Related papers: Topological states from topological crystals

Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…

In topological crystalline insulators the topological conducting surface states are protected by crystal symmetry, in principle making it possible to pattern nanoscale insulating and conductive motifs solely by breaking local symmetries on…

Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended-states in two-dimensional (2D) quantum Hall…

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five…

It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the…

Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…

A crystalline topological phase is a topological phase with spatial symmetries. In this work, we give a very general physical picture of such phases: a topological phase with spatial symmetry $G$ (with internal symmetry $G_{\mathrm{int}}…

Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…

Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: `higher-order symmetry protected topological (HOSPT) phases'. While the usual (1st-order) SPT phases in d…

Rich topological phenomena, edge states and two types of corner states, are unveiled in a two-dimensional square-lattice dielectric photonic crystal without both $C_4$ and $M_{x(y)}$ symmetries. Specifically, non-trivial type-I corner…

Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although…

A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…

Confined electronic states and optical transitions in 3D topological insulator nanoparticles have been studied in the literature, assuming idealized geometries such as spheres or infinitely long cylinders, that allow to obtain analytical…

We discuss the relation between particle number conservation and topological phases. In four spatial dimensions, we find that systems belonging to different topological phases in the presence of a U(1) charge conservation can be connected…

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…

A band gap for electronic states in crystals governs various properties of solids, such as transport, optical and magnetic properties. Its estimation and control have been an important issue in solid state physics. The band gap can be…

We classify time-reversal breaking (class A) spinful topological crystalline insulators with crystallographic non-magnetic (32 types) and magnetic (58 types) point groups. The classification includes all possible magnetic topological…

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a…