Nonlinear Dirac cones

Abstract

Physics arising from two-dimensional (2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such 2D Dirac cones are often characterized by a π Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a novel type of Dirac cones that are robust to local perturbations without symmetry restrictions. Due to a different pseudo-spin texture, the Berry phase of the Dirac cone is no longer quantized in π, and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm (AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be π both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different.We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase. *

Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

“…It is obtained by measuring the long-time average of chiral displacement operator Sn, where S is the unitary and Hermitian operator that defines the chiral symmetry of the system, andn is the unit cell position operator. The MCD was first proposed for 1d non-driven systems in the symmetry classes AIII and BDI [90], and later extended to Floquet systems [61,91], non-Hermitian systems [52,53] and systems in two dimensions [46]. In this work, we further extend the MCD to 1d Floquet systems in the symmetry class CII, and employ it to probe the topological phases of the PQSCL dynamically.…”

“…On application side, Floquet states have the potential of realizing setups with many topological transport channels [40][41][42] and creating new schemes of topological quantum computations [43][44][45]. In recent years, the study of Floquet topological matter has also been extended to higher-order topological models [46][47][48][49][50] and non-Hermitian systems [51][52][53][54][55][56][57][58].…”

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice

“…Theoretically, the hexagonal lattice is also amazing because it has two sites per unit cell (say, A-site and B-site), so this system can be described by the two-band model. Earlier studies [49,50] have shown that a self-crossing loop would exist in one-dimensional system and a nonlinear two-band model would develop a looped band structure. In the following, we will discuss the dependence of the looped structure [51,52] on the parameters of the system, and shed more light on the nonlinear Dirac cone (NDC) [50] in this two-dimensional system.…”

“…Earlier studies [49,50] have shown that a self-crossing loop would exist in one-dimensional system and a nonlinear two-band model would develop a looped band structure. In the following, we will discuss the dependence of the looped structure [51,52] on the parameters of the system, and shed more light on the nonlinear Dirac cone (NDC) [50] in this two-dimensional system. We find that there are two NDCs in the Brillouin Zone (BZ), and the phase acquired by adiabatically transporting the system on the lowest band around the two NDCs in the BZ is zero, while the phase acquired in the same processing is quantized around only one of the NDCs.…”

Topological Edge States and Gap Solitons in the Nonlinear Dirac Model

“…Introducing Kerr nonlinearity, using the soliton solution () we derive the edge states' nonlinear dispersion which undergoes a shift in the band gap . The valley Chern number formally stays the same as its linear counterpart until the upper band of nonlinear Bloch waves forms a self‐crossing loop at above‐threshold bulk intensities . Thereby, nonlinearity grants control over the frequency and transverse structure of the edge state as defined by .…”