We extend the theory of dipole moments in crystalline insulators to higher multipole
moments. As first formulated in Benalcazar et al.[Science 357, 61 (2017) SCIEAS 0036-8075 …

Second-order topological insulators are crystalline insulators with a gapped bulk and
gapped crystalline boundaries, but with topologically protected gapless states at the …

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry
in two and three dimensions (d= 2, 3). We show that in both cases nontrivial topology is …

A second-order topological insulator in d dimensions is an insulator which has no d-1
dimensional topological boundary states but has d-2 dimensional topological boundary …

Higher-order topological phases in crystalline and non-crystalline systems: a review Page 1
Journal of Physics: Condensed Matter ACCEPTED MANUSCRIPT • OPEN ACCESS Higher-order …

Second-order topological insulators and superconductors have a gapped excitation
spectrum in bulk and along boundaries, but protected zero modes at corners of a two …

We study the bulk-boundary correspondence for topological crystalline phases, where the
crystalline symmetry is an order-two (anti) symmetry, unitary or antiunitary. We obtain a …

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the
surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points …

We introduce two-dimensional topological insulators in proximity to high-temperature
cuprate or iron-based superconductors as high-temperature platforms of Majorana Kramers …

Conventional topological superconductors are fully gapped in the bulk but host gapless
Majorana modes on their boundaries. We instead focus on a new class of superconductors …