Dephasing in (Ga,Mn)As Nanowires and Rings

To understand quantum mechanical transport in a ferromagnetic semiconductor, the knowledge of basic material properties such as the phase coherence length and corresponding dephasing mechanism are indispensable ingredients. The lack of observable quantum phenomena has prevented experimental access to these quantities so far. Here we report the observations of universal conductance fluctuations in ferromagnetic (Ga,Mn)As. The analysis of the length and temperature dependence of the fluctuations reveals a $T^{-1}$ dependence of the dephasing time.

Figure 1

Magnetoresistance of a (Ga,Mn)As ring ($w1$) with a diameter of 400 nm and a ring width of 40 nm. The inset displays a top view of the ring. The temperature was varied from 1 K (bottom trace) to 30 mK (top trace) and the current through the device was set to 100 pA. To demonstrate the reproducibility of the resistance oscillations observed below $\sim 200\mathrm{mK}$ the 30 mK trace is shown for an up (blue line) and down sweep (dashed black line) of the $B$ field.

Figure 2

(a) Conductance fluctuations for three wires ($w2$) of different length $L$. For the shortest wire the amplitude of the conductance fluctuations is about $e^2/h$, expected for conductors with all spatial dimensions smaller or comparable than $L_{\varphi }$. The inset shows an electron micrograph of a $\sim 20\mathrm{nm}$ wide wire with a potential probe separation of $\sim 100\mathrm{nm}$ (the 100 nm wire). (b) $G$ vs $B$ of the 200 nm wire for different temperatures between 20 mK and 1 K. In both experiments the current through the wire was 10 pA (exception: 30 pA at 1 K). The conductance traces in the low $B$ regime have been omitted in both graphs.

Figure 3

$\delta G$ in units of $e^2/h$ for wires of length 100 nm, 200 nm, and 800 nm. The measurements were carried out using currents of 10–500 pA. The maximum current at a given temperature was adjusted such that the fluctuation amplitude $\delta G$ was not affected. Inset: $\delta G{L}^{3/2}/(e^2/h)=L_{\varphi }^{3/2}$ vs $T$.

Figure 4

(a) Electron micrograph of a (Ga,Mn)As ring sample with a diameter of $\sim 100\mathrm{nm}$. (b) Comparison of the magnetoconductance trace of the ring sample with the conductance of a wire of comparable length and 20 nm width. (c) Corresponding Fourier transform taken from the conductance of ring and wire. The region where AB oscillations are expected is highlighted.