Spinless composite fermions in an ultrahigh-quality strained Ge quantum well

We report on an observation of a fractional quantum Hall effect in an ultrahigh-quality two-dimensional hole gas hosted in a strained Ge quantum well. The Hall resistance reveals precisely quantized plateaus and vanishing longitudinal resistance at filling factors $\nu =2/3,4/3$, and $5/3$. From the temperature dependence around $\nu =3/2$ we obtain the composite fermion mass of $m^{☆}\approx 0.4m_e$, where $m_e$ is the mass of a free electron. Owing to large Zeeman energy, all observed states are spin polarized and can be described in terms of spinless composite fermions.

Figure 1

(a) $R_{xx}$ (left axis) and $R_{xy}$ (right axis) versus $B$. (b) $R_{xx}$ (left axis, dotted line) and $B(d{R}_{xy}/dB)$ (right axis, solid line) versus $B$. Integers and fractions next to the traces mark filling factors. Inset shows $R_{xx}\left(B\right)$ (dotted line) and $B[d{R}_{xy}\left(B\right)/dB]$ (solid line) in the $N=1$ Landau level. Vertical arrows are drawn at corresponding $\nu$, as marked.

Figure 2

$R_{xx}$ (left axis) and $R_{xy}/R_K$ (right axis) as functions of the filling factor $\nu$. Horizontal dotted lines are drawn at $R_{xy}/R_K=1/3,1/2,3/5,3/4,1$, and 3/2. Integers and fractions next to the traces mark filling factors.

Figure 3

$R_{xx}$ as a function of $B$ (bottom axis) and $B^{☆}$ (top axis) in the $N=0$, spin-up Landau level at different temperatures from $T\approx 0.3$ K to $T\approx 1.1$ K. Inset shows $R_{xx}$ at $\nu =5/3$ (circles), $\nu =4/3$ (squares), and $\nu =8/5$ (triangles) versus $1/T$ on a log-linear scale. The fits with $R_{xx}\sim exp(-{\mathrm{\Delta }}_{\nu }/2T)$ (solid lines) generate ${\mathrm{\Delta }}_{5/3}=3.1$ K and ${\mathrm{\Delta }}_{4/3}=3.3$ K.

Figure 4

(a) Resistance oscillation amplitude $A$ normalized to temperature $T$ at ${\nu }^{☆}\approx 3/2$ (circles) and ${\nu }^{☆}\approx 5/2$ (squares) as a function of temperature. Solid lines are fits with $A/T\sim 1/sinh(2{\pi }^2{k}_{B}T/\hslash {\omega }_{\mathrm{c}}^{☆})$. (b) Resistance oscillation amplitude $A$ normalized to $D_T$ as a function of $1/B^{☆}$. Solid line is the fit to $A/D_T\sim exp(-\pi /{\tau }_{\mathrm{q}}^{☆}{\omega }_{\mathrm{c}}^{☆})$.