Cascade of phase transitions and Dirac revivals in magic-angle graphene.

Twisted bilayer graphene near the magic angle1-4 exhibits rich electron-correlation physics, displaying insulating3-6, magnetic7,8 and superconducting phases4-6. The electronic bands of this system were predicted1,2 to narrow markedly9,10 near the magic angle, leading to a variety of possible symmetry-breaking ground states11-17. Here, using measurements of the local electronic compressibility, we show that these correlated phases originate from a high-energy state with an unusual sequence of band population. As carriers are added to the system, the four electronic 'flavours', which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. At each transition, a single spin/valley flavour takes all the carriers from its partially filled peers, 'resetting' them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breaking. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state that we report here, with its strongly broken electronic flavour symmetry and revived Dirac-like electronic character, is important in the physics of magic-angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

Electron attraction mediated by Coulomb repulsion.

One of the defining properties of electrons is their mutual Coulomb repulsion. However, in solids this basic property may change; for example, in superconductors, the coupling of electrons to lattice vibrations makes the electrons attract one another, leading to the formation of bound pairs. Fifty years ago it was proposed that electrons can be made attractive even when all of the degrees of freedom in the solid are electronic, by exploiting their repulsion from other electrons. This attraction mechanism, termed 'excitonic', promised to achieve stronger and more exotic superconductivity. Yet, despite an extensive search, experimental evidence for excitonic attraction has yet to be found. Here we demonstrate this attraction by constructing, from the bottom up, the fundamental building block of the excitonic mechanism. Our experiments are based on quantum devices made from pristine carbon nanotubes, combined with cryogenic precision manipulation. Using this platform, we demonstrate that two electrons can be made to attract each other using an independent electronic system as the 'glue' that mediates attraction. Owing to its tunability, our system offers insights into the underlying physics, such as the dependence of the emergent attraction on the underlying repulsion, and the origin of the pairing energy. We also demonstrate transport signatures of excitonic pairing. This experimental demonstration of excitonic pairing paves the way for the design of exotic states of matter.

Persistent currents in normal metal rings.

Quantum mechanics predicts that the equilibrium state of a resistive metal ring will contain a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. We have developed a technique for detecting persistent currents that allows us to measure the persistent current in metal rings over a wide range of temperatures, ring sizes, and magnetic fields. Measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.

Fractional charges on an integer quantum Hall edge.

We propose ways to create and detect fractionally charged excitations in integer quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fractional charge of the solitonlike collective excitations can be observed in time-resolved or frequency-dependent shot noise measurements.

Correlated defects, metal-insulator transition, and magnetic order in ferromagnetic semiconductors.

The effect of disorder on transport and magnetization in ferromagnetic III-V semiconductors, in particular (Ga,Mn)As, is studied theoretically. We show that Coulomb-induced correlations of the defect positions are crucial for the transport and magnetic properties of these highly compensated materials. We employ Monte Carlo simulations to obtain the correlated defect distributions. Exact diagonalization gives reasonable results for the spectrum of valence-band holes and the metal-insulator transition only for correlated disorder. Finally, we show that the mean-field magnetization also depends crucially on defect correlations.

Oscillating sign of drag in high Landau levels.

Motivated by experiments, we study the sign of the Coulomb drag voltage in a double layer system in a strong magnetic field. We show that the commonly used Fermi golden rule approach implicitly assumes a linear dependence of intralayer conductivity on density, and is thus inadequate in strong magnetic fields. Going beyond this approach, we show that the drag voltage commonly changes sign with density difference between the layers. We find that, in the quantum Hall regime, the Hall and longitudinal drag resistivities may be comparable. Our results are also relevant for pumping and acoustoelectric experiments.

Conductivity tensor of striped quantum hall phases

We study the transport properties of pinned striped quantum Hall phases. We show that, under quite general assumptions, the macroscopic conductivity tensor satisfies a semicircle law. In particular, this result is valid for both smectic and nematic stripe phases, independent of the presence of topological and orientational defects such as dislocations and grain boundaries. As a special case, our results explain the experimental validity of a product rule for the dissipative part of the resistivity tensor, which was previously derived by MacDonald and Fisher (cond-mat/9907278) for a perfect stripe structure.