Higher-Order Band Topology in Twisted Moiré Superlattice

Abstract

The two-dimensional (2D) twisted bilayer materials with van der Waals coupling have ignited great research interests, paving a new way to explore the emergent quantum phenomena by twist degree of freedom. Generally, with the decreasing of twist angle, the enhanced interlayer coupling will gradually flatten the low-energy bands and isolate them by two high-energy gaps at zero and full filling, respectively. Although the correlation and topological physics in the low-energy flat bands have been intensively studied, little information is available for these two emerging gaps. In this Letter, we predict a 2D secondorder topological insulator (SOTI) for twisted bilayer graphene and twisted bilayer boron nitride in both zero and full filling gaps. Employing a tight-binding Hamiltonian based on first-principles calculations, three unique fingerprints of 2D SOTI are identified, that is, nonzero bulk topological index, gapped topological edge state, and in-gap topological corner state. Most remarkably, the 2D SOTI exists in a wide range of commensurate twist angles, which is robust to microscopic structure disorder and twist center, greatly facilitating the possible experimental measurement. Our results not only extend the higher-order band topology to massless and massive twisted moiré superlattice, but also demonstrate the importance of high-energy bands for fully understanding the nontrivial electronics.

Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates

“…Until now, SOTIs have only been realized in 3D bismuth single crystal [18] and some artificial systems [19][20][21][22][23][24][25][26][27][28][29][30]. In addition, in the literature there are a few theoretical material proposals for 3D and 2D SO-TIs [31][32][33][34][35][36][37][38][39][40][41]. However, a simple and feasible program to achieve SOTI with abundant real material candidates is still absent, which greatly impeded the experimental and further theoretical studies on SOTIs, especially for 2D.…”

Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide

“…In a d-dimensional (dD) topological insulator, a topologically non-trivial bulk band structure implies the existence of (d − 1)D boundary states. Instead, a dD second-order topological insulator (SOTI) exhibits (d − 2)D topological states [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For example, there are symmetry protected corner states with localized fractional charge in a 2D SOTI [4, 5, 7-11, 15, 16].…”

“…In 2017, the concept of higher-order topological insulators is introduced and characterized by quantized multipole [4]. SOTIs and their corner states are investigated in systems with electronic quadruples [8][9][10][14][15][16]. Further in 2018, Ezawa further proposed that the electronic dipole could also induce second-order corner states in a breathing kagome model [5,7,17].…”

Transport features of topological corner states in honeycomb lattice with multihollow structure

“…In 2-dimensional (2D) systems, the second order topological phases are characterized by 0D in-gap corner states, while a 3D HOTI may host 1D gapless hinge states or in-gap corner states 5 . Up to now, HOTIs have been reported in various systems [9][10][11][12][13][14][15][16][17] , including quasicrystals [18][19][20] and Anderson insulators 21,22 .…”