Multiple mobility rings in non-Hermitian Su-Schrieffer-Heeger chain with quasiperiodic potentials

Abstract

The localization property of a non-Hermitian Su-Schrieffer-Heeger (SSH) chain with quasi-periodic on-site potential is investigated. In contrast to the preceding investigations, the quantum phase transition between localized state and extended one is achieved by adjusting the strength of intracellular or intercellular hopping. The energy spectra and eigenstate distributions of the system's Hamiltonian near the boundary of the phase transition exhibit different behaviors when the Hermiticity, non-Hermiticity and mosaic modulation of the quasi-periodic potential are considered, respectively. The existence of the mobility ring is revealed in the non-Hermitian SSH chain by studying of the critical behaviors near the boundary. More interestingly, the multiple mobility rings emerge when the period number of the mosaic modulation is increased. The result is helpful for the investigation of the localization-delocalization transition in the SSH-type system under the combined action of the non-Hermiticity and quasi-periodicity.

Figures (6)

• Figure 1: Schematic diagram of the SSH model for the quasi-periodic potential $V_{j}$ with the mosaic modulation. Two sites per unit cell are represented by $A$ and $B$, $v$ represents the strength of the intracellular hopping, while $w$ denotes the strength of the intercellular hopping.
• Figure 2: (a) Change of the fractal dimension $\Gamma$ with the energy $E$ and the strength ratio $w/v$. The two red dashed lines mark the exact MEs. (b)-(e) The spatial distributions of the four typical eigenstates corresponding to the eigenvalues marked by black circle, triangle, square and star in (a) when $w/v=0.44$. The other parameters are set to $\kappa=1$, $h=0$ and $\delta=0$.
• Figure 3: (a) Change of the fractal dimension $\Gamma$ with the energy $E$ and the strength ratio $w/v$, the red dashed lines denote the exact MEs. (b)-(e) The spatial distributions of the four typical eigenstates corresponding to the eigenvalues marked by black circle, triangle, square and star in Fig. \ref{['figure3']}(a) when $w/v=0.4$. The other parameters are set to $\kappa=2$, $h=0$ and $\delta=0$.
• Figure 4: (a) Change of the fractal dimension $\Gamma$ with the energy $Re(E)$ and the strength ratio $w/v$. The red dashed lines are the exact MEs. (b) The fractal dimension $\Gamma$ versus $Re(E)$ and $Im(E)$ over the range of $w/v\in[0,2]$. (c) The distribution of the fractal dimension on the complex plane constructed by the real and imaginary parts of the energy when $w/v=1.0$. The red dashed line denotes the MR obtained from Eq.(\ref{['E11']}). (d)-(g) The spatial distributions of the four typical eigenstates corresponding to the eigenvalues marked by black circle, triangle, square and star in Fig. \ref{['figure4']}(a) when $w/v=0.6$. The other parameters are set to $\kappa=1$, $h=1$ and $\delta=0$.
• Figure 5: (a) Change of the fractal dimension $\Gamma$ with the energy $Re(E)$ and the strength ratio $w/v$. The red dashed lines are the exact MEs. (b) The fractal dimension $\Gamma$ versus $Re(E)$ and $Im(E)$ over the range of $w/v\in[0,2]$. (c) and (d) The distribution of the fractal dimension on the complex plane constructed by the real and imaginary parts of the energy when $w/v=1$ and $w/v=1.9$. The red dashed lines are the MRs obtained from Eq. (\ref{['E18']}). The other parameters are set to $\kappa=2$, $h=1$ and $\delta=0$.