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We study a simple model of interacting bosons on a d-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal…
The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models…
Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some…
We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the $p_x$- and $p_y$-orbital bands in the honeycomb lattice. The multiorbital structure allows the…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
Spin-orbit interaction affects the band structure of topological insulators beyond the opening of an inverted gap in the bulk bands, and the understanding of its effects on the surface states is of primary importance to access the…
In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an {\em octopole} coupling between two neighboring…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
Topological photonics provides a new degree of freedom to robustly control electromagnetic fields. To date, most of established topological states in photonics have been employed in Euclidean space. Motivated by unique properties of…
When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect \cite{Klitzing,Tsui} dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted…
We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling,…
The large spin orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin-orbit torque on proximal magnetic moments…
Mobile holes in an antiferromagnetic insulator form a slowly fluctuating array of quasi one-dimensional metallic stripes, which induce a spin gap or pseudogap in the intervening Mott-insulating regions. The mobile holes on an individual…
In condensed matter physics, various mechanisms give rise to distinct insulating phases. The competition and interplay between these phases remain elusive, even for the seemingly most distinguishable band and Mott insulators. In multilayer…
The quadrupole insulator is a well-known instance of higher-order topological insulators in two dimensions, which possesses midgap corner states in both the energy spectrum and entanglement spectrum. Here, by constructing and exploring a…