Generation of higher-order topological insulators using periodic driving

• Published in: Journal of physics. Condensed matter 2024-03, Vol.36 (9), p.93001
• Main Authors: Ghosh, Arnob Kumar, Nag, Tanay, Saha, Arijit
• Format: Article
• Language: English
• Subjects: Floquet systems; generation; higher-order; insulators; periodic; topological
• ISSN: 0953-8984; 1361-648X; 1361-648X
• DOI: 10.1088/1361-648X/ad0e2d

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensions d  > 1. These HOTIs possess ( d − 1 ) -dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, an n th order d -dimensional higher-order TI is characterized by the presence of boundary modes that reside on its d c = ( d − n ) -dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized by d c = 1 ( 0 ) . Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states ( d c = 0 ). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalous π -modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- and π corner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.