edge states accommodated by the quasiflat band that characterizes the phosphorene energy spectrum. We show, in the particular case of phosphorene, how the breaking of the bipartite lattice structure gives rise to the electron-hole asymmetry of the energy spectrum. The properties of the topological edge states in the zigzag nanoribbons are analyzed under different aspects: degeneracy, localization, extension in the Brillouin zone, dispersion of the quasiflat band in magnetic field. The finite-size phosphorene plaquette exhibits a Hofstadter-type spectrum made up of two unequal butterflies separated by a gap, where a quasiflat band composed of zigzag edge states is located. The transport properties are investigated by simulating a four-lead Hall device (importantly, all leads are attached on the same zigzag side), and using the Landauer-Buttiker formalism. We find out that the chiral edge states due to the magnetic field yield quantum Hall plateaus, but the topological edge states in the gap do not support the quantum Hall effect and prove a dissipative behavior. By calculating the complex eigenenergies of the non-Hermitian effective Hamiltonian that describes the open system (plaquette+leads), we prove the superradiance effect in the energy range of the quasiflat band, with consequences for the density of states and electron transmission properties.

We develop a manifest non-Hermitian approach of spectral and transport properties of two-dimensional mesoscopic systems in a strong magnetic field. The finite system to which several terminals are attached constitutes an open system that can be described by an effective Hamiltonian. The lifetime of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quantum Hall effect, and superradiant. The discussion is carried on in terms of edge state lifetime in different gaps, channel formation, role of hybridization, and transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.

We investigate the properties of Dirac electrons in a finite graphene sample under a perpendicular magnetic field that emerge when an in-plane electric bias is also applied. The numerical analysis of the Hofstadter spectrum and of the edge-type wave functions evidence the presence of shortcut edge states that appear under the influence of the electric field. The states are characterized by a specific spatial distribution, which follows only partially the perimeter, and exhibit ridges that connect opposite sides of the graphene plaquette. Two kinds of such states have been found in different regions of the spectrum, and their particular spatial localization is shown along with the diamagnetic moments that reveal their chirality. By simulating a four-lead Hall device, we investigate the transport properties and observe unconventional plateaus of the integer quantum Hall effect that are associated with the presence of the shortcut edge states. We show the contributions of the novel states to the conductance matrix that determine the new transport properties. The shortcut edge states resulting from the splitting of the n = 0 Landau level represent a special case, giving rise to nontrivial transverse and longitudinal resistance.

We address theoretically the electronic transport through graphene quantum dots with the emphasis on the transmission phase. Analytical and numerical results are presented regarding the existence - or not - of a lapse of the transmittance phase (and, consequentially, a Fano zero in the transmittance) at the charge neutrality point. A simple universal criterium is found, the phase lapses being always present if the contact sites belong to the same sub-lattice. ((c) 2014 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim)

We study the electronic properties of the confined honeycomb lattice in the presence of the intrinsic spin-orbit (ISO) interaction and perpendicular magnetic field, and report on uncommon aspects of the quantum spin Hall conductance corroborated by peculiar properties of the edge states. The ISO interaction induces two specific gaps in the Hofstadter spectrum, namely the "weak" topological gap defined by Beugeling et al. [Phys. Rev. B 86, 075118 (2012)], and spin-imbalanced gaps in the relativistic range of the energy spectrum. We analyze the evolution of the helical states with the magnetic field and with increasing Anderson disorder. The "edge" localization of the spin-dependent states and its dependence on the disorder strength is shown. The quantum transport, treated in the Landauer-Buttiker formalism, reveals interesting new plateaus of the quantum spin Hall effect (QSHE), and also of the integer quantum Hall effect (IQHE), in the energy ranges corresponding to the spin-imbalanced gaps. The properties of the spin-dependent transmittance matrix that determine the symmetries with respect to the spin, energy, and magnetic field of the longitudinal and transverse resistance are shown.

The specific topology of the line-centered square lattice (known also as the Lieb lattice) induces remarkable spectral properties such as the macroscopically degenerated zero-energy flat band, the Dirac cone in the low-energy spectrum, and the peculiar Hofstadter-type spectrum in a magnetic field. We study here the properties of the finite Lieb lattice with periodic and vanishing boundary conditions. We investigate the behavior of the flat band induced by disorder and external magnetic and electric fields. We show that in the confined Lieb plaquette threaded by a perpendicular magnetic flux there are edge states with nontrivial behavior. The specific class of twisted edge states, which have alternating chirality, are sensitive to disorder and do not support integer quantum Hall effect (IQHE), but contribute to the longitudinal resistance. The symmetry of the transmittance matrix in the energy range where these states are located is revealed. The diamagnetic moments of the bulk and edge states in the Dirac-Landau domain, and also of the flat states in crossed magnetic and electric fields are shown. DOI: 10.1103/PhysRevB.87.125428

Persistent, oscillatory charge and spin currents are shown to be driven by a two-component terahertz laser pulse in a one-dimensional mesoscopic ring with Rashba and Dresselhaus spin-orbit interactions (SOI) linear in the electron momentum. The characteristic interference effects result from the opposite precession directions imposed on the electron spin by the two SOI couplings. The time dependence of the currents is obtained by solving numerically the equation of motion for the density operator, which is later employed in calculating statistical averages of quantum operators on few electron eigenstates. The parameterization of the problem is done in terms of the SOI coupling constants and of the phase difference between the two laser components. Our results indicate that the amplitude of the oscillations is controlled by the relative strength of the two SOI's, while their frequency is determined by the difference between the excitation energies of the electron states. Furthermore, the oscillations of the spin current acquire a beating pattern of higher frequency that we associate with the nutation of the electron spin between the quantization axes of the two SOI couplings. This phenomenon disappears at equal SOI strengths, whereby the opposite precessions occur with the same probability. (c) 2012 Elsevier B.V. All rights reserved.

The phase of the electronic wave function is not directly measurable but, quite remarkably, it becomes accessible in pairs of isospectral shapes, as recently proposed in the experiment by Moon et al. [Science 319, 782 (2008)]. The method is based on a special property, called transplantation, which relates the eigenfunctions of the isospectral pairs, and allows us to extract the phase distributions, if the amplitude distributions are known. We numerically simulate such a phase extraction procedure in the presence of disorder, which is introduced both as Anderson disorder and as roughness at edges. With disorder, the transplantation can no longer lead to a perfect fit of the wave functions, however we show that a phase can still be extracted-defined as the phase that minimizes the misfit. Interestingly, this extracted phase coincides with (or differs negligibly from) the phase of the disorder-free system, up to a certain disorder amplitude, and a misfit of the wave functions as high as similar to 5%, proving a robustness of the phase extraction method against disorder. However, if the disorder is increased further, the extracted phase shows a puzzle structure, no longer correlated with the phase of the disorder-free system. A discrete model is used, which is the natural approach for disorder analysis. We provide a proof that discretization preserves isospectrality and the transplantation can be adapted to the discrete systems.

When subjected to a linearly polarized terahertz pulse, a mesoscopic ring endowed with spin-orbit interaction (SOT) of the Rashba-Dresselhaus type exhibits non-uniform azimuthal charge and spin distributions. Both types of SOT couplings are considered linear in the electron momentum. Our results are obtained within a formalism based on the equation of motion satisfied by the density operator which is solved numerically for different values of the angle 0, the angle determining the polarization direction of the laser pulse. Solutions thus obtained are later employed in determining the time-dependent charge and spin currents, whose values are calculated in the stationary limit. Both these currents exhibit an oscillatory behavior complicated in the case of the spin current by a beating pattern. We explain this occurrence on account of the two spin-orbit interactions which force the electron spin to oscillate between the two spin quantization axes corresponding to Rashba and Dresselhaus interactions. The oscillation frequencies are explained using the single particle spectrum.