Related papers: Bulk-Boundary Correspondence for Topological Insul…

The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the…

The strong topological insulator in 3D is expected to realize a quantized magneto-electric response, the so-called axion response. However, many of the materials predicted to be topological insulators have turned out to be metallic, with…

The effect of boundaries and how these can be used to influence the bulk behaviour in geometrically frustrated systems are both long-standing puzzles, often relegated to secondary role. Here we use numerical simulations and "proof of…

In this work, we establish the bulk-edge correspondence principle for finite two-dimensional photonic structures. Specifically, we focus on the divergence-form operator with periodic coefficients and prove the equality between the…

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 insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…

The Chern-Hopf insulator is an unconventional three-dimensional topological insulator with a bulk gap and gapless boundary states without protection from global discrete symmetries. This study investigates its fate in the presence of…

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality:…

We present an ab initio relativistic k.p theory of the effect of magnetic exchange field on the band structure in the gap region of bulk crystals and thin films of three-dimensional layered topological insulators. For the field…

The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate…

We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of non-perturbative high-order harmonic generation from the…

The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT…

The indirect exchange interaction between local magnetic moments via surface electrons has been long predicted to bolster the surface ferromagnetism in magnetic topological insulators (MTIs), which facilitates the quantum anomalous Hall…

The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via…

We investigate the role of self-adjoint extensions in the bulk-edge correspondence for topological insulators. While the correspondence is well understood in discrete models with spectral gaps, complications arise in the presence of…

We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk scattering matrix elements and…

We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing…

The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which…

The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly…

Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological…