Vertex coupling interpolation in quantum chain graphs

Abstract

We analyze band spectrum of the periodic quantum graph in the form of a chain of rings connected by line segments with the vertex coupling which violates the time reversal invariance, interpolating between the $δ$ coupling and the one determined by a simple circulant matrix. We find that flat bands are generically absent and that the negative spectrum is nonempty even for interpolation with a non-attractive $δ$ coupling; we also determine the high-energy asymptotic behavior of the bands.

Figures (4)

• Figure 1: Periodic quantum chain; the elementary cell is highlighted BaExTa20.
• Figure 2: The volume satisfying the band condition of \ref{['Interpol_band_gap_cond_t_0']}.
• Figure 3: The band-gap structure dependence on interpolation parameter $t$ for a quantum chain with $l = 1$, $l_1 = 2$, $l_3 = \frac{\pi}{2}$ and $\gamma = 0$.
• Figure 4: The same as Fig. \ref{['Interpol_plot_Kirch']}, but with $\gamma = -\frac{3\pi}{4}$.