Related papers: Topological Matter and Fractional Entangled Quantu…
A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the…
We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to…
Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is…
We use magnetotransport in dual-gated magnetic topological insulator heterostructures to map out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical potential (primarily determined by the…
The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are…
The quantum geometry, comprising Berry curvature and quantum metric, plays a fundamental role in governing electron transport phenomena in solids. Recent studies show that the quantum metric dipole drives scattering-free nonlinear Hall…
We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in both directions. When the difference between the two tilted fields is large, Bloch…
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $\nu=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in…
Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical…
Irradiation with light provides a powerful tool to interrogate, control or induce new quantum states of matter out of equilibrium, however a microscopic understanding of light-matter coupling in interacting electron systems remains a…
We investigate interference between topological interfacial modes in a semiconductor photonic crystal platform with Dirac frequency dispersions, which can be exploited for interferometry switch. It is showcased that, in a two-in/two-out…
The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
We report the entanglement of topological features, namely, isolated, linked optical vortex loops in the light from spontaneous parametric down-conversion (SPDC). In three dimensions, optical vortices are lines of phase singularity and…