Second-order topological phases protected by chiral symmetry

Abstract

We study second-order topological phases characterized by chiral symmetry in the absence of crystal symmetries. We investigate topological phase transitions of a model for the two-dimensional second-order topological insulators protected by chiral symmetry. By the theory of the phase transitions, we propose chiral-symmetric second-order topological semimetals. Various second-order topological semimetals can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry allows a topological phase transition from the second-order topological semimetal to a second-order topological insulator with chiral hinge states in the three-dimensional system. We also demonstrate the secondorder topological phases by using a lattice model.

Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator

“…The results are shown in Fig. 3(d (11) . Blue and red regions represent the edge bands and the bulk bands, respectively.…”

“…4(d). This indicates that as the corner-state energy approaches the edges of the edge band at E = ±0.9 and E = ±1.1 from inside the gaps, the penetration depth l (01) along the edge diverges toward infinity but that toward the bulk l (11) does not. Through this evolution of the corner state, it eventually becomes an edge state, and is absorbed into the edge bands, with its spatial distribution approaching that of an edge state.…”

“…Recently, a notion of higher-order topological insulators (HOTIs) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] has been proposed as an analogue to TIs. While TIs in d dimensions have (d − 1)-dimensional boundary states, HOTIs in d dimensions have (d − 2)-or (d − 3)dimensional boundary states.…”

Higher-Order Semimetals and Chiral Hinge States in Topolectrical Circuit Model

“…They are also applicable to the study of Majorana fermions which are actively being investigated for their applications to faulttolerant quantum computing [59]. This robust unidirectional property, in which current flow is allowed only one direction along a hinge, implies that a chiral hinge current excited at one hinge in a cuboid circuit cannot flow into another hinge situated diagonally opposite from the hinge being excited [60,64]. This property can therefore be exploited for robust topological signal multiplexing by utilizing the multiple discrete degrees of freedom in the system [61].…”

Classification of topological invariants related to corner states

“…Class AIII codimension-two systems are also studied through this method in [34] and, as an application to HOTIs, the appearance of topological corner states in Benalcazar-Bernevig-Hughes' 2-D model [12] is explained based on the chiral symmetry. The construction of examples in [34] leads to a proposal of second-order semimetallic phase protected by the chiral symmetry [52].…”