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First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice

In this work, topological properties of a ferromagnetic Heisenberg model on a breathing kagome lattice are investigated extensively in the presence of Dzyaloshinskii-Moriya interaction. While the kagome ferromagnet hosts only a single first order topological phase, the breathing kagome system exhibits multiple first and second order topological phases along with their coexistence. Magnon dispersion relation is obtained by using linear spin wave theory. Flat band and Dirac cones are obtained in the absence of Dzyaloshinskii-Moriya interaction. A topological phase diagram is presented where several first and second order phases as well as their overlap are identified. Values of thermal Hall conductivity for all the first order phases are obtained. Distinct first order phases are characterized by different sets of Chern numbers in association with the necessary chiral edge states in accordance to the first order bulk-boundary-correspondence rule. Second order phase is characterized by polarization along with the emergence of corner states. Violation of the second order bulk-corner-correspondence rule has been noted in some regions.