Related papers: Atomic limit and inversion-symmetry indicators for…
We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the…
Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned…
Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter…
Using a prototype model for proximity induced superconductivity on a bilayer square lattice, we show that interlayer tunneling can drive change in topology of the Bogoliubov quasiparticle bands. Starting with topologically trivial…
Topology is a central notion in the classification of band insulators and characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being…
In this manuscript, we derive symmetry indicator formulas for the filling anomaly on 2D square lattices with and without time reversal, inversion symmetry, or their product, in the presence of spin-orbit coupling. We go beyond previous work…
We show that the complex phase diagram of high $T_c$ superconductors can be deduced from a simple symmetry principle, a $SO(5)$ symmetry which unifies antiferromagnetism with $d$ wave superconductivity. We derive the approximate $SO(5)$…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…
We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that…
Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates…
Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-two and four period-eight cycles,…
In this letter, we investigate topological phases of full-gapped odd-parity superconductors, which are distinguished by the bulk topological invariants and the topologically protected gapless boundary states. Using the particle-hole…
We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. To date, such a database for topological…
The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…