Manipulating a quantum state via electrostatic gating has been of great importance for many model systems in nanoelectronics. Until now, however, controlling the electron spins or, more specifically, the magnetism of a system by electric-field tuning has proven challenging. Recently, atomically thin magnetic semiconductors have attracted significant attention due to their emerging new physical phenomena. However, many issues are yet to be resolved to convincingly demonstrate gate-controllable magnetism in these two-dimensional materials. Here, we show that, via electrostatic gating, a strong field effect can be observed in devices based on few-layered ferromagnetic semiconducting CrGeTe. At different gate doping, micro-area Kerr measurements in the studied devices demonstrate bipolar tunable magnetization loops below the Curie temperature, which is tentatively attributed to the moment rebalance in the spin-polarized band structure. Our findings of electric-field-controlled magnetism in van der Waals magnets show possibilities for potential applications in new-generation magnetic memory storage, sensors and spintronics.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.

The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to the trivial case of low Bloch band filling where only the Landau level index plays a significant role. Here we report measurement of high mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observe coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, a new series of states appear at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point towards a new type of many-body state.In a 2D electron gas (2DEG) subjected to a magnetic field, the Hall conductance is generically quantized whenever the Fermi energy lies in a gap 1 . The integer quantum Hall effect (IQHE) results from the cyclotron gap that separates the Landau energy levels (LLs). The longitudinal resistance drops to zero, and the Hall conductance develops plateaus quantized to σ XY = νe 2 /h, where ν, the Landau level filling fraction, is integer valued. When the 2DEG is modified by a spatially-periodic potential, the LL's develop additional subbands separated by minigaps, resulting in the fractal energy diagram known as the Hofstadter butterfly 2 . When plotted against normalized magnetic flux, φ/φ o , and normalized density, n/n o , representing the magnetic flux quanta and electron density per unit cell of the superlattice, respectively, the fractal mini-gaps follow linear trajectories 3 according to a Diophantine equation, n/n o = tφ/φ o + s, where s and t are integer valued. s is the Bloch band filling index associated with the superlattice and t is a similar index related to the gap structure along the field axis 4 (in the absence of a superlattice, t reduces to the LL filling fraction). The fractal mini-gaps give rise to QHE features at partial Landau level filling, but in this case t, rather than the filling fraction determines the quantization value 1,5 , and the Hall plateaux remain integer valued.In very high mobility 2DEGs, strong Coulomb interactions can give rise to many-body gapped-states also appearing at partial Landau fillings [6][7][8] . Again the Hall conductance exhibits a plateau, but in this case quantized to fractional values of e 2 /h. This effect is termed the fractional quantum Hall effect (FQHE), and represents an example of emergent behaviour in which electron interactions give rise to collective excitations with properties fundamentally distinct from the fractal IQHE states. A natural theoretical question arises regarding how interactions manifest in a patterned 2DEG 9-12 . In particular, since both the FQHE many-body gaps, and the singleparticle fractal mini-gaps, can appear at the same filling fraction, it remains unclear whether the FQHE is even possible within the fractal Hofst...