Quantized Majorana pump in semiconductor-superconductor heterostructures

We propose a quantized Majorana pump (QMP) in semiconductor-superconductor heterostructures. The pump consists of a Majorana nanowire, i.e., a Rashba wire in proximity to an $s$-wave superconductor and in a magnetic field, and two ferromagnetic leads. When the orientation of the magnetic field is rotated by $2\pi$, an elementary charge $e$ is transferred between two leads. The number of the pumped charge in a cycle is related to the winding number of the Andreev reflection amplitude. In the topologically trivial phase without Majorana zero mode (MZM), the pumped charge decreases rapidly to zero. More importantly, the pump works at zero bias and provides a more effective way to distinguish MZMs from trivial partially separated Andreev bound states. Therefore, this QMP provides not only a smoking-gun signature of MZMs, but also an ideal platform to realize topological single-electron pumps with the potential for realizing novel current standards in electrical metrology.

Figure 1

Sketch of the quantized Majorana pump. A Majorana wire (a Rashba wire in proximity to an $s$-wave superconductor and in a magnetic field) is sandwiched between two ferromagnetic leads. The rotating magnetic field induces a rotating Zeeman field h in the $x\text{−}y$ plane. The magnetization orientation of two ferromagnetic leads is along the $z$ direction.

Figure 2

(a) and (b) are the static differential conductance and the pumped current as functions of the energy of electrons at zero temperature, respectively. Various $t_c$ are considered. (c) and (d) are the pumped current at various temperatures, as functions of the chemical potential (c) and the Zeeman field strength (d). The length of Majorana wire is $L=2\mu m$ and the other parameters are $\mathrm{\Delta }=0.25$ meV, $t_w=t_l=9.5$ meV, $\alpha =40\mathrm{meV}·\mathrm{nm}, a=0.648nm, m_z=2$ meV, $U_l=-0.95$ meV. In (a) and (b), $h=2\mathrm{\Delta }, \mu =0.5{\mu }_c$ with ${\mu }_c=\sqrt{h^2-{\mathrm{\Delta }}^2}$. In (c), $t_c=t_w, h=2\mathrm{\Delta }$. In (d), $t_c=t_w, \mu =4\mathrm{\Delta }$ and $h_c=\sqrt{{\mu }^2+{\mathrm{\Delta }}^2}$.

Figure 3

(a) and (b) are the static differential conductances and the pumped currents as functions of the energy of electrons at zero temperature for the junction with a quantum dot, respectively. Two values of $h$ are considered. (c) and (d) are the pumped currents as functions of the Zeeman field strength for various temperatures(c) or various disorder strengths (d), respectively. $V=5.5\mathrm{\Delta }, V_b=16\mathrm{\Delta }, L_b=10$ nm, $L_d=250$ nm, $L=1\mu m$, and ${\sigma }_v={\sigma }_{\mathrm{\Delta }}=12.5$ nm. The other parameters are the same as those in Fig. 2. In (d), the temperature is $T=1$ mK.