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Topological phases can not only be protected by internal symmetries (e.g., time-reversal symmetry), but also by crystalline symmetries, such as reflection or rotation symmetry. Recently a complete topological classification of reflection…
A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry. The surface state can be gapped by introducing ferromagnetism to break time-reversal symmetry,…
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…
Topological semimetals, representing a new topological phase that lacks a full bandgap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a…
Topological insulators are a class of solids in which the nontrivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity scattering. In three-dimensional (3D) topological insulators, however,…
Three-dimensional higher-order topological semimetals in crystalline systems exhibit higher-order Fermi arcs on one-dimensional hinges, challenging the conventional bulk-boundary correspondence. However, the existence of higher-order Fermi…
The electronic band structure of iron pnictides exhibits four Dirac cones, which are due to crystal symmetry and orbital bonding orientation. This hallmark signature presents the pnictide family as an ideal candidate in the search for…
Although, the long-standing debate on the resistivity anomaly in ZrTe$_{5}$ somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk…
In the recently discovered topological crystalline insulators SnTe and Pb_{1-x}Sn_{x}(Te,Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
The unusual surface states of topological semimetals have attracted a lot of attention. Recently, we showed [PNAS 113, 8648 (2016)] that for a Dirac semimetal (DSM) arising from band-inversion, such as Na$_3$Bi and Cd$_3$As$_2$, the…
Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
We proposed that BaHgSn is a Dirac semimetal (DSM) which can host hourglass-like surface states (HSSs) as protected by nonsymmorphic glide symmetry. Compared to KHgSb, an isostructural topological crystalline insulator with the same HSSs,…
The tunability of topological surface states (SS) and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In topological crystalline insulators (TCIs), a spontaneously…
Weak topological insulators and Dirac semimetals are gapped and nodal phases with distinct topological properties, respectively. Here, we propose a novel topological phase that exhibits features of both and is dubbed composite Dirac…
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…
The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly-dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal…