Magnon Hall effect on the Lieb lattice

Abstract

Ferromagnetic insulators without inversion symmetry may show magnon Hall effect (MHE) in the presence of a temperature gradient due to the existence of Dzyaloshinskii-Moriya interaction (DMI). In this theoretical study, we investigate MHE on a lattice with inversion symmetry, namely the Lieb lattice, where the DMI is introduced by adding an external electric field. We show the nontrivial topology of this model by examining the existence of edge states and computing the topological phase diagram characterized by the Chern numbers of different bands. Together with the topological phase diagram, we can further determine the sign and magnitude of the transverse thermal conductivity. The impact of the flat band possessed by this model on the thermal conductivity is discussed by computing the Berry curvature analytically.

Floquet topological magnons

“…The associated magnon bands in the magnetically ordered systems have a nontrivial topology with Chern number protected chiral magnon edge modes in two-dimensional (2D) systems and magnon surface states in three-dimensional (3D) systems. They are dubbed topological magnon Chern insulators [3][4][5][6][7][8][9] and Weyl magnons [10][11][12][13] respectively. They are the analogs of electronic topological (Chern) insulators [14][15][16] and Weyl semimetals [17][18][19].…”

Localized gap modes in nonlinear dimerized Lieb lattices

“…Seminal papers showed that interesting effects in condensed matter systems [14][15][16] are observed. Additionally, the influence of the singularity of flat band systems was investigated in the frame of the fractional quantum and magnon Hall effect [17,18] and energy localization in the presence of magnetic fields [19], spin-orbit coupling [20,21], or disorder [22,23]. Recently this topic attracted a lot of attention.…”

“…However, the presence of Kerr nonlinearity in the system may exhibit conical diffraction at the Dirac cone [30,34]. Due to their simple geometry, Lieb lattices are in the focus of research in ultracold systems as an optical trap for fermions [35], providing existence of magnon Hall effect in spite of the presence of inversion symmetry [18], protection and formation of robust zero modes localized at point defects [36], optimization of the BCS critical temperature and superfluid weight [37], and lifting the flat band modes by PT-symmetric perturbation due to thresholdless PT-symmetry breaking [38]. Moreover, it has been shown that the Lieb lattice acts as a good platform for analyzing various topological transitions in Chern insulators [20,[39][40][41].…”

Magnonic analogs of topological Dirac semimetals

“…A rapidly developing field is the extension of topological concepts to nonelectronic bosonic systems such as magnons [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and phonons [31][32][33][34][35][36][37][38][39]. Unlike electronic systems these bosonic quasi-particles are chargeneutral which makes them potential candidates to design systems with low-dissipation and good coherent transport applicable to spin-based computing and magnon spintronics [40].…”