Electron-state effect induced by helical structure of metal nanowires formulated by path integrals in Riemann space

Thin nanowires of a metal have a multishell structure in which several deformed helical shells are stacked. The purpose of this paper is to give a perspective on the electron state in a helical nanowire based on the Riemann geometrical formulation of quantum mechanics within the continuum approximation of a wire. The helical configuration of atoms in the wires results in a sort of vector potential, and the electron state is modulated by the winding number and the shear modulus of the shell. The energy dispersion curve depends on the imbalance of the slide and distortion angles of the wire.

Figure 1

A schematic diagram of the helical shell in a nanowire (a) and its unfolded diagram (b).

Figure 2

Dispersion relation of the electron energy when ${\alpha }_R=17°$ $\beta =14°$ (a), ${\alpha }_R=0°$ $\beta =14°$ (b), and ${\alpha }_R=17°$ $\beta =0°$ (c). Thin curves for ${\alpha }_R={\beta }_R=0°$ are also depicted for the sake of comparison. The meaning of the indexes is discussed in the text.