Related papers: Wavefunction tomography of topological dimer chain…
Periodic driving is a powerful tool to generate exotic topological phases without static counterparts, such as the anomalous chiral edge modes from bulk bands with zero Chern number and topological $\pi$ modes exhibiting period-doubled…
The topological properties of open quantum lattice systems have attracted much attention, due to their fundamental significance and potential applications. However, experimental demonstrations with large-scale lattice models remain…
One-dimensional superlattices with modulated coupling constants show rich topological properties and tunable edge states. Beyond the dimeric case, probing the topological properties of superlattices is a challenge. Here we suggest a rather…
We explore topology-localization phase diagram by simulating one-dimensional Su-Schrieffer-Heeger (SSH) model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping amplitudes can induce a series of bulk energy gap openings in the…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
The emergence of complex spectra in non-Hermitian systems causes dramatic changes even under weak perturbations, significantly hindering their precise control for study and integration into practical applications. Achieving a controlled…
We employ two Tight-Binding (TB) approaches to study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of $N$ monomers (base pairs): (I) at the base-pair level, using the on-site…
The Su-Schrieffer-Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer $trans$-polyacetylene, provides perhaps the most basic model system supporting topological excitations. The…
Topological metamaterials promise unprecedented wave control. Here, we theoretically and numerically investigate a one-dimensional Su-Schrieffer-Heeger (SSH) inspired stiffness dimer modified with a local resonator, which imparts a…
Synthetic dimensions based on particles' internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological…
We suggest and experimentally realize a spectral photonic lattice - a signal can hop between discrete frequency channels, driven by nonlinear interaction with stronger pump lasers. By controlling the complex envelope and frequency…
A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…
Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as…
The question of whether the topological insulators can host a stable nontrivial phase in the presence of spatially correlated disorder is a fundamental question of interest. Based on theoretical investigations, we analyze the effect of…
The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of `vortex' Bloch states and a Wannier-like…
We consider the scattering of in-plane waves that interact with an edge of a structured {penetrable (inertial)} line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods.…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…
Topological edge states typically arise at the boundaries of topologically nontrivial structures or at interfaces between regions with differing topological invariants. When topological systems are extended into the nonlinear regime, linear…