Fig. 1: Comparison of the three phase transition mechanisms for non-Hermitian energy braids. | Communications Physics

Fig. 1: Comparison of the three phase transition mechanisms for non-Hermitian energy braids.

From: Observing non-Bloch braids and phase transitions by precise manipulation of the non-Hermitian boundary and size

Fig. 1

a Schematic of the static mechanical lattice. The stiffnesses of bulk elastic struts are \({k}_{1}\) to \({k}_{4}\) (solid lines), while the boundary stiffnesses between cells \(m=1\) and M are \({k}_{3}^{{{{\rm{b}}}}}\) and \({k}_{4}^{{{{\rm{b}}}}}\) (dashed lines). The leftmost (rightmost) column of nodes are equivalent to the sublattice-2 (sublattice-1) in cells \(m=M\) (\(m=1\)). b Summary of the three braid phase transition mechanisms: Bloch braid phase transition driven by the bulk modulation, and non-Bloch braid phase transition driven by the boundary or size modulation. Each 3D graph shows schematically a braid structure in the \(({{{\mathrm{Re}}}}\lambda ,{{{\rm{Im}}}}\lambda ,q)\) space for Bloch bands or the \(({{{\mathrm{Re}}}}\lambda ,{{\mbox{Im}}}\lambda ,\bar{q})\) space for non-Bloch bands, with its projection on the complex \(\lambda\) plane also presented. The 2D graph adjacent to the braid structure depicts the distribution of EPs for Riemann surfaces and BZ/GBZ on the complex z plane, see the notations in (c).

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