Field-induced gap and quantized charge pumping in a nanoscale helical wire

We propose several physical phenomena based on nanoscale helical wires. Applying a static electric field transverse to the helical wire induces a metal to insulator transition, with the band gap determined by the applied voltage. A similar idea can be applied to “geometrically” construct one-dimensional systems with arbitrary external potential. With a quadrupolar electrode configuration, the electric field could rotate in the transverse plane, leading to a quantized dc charge current proportional to the frequency of the rotation. Such a device could be used as a standard for the high-precession measurement of the electric current. The inverse effect implies that passing an electric current through a helical wire in the presence of a transverse static electric field can lead to a mechanical rotation of the helix. This effect can be used to construct nanoscale electromechanical motors. Finally, our methodology also enables ways of controlling and measuring the electronic properties of helical biological molecules such as the DNA.

Figure 1

(Color online) (a) Schematic picture of a nanohelix. (b) The definition of length scales $d,R,P,L$ shown for one pitch period of a helical wire.

Figure 2

(Color online) (a) Definition of coordinates and direction of transverse electric field. (b) Lowest four subbands under transverse field $eER=0.02{\hslash }^2/2m{a}^2$ and $L=30a$, with $a$ being the lattice constant. The dashed line shows the band structure in the reduced zone scheme when $E=0$.

Figure 3

(Color online) (a) Illustration of the on and off state of the nanohelix switch. The gate voltage is given by $V_g=V_{g1}-V_{g2}$ and source-drain voltage is given by $V_{sd}=V_s-V_d$. (b) dc conductance of the nanohelix connected with two metallic leads. The blue dash-dot line and red solid line stand for the cases with $eER=0$ and $eER=0.2t$, respectively, where the error bar stands for the impurity effect with the impurity potential $W=0.05t$. The dashed line is the conductance without impurity under the same electric field $eER=0.2t$. The arrow marks the first gap induced by electric field. All the calculations are done under the temperature $T=0.01t$ for the helix system with $N=200$, $L=20$, and $\Gamma /2\pi =0.1t$. The inset shows the temperature dependence of conductance with the electric field $eER=0$ (blue line) or $eER=0.2t$ (red line).

Figure 4

(Color online) Schematic illustration of the geometrical design of one-dimensional potentials. (a) A straight quantum wire in a sine-wave potential (blue line) is equivalent to (b) a periodically curved quantum wire in a uniform electric field $\mathbf{E}$. (c) More generally, a straight quantum wire in an arbitrary-potential $V\left(r\right)$ (blue line) is equivalent to (d) a curved quantum wire in a uniform electric field $\mathbf{E}$.

Figure 5

(Color online) (a) Illustration of the quantized charge pumping effect, with four electrodes causing a rotating electric field. (b) Pumping conductance $G_{\text{pump}}=J_{\text{pump}}/e\omega$ under zero temperature (red solid line) and finite temperature $T=0.01t$ (blue dashed line). The error bar shows the fluctuation induced by the disorder-strength $W=0.1t$. The parameters of the tight-binding system are taken as $N=100$, $L=20$, $eER=0.2t$, and $\Gamma /2\pi =0.1t$.

Figure 6

(Color online) Illustration of the quantum helical nanomotor.