Related papers: Bulk-Edge Correspondence for Finite Two-dimensiona…
The connected wedge theorem states that in order to have a scattering process in the bulk, it is necessary to have $O(1/G_N)$ mutual information between certain "decision" regions in the boundary theory. While this large mutual information…
We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact…
In a recent experiment, Young et al. [Nature {\bf 505}, 528 (2014)] observed a metal to insulator transition as well as transport through helical edge states in monolayer graphene under a strong, tilted magnetic field. Under such…
To clarify the relationship between edge electronic states in open-boundary crystalline systems and their corresponding bulk electronic structure, Alase et al. [Phys. Rev. Lett. 117, 076804 (2016)] have recently generalized Bloch's theorem…
To account for the anomalous/spin Hall conductivities and spin-orbit torque in the zeroth order of electron scattering time in strongly spin-orbit coupled systems, the Boltzmann transport theory in the case of weak disorder-potentials has…
Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the…
One of the most intriguing and fundamental properties of topological materials is the correspondence between the conducting edge states and the gapped bulk spectrum. So far, it has been impossible to access the full evolution of edge states…
The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined…
We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform…
Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the…
Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
It is well-known that the standard bulk-boundary correspondence does not hold for non-Hermitian systems in which also new phenomena such as exceptional points do occur. Here we study, mostly by analytical means, a paradigmatic…
The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder…
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a…
We consider random gradient fields with disorder where the interaction potential $V_e$ on an edge $e$ can be expressed as $e^{-V_e(s)} = \int \rho(\mathrm{d}\kappa)\, e^{-\kappa \xi_e} e^{-\frac{\kappa s^2}{2}}$. Here $\rho$ denotes a…
The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of…
The spin and integer quantum Hall effects are two cousins of topological phase transitions in two-dimensional electronic systems. Their close relationship makes it possible to transform spin to integer quantum Hall effect in two-dimensional…
We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band…
We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…