Vanishing cyclotron gaps in a two-dimensional electron system with a strong short-period modulation

Magnetotransport in a density-tunable two-dimensional electron gas that is modulated with a strong, atomically precise superlattice potential of a $15\mathrm{nm}$ period is investigated. For low densities, the system shows typical two-dimensional behavior. In the regime of large densities, however, a quasi-one-dimensional state is entered, in which the cyclotron gaps vanish and the quantum Hall effect breaks down. Both regimes, and the transition between them, are theoretically described in the framework of a quantum-mechanical tight-binding model.

Figure 1

Miniband width and Fermi energy of the $5\mathrm{nm}$ CEW sample plotted for increasing density. The voltage scale on the top axis connects the experimental gate voltage to the calculated densities and energy values. The inset shows a schematic drawing of the sample structure.

Figure 2

(a) MR measurements for a $5\mathrm{nm}$ CEW sample at three different gate voltages in the small magnetic field regime. (b) Same traces at higher magnetic fields.

Figure 3

DOS of a 2DES with strong short-period modulation calculated in tight-binding approximation for $\Delta =6\mathrm{meV}$. The dashed vertical lines mark the extension of the miniband.

Figure 4

MR data of the $5\mathrm{nm}$ CEW sample vs inverse filling factor. The gate voltage ranges from 2.5 to $7.5\mathrm{V}$ in $0.5\mathrm{V}$ steps. Higher gate voltage data are consecutively shifted upwards by $5.5\mathrm{k}\mathrm{\Omega }$.

Figure 5

(a) MR data of the $1.6\mathrm{nm}$ CEW (symbol, $5\mathrm{k}\mathrm{\Omega }$ shift), the $5\mathrm{nm}$ CEW (black line, no shift), and the $10\mathrm{nm}$ CEW (gray line, $2.5\mathrm{k}\mathrm{\Omega }$ shift) samples at a density of about $3.5\times {10}^{11}{\mathrm{cm}}^{-2}$. (b) MR data of the $5\mathrm{nm}$ CEW sample (black lines) at gate voltages of 4.5 and $7\mathrm{V}$ (shifted upwards by $12\mathrm{k}\mathrm{\Omega }$). The thin gray lines are theoretical calculations corresponding to the same densities. The theoretical lines are offset from the experimental data by $+1.5$ and $-1.5\mathrm{k}\mathrm{\Omega }$ (marked “improved”).