Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed t
o be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. Here, we use scanning nanoSQUID magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi,Sb)$_2$Te$_3$ thin film. Contrary to naive expectations based upon macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can in turn drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.
We report torque magnetometry measurements of an oxide heterostructure consisting of an amorphous Al$_2$O$_3$ thin film grown on a crystalline SrTiO$_3$ substrate ($a$-AO/STO) by atomic layer deposition. We find a torque response that resembles previ
ous studies of crystalline LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterointerfaces, consistent with strongly anisotropic magnetic ordering in the plane of the interface. Unlike crystalline LAO, amorphous Al$_2$O$_3$ is nonpolar, indicating that planar magnetism at an oxide interface is possible without the strong internal electric fields generated within the polarization catastrophe model. We discuss our results in the context of current theoretical efforts to explain magnetism in crystalline LAO/STO.
Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires, and graphene. Recently, a new paradi
gm has emerged with the advent of symmetry-protected surface states on the boundary of topological insulators, enabling the creation of electronic systems with novel properties. For example, time reversal symmetry (TRS) endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, locking the orientation of their spin relative to their momentum. Weakly breaking this symmetry generates a gap on the surface, resulting in charge carriers with finite effective mass and exotic spin textures. Analogous manipulations of the one-dimensional boundary states of a two-dimensional topological insulator are also possible, but have yet to be observed in the leading candidate materials. Here, we demonstrate experimentally that charge neutral monolayer graphene displays a new type of quantum spin Hall (QSH) effect, previously thought to exist only in TRS topological insulators, when it is subjected to a very large magnetic field angled with respect to the graphene plane. Unlike in the TRS case, the QSH presented here is protected by a spin-rotation symmetry that emerges as electron spins in a half-filled Landau level are polarized by the large in-plane magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic (CAF) state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with tunable band gap and associated spin-texture.
Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer graphene flake
coupled to a rotationally-aligned hexagonal boron nitride substrate. The spatially-varying interlayer atomic registry results both in a local breaking of the carbon sublattice symmetry and a long-range moire superlattice potential in the graphene. This interplay between short- and long-wavelength effects results in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality, both of which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states reflecting the massive Dirac dispersion that results from broken sublattice symmetry. At ultra-high fields, integer conductance plateaus are observed at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level.
The advent of few-layer graphenes has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic wavefunctions with pseudo
spin, a lattice analog of the relativistic electron spin, while the multilayer structure leads to electric field effect tunable electronic bands. Here we use these properties to realize giant conductance oscillations in ballistic trilayer graphene Fabry-Perot interferometers, which result from phase coherent transport through resonant bound states beneath an electrostatic barrier. We cloak these states by selectively decoupling them from the leads, resulting in transport via non-resonant states and suppression of the giant oscillations. Cloaking is achieved both classically, by manipulating quasiparticle momenta with a magnetic field, and quantum mechanically, by locally varying the pseudospin character of the carrier wavefunctions. Our results illustrate the unique potential of trilayer graphene as a versatile platform for electron optics and pseudospintronics.
We have measured the microwave conductance of mechanically exfoliated graphene at frequencies up to 8.5 GHz. The conductance at 4.2 K exhibits quantum oscillations, and is independent of the frequency.
