Related papers: Topological inverse band theory in waveguide quant…
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the…
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have…
We investigate the spectrum of finite-length carbon nanotubes in the presence of onsite and nearest-neighbor superconducting pairing terms. A one-dimensional ladder-type lattice model is developed to explore the low-energy spectrum and the…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
We classify the topology of bands defined by the energy states of quantum systems with scale separation between slow and fast degrees of freedom, invariant under fermionic time reversal. Classical phase space transforms differently from…
Twisted bilayer MoTe$_2$ is a promising platform to investigate the interplay between band topology and many-body interaction. We present a theoretical study of its interaction-driven quantum phase diagrams based on a three-orbital model,…
In moir\'e materials with flat electronic bands and suitable quantum geometry, strong correlations can give rise to novel topological states of matter. The nontrivial band topology of twisted molybdenum ditelluride (tMoTe$_2$) --…
We present a methodology to perform inverse analysis on reconfigurable topological insulators for flexural waves in plate-like structures. First the unit cell topology of a phononic plate is designed, which offers two-fold degeneracy in the…
We explore the gapless topological phases of a $p$-wave superconductor, probing its rich topologically ordered phases and underlying quantum phenomena. The topological order of the system is characterized by studying its entanglement…
We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest set-up of two qubits,…
Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been…
We show that in quantum Hall systems at half-filling, edge potentials alone can drive transitions between the Pfaffian and anti-Pfaffian topological phases. We conjecture this is true in realistic systems even in the presence of weak bulk…
We investigate an interesting interplay of destructive interference due to lattice geometry and band folding due to enlargement of the Brillouin zone in generating and subsequently modifying the band topology in a twisted bilayer…
Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…
Stacking and twisting atom-thin sheets create superlattice structures with unique emergent properties, while tailored light fields can manipulate coherent electron transport on ultrafast timescales. The unification of these two approaches…
Topological physics and strong electron-electron correlations in quantum materials are typically studied independently. However, there have been rapid recent developments in quantum materials in which topological phase transitions emerge…
Topological boundary modes utilizing valley mode waveguides have opened opportunities in, for instance, the design of high transmission waveguides with tolerance to geometrical defects and sharp bends. Applications of these waveguides…
We propose a concrete application of the Atiyah-Singer index formula in molecular physics, giving the exact number of levels in energy bands, in terms of vector bundles topology. The formation of topologically coupled bands is demonstrated.…