Magnetic Quantum Oscillations in Nanowires

Analytical expressions for the magnetization and the longitudinal conductivity of nanowires are derived in a magnetic field, $B$. We show that the interplay between size and magnetic field energy-level quantizations manifests itself through novel magnetic quantum oscillations in metallic nanowires. There are three characteristic frequencies of de Haas–van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations, $F=F_0/(1+\gamma {)}^{3/2}$, and $F^{\pm }=2F_0/|1+\gamma \pm (1+\gamma {)}^{1/2}|$, in contrast with a single frequency $F_0=S_F\hslash c/(2\pi e)$ in simple bulk metals. The amplitude of oscillations is strongly enhanced in some magic magnetic fields. The wire cross-section area $S$ can be measured using the oscillations as $S=4{\pi }^2{S}_F{\hslash }^2{c}^2/(\gamma e^2{B}^2)$ along with the Fermi-surface cross-section area, $S_F$.

Figure 1

Oscillating part of the magnetization vs the magnetic field for relatively low fields and three temperatures. The resonance at ${\omega }_c={\omega }_s/\sqrt{2}$ is due to a partial recovery of the energy-level degeneracy.

Figure 2

Oscillating magnetization for intermediate fields and three temperatures. Magic resonances are observed in many Fourier harmonics at low temperatures.

Figure 3

Oscillating magnetization for high fields and two temperatures.