Related papers: Thouless Pumps and Bulk-Boundary Correspondence in…
We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion…
Nonlinear transport has emerged as a powerful approach to probe the quantum geometry of electronic wavefunctions, such as Berry curvature and quantum metric, in topological materials. While nonlinear responses governed by bulk quantum…
We demonstrate the existence of a conceptually distinct topological pumping phenomenon in one-dimensional chains undergoing topological adiabatic cycles. Specifically, for a stack of two semi-infinite chains cycled in opposite directions…
We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination…
The interplay between topology and soliton is a central topic in nonlinear topological physics. So far, most studies have been confined to conservative settings. Here, we explore Thouless pumping of dissipative temporal solitons in a…
We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
We introduce a class of intrinsic symmetry-protected topological mixed-state(mSPT) in open quantum systems that feature modulated symmetries, such as dipole and subsystem symmetries. Intriguingly, these mSPT phases cannot be realized as the…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
We study bulk-boundary correspondences and related surface phenomena stabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis…
Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order…
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 discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
A higher-order topological superconductor can experience topological phase transitions driven by variations in a bulk parameter without closing the bulk gap. This presents a challenge in establishing a direct bulk-boundary correspondence,…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk…
The interplay between nonlinear and topological physics has led to intriguing emergent phenomena, such as quantized and fractionally quantized Thouless pumping of solitons dictated by the topological invariants of the underlying band…
This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian,…
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a…
We investigate the dynamics of nonlinear optical Thouless pumps in the presence of disorder, using optical waveguide arrays. It was previously known that the displacement of solitons in Thouless pumps is quantized and may exhibit integer…