Fig. 4: Non-Hermitian non-Bloch braids under the size modulation. | Communications Physics

Fig. 4: Non-Hermitian non-Bloch braids under the size modulation.

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

Fig. 4

a–c Outer contours of GBZ (colored dots) lying inside the BZ (gray circles). The color encodes the phase of non-Bloch wavenumber, \(\bar{q}\). The bordered dots mark the EPs within the axis range, and the blue lines linking two EPs are branch cuts. d–f Non-Bloch braids in the R3 space and their projections on the complex \(\lambda\) plane. g–i Non-Bloch vectors on the Bloch sphere. The insets depict the corresponding braid diagrams. j Sketch of the non-Bloch braid phase transition under the modulation of size M, which is 40 (a, d, g), 60 (b, e, h), and 80 (c, f, i), respectively. The stiffnesses are common, \({k}_{1}=8\), \({k}_{2}=1\), \({k}_{3}={k}_{4}=2\), and \({k}_{3}^{{{{\rm{b}}}}}={k}_{4}^{{{{\rm{b}}}}}={\bar{k}}_{4}^{{{{\rm{b}}}}}\).

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