Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain

Motivated by the recent experimental observation of the topological Anderson insulator in disordered atomic wires based on the Su-Schrieffer-Heeger (SSH) model, we study disorder effects on a dimerized Kitaev superconductor chain, which is regarded as the superconductor version of the SSH model. By computing the real-space winding number and the zero-bias differential conductance, we analyze the topological phase transitions occurring in a dimerized Kitaev superconductor chain with disorder. It is found that disorder can induce a topologically nontrivial superconductor phase hosting Majorana zero modes (MZMs). We can regulate the appearance of disorder-induced MZMs by adjusting the dimerization parameter. Finally, we use the self-consistent Born approximation method to verify the numerical results.

Figure 1

Schematic illustration of the dimerized Kitaev superconductor chain. $j$ denotes the $j\mathrm{th}$ unit cell enclosed by a black dashed box, and a unit cell contains two sublattices marked by a filled red (green) circle $a$ ($b$). The (thin blue and thick cyan) lines represent the dimerization of the particles, and the thin (thick) lines indicate the intercell (intracell) couplings. The spatial differences ($1\pm \eta$) of the dimerization parameter are shown.

Figure 2

Phase diagram of the clean dimerized Kitaev chain model on the $\eta \text{−}\mathrm{\Delta }/t$ plane. The red and white regions represent the topologically nontrivial and trivial phases, respectively. The white point A and black point B correspond to $(\eta ,\mathrm{\Delta }/t)=(0.4,0.5)$ and (0.6,0.5), respectively. Here $\mu =0$.

Figure 3

The RSWN ($\nu$) and the ZBDC ($dI/dV$) as a function of the disorder strength for (a) $\eta =0.4$ and (b) $\eta =0.6$. We take the parameters $\mathrm{\Delta }/t=0.5$ and $\mu =0$. In calculating the RSWN (the ZBDC), the size of the superconductor chain is taken as $L=500$ (1000), and the error bar indicates a standard deviation of 500 (1000) samples.

Figure 4

Phase diagram in ($W/t$, $\eta$) space for the dimerized Kitaev chain with disorder obtained by calculating the RSWN. We take the parameters $\mathrm{\Delta }/t=0.5$ and $\mu =0$. The red region denotes the topologically nontrivial phase ($\nu =1$), and the white region denotes the topologically trivial phase ($\nu =0$). The black dashed lines are determined by the self-consistent Born approximation method. The size of the superconductor chain is taken as $L=1000$.

Figure 5

Phase diagram in ($W/t,\mathrm{\Delta }/t$) space for the dimerized Kitaev chain with disorder obtained by calculating the RSWN. We take the parameter (a) $\eta =0$ and (b) $\eta =0.5$. The red region denotes the topologically nontrivial phase ($\nu =1$), and the white region denotes the topologically trivial phase ($\nu =0$). The black dashed lines are determined by the self-consistent Born approximation method. The size of the superconductor chain is taken as $L=1000$. Here $\mu =0$.

Figure 6

The finite-size energy gap $E_g$ (semilogarithmic plot) and the RSWN $\nu$ of the dimerized Kitaev chain model in the clean limit as a function of the length of the chain for different dimerization parameter $\eta$. We take the parameters $\mathrm{\Delta }/t=0.5$ and $\mu =0$. The different dimerization parameter $\eta$ is shown.