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In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been…
The possibility of realizing topological insulators by spontaneous formation of electronic superstructure is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a…
The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are…
Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry…
Transition metal dichalcogenide homobilayers unite two frontiers of quantum materials research: sliding ferroelectricity, arising from rhombohedral (R) stacking, and moir\'e quantum matter, emerging from small-angle twisting. The…
Surface states of a topological insulator demonstrate interesting quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the quantum magnetoelectric effect. Fermi energy tuning plays a role in inducing phase transitions and…
Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here…
Two-dimensional topological insulators possess two counter propagating edge channels with op- posite spin direction. Recent experimental progress allowed to create ferromagnetic topological insulators realizing a quantum anomalous Hall…
Ferroelectric higher-order topological insulators (HOTIs) exhibit tunable physical properties arising from the interplay between ferroelectric polarization and band topology. This work investigates the topological origin of two classes of…
We explore the emergence of topological phases in moir\'{e} MoTe$_2$/WSe$_2$ bilayer, highlighting the crucial role of spin-orbit coupling and Coulomb interactions at two holes per moir\'e unit cell \(v = 2\). Our analysis uncovers robust…
Two-dimensional (2D) topological insulators (TIs), also known as quantum spin Hall (QSH) insulators, are excellent candidates for coherent spin transport related applications because the edge states of 2D TIs are robust against nonmagnetic…
The wealth of complex polar topologies recently found in nanoscale ferroelectrics result from a delicate balance between the materials intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary…
The electronic states of a single Bi(111) bilayer and its edges, suggested as a two dimensional topological insulator, are investigated by scanning tunneling spectroscopy (STS) and first-principles calculations. Well-ordered bilayer films…
The quantum spin Hall insulators predicted ten years ago and now experimentally observed are instrumental for a breakthrough in nanoelectronics due to non-dissipative spin-polarized electron transport through their edges. For this transport…
The electric field induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor [1-4]. In this scheme an electric field can switch 'on' the ballistic…
Generally, stacking two quantum spin Hall insulators gives rise to a trivial insulator. Here, based on first-principles electronic structure calculations, we confirm that monolayer TaIrTe$_{4}$ is a quantum spin Hall insulator and…
The control of unconventional magnetism, which displays ferromagnetism-like properties with compensated magnetization, has drawn intense attention for advancing antiferromagnetic spintronics. Here, through symmetry analysis, we propose a…
We present a theoretical study of an interaction-driven quantum phase diagram of twisted bilayer MoTe$_2$ at hole filling factor $\nu_h=1$ as a function of twist angle $\theta$ and layer potential difference $V_z$, where $V_z$ is generated…
Quantum spin Hall insulators (QSHIs) and excitonic insulators (EIs) are prototypical topological and correlated states of matter, respectively. The topological phase transition between the two has attracted much theoretical interest but…
Topological crystalline insulators (TCIs) host topological phases of matter protected by crystal symmetries. Topological surface states in three-dimensional TCIs have been predicted and observed in IV-VI SnTe-class semiconductors. Despite…