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Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
We study the interplay between topological and conventional long range order of attractive fermions in a time reversal symmetric Hofstadter lattice using quantum Monte Carlo simulations, focussing on the case of one-third flux quantum per…
Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting…
Heavy fermion materials naturally combine strong spin-orbit interactions and electronic correlations. When there is precisely one conduction electron per impurity spin, the coherent heavy fermion state is insulating. This Kondo insulating…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…
Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moir\'e materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions…
Interfaces between normal and topological insulators are bound to host metallic states that are protected by time-reversal symmetry and are therefore robust against disorder and interface reconstruction. Two-dimensional topological…
In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state…
Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for…
We theoretically investigate a tight binding model of fermions hopping on the square-octagon lattice which consists of a square lattice with plaquette corners themselves decorated by squares. Upon the inclusion of second neighbor spin-orbit…
Physical phenomena driven by topological properties, such as the quantum Hall effect, have the appealing feature to be robust with respect to external perturbations. Lately, a new class of materials has emerged manifesting their topological…
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He$_3$, where vortices are associated with low energy excitations in…
Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility…
Conventional wisdom holds that, in the simplest time-reversal-symmetric setting, strongly coupling two QSH layers yields a trivial $\mathbb Z_2$ phase and no protected topological edge states. We demonstrate that, in a regime with…
The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators,…
The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…
e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
We present an example for the phase transition between a topological non-trivial solid phase and a trivial solid phase in the quantum dimer model(QDM) on triangular lattice. Such a transition is beyond the Landau's paradigm of phase…