Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions.

We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.

The quantum twisting microscope.

The invention of scanning probe microscopy revolutionized the way electronic phenomena are visualized1. Whereas present-day probes can access a variety of electronic properties at a single location in space2, a scanning microscope that can directly probe the quantum mechanical existence of an electron at several locations would provide direct access to key quantum properties of electronic systems, so far unreachable. Here, we demonstrate a conceptually new type of scanning probe microscope-the quantum twisting microscope (QTM)-capable of performing local interference experiments at its tip. The QTM is based on a unique van der Waals tip, allowing the creation of pristine two-dimensional junctions, which provide a multitude of coherently interfering paths for an electron to tunnel into a sample. With the addition of a continuously scanned twist angle between the tip and sample, this microscope probes electrons along a line in momentum space similar to how a scanning tunnelling microscope probes electrons along a line in real space. Through a series of experiments, we demonstrate room-temperature quantum coherence at the tip, study the twist angle evolution of twisted bilayer graphene, directly image the energy bands of monolayer and twisted bilayer graphene and, finally, apply large local pressures while visualizing the gradual flattening of the low-energy band of twisted bilayer graphene. The QTM opens the way for new classes of experiments on quantum materials.

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.

Pseudospin-resolved transport spectroscopy of the Kondo effect in a double quantum dot.

We report measurements of the Kondo effect in a double quantum dot, where the orbital states act as pseudospin states whose degeneracy contributes to Kondo screening. Standard transport spectroscopy as a function of the bias voltage on both dots shows a zero-bias peak in conductance, analogous to that observed for spin Kondo in single dots. Breaking the orbital degeneracy splits the Kondo resonance in the tunneling density of states above and below the Fermi energy of the leads, with the resonances having different pseudospin character. Using pseudospin-resolved spectroscopy, we demonstrate the pseudospin character by observing a Kondo peak at only one sign of the bias voltage. We show that even when the pseudospin states have very different tunnel rates to the leads, a Kondo temperature can be consistently defined for the double quantum dot system.

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.

Mesoscopic to universal crossover of the transmission phase of multilevel quantum dots.

Transmission phase alpha measurements of many-electron quantum dots (small mean level spacing delta) revealed universal phase lapses by pi between consecutive resonances. In contrast, for dots with only a few electrons (large delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multilevel quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of alpha for small delta follows from Fano-type antiresonances of the renormalized single-particle levels.

Luttinger-liquid behavior in weakly disordered quantum wires.

We have measured the temperature dependence of the conductance in long V-groove quantum wires fabricated in GaAs/AlGaAs heterostructures. Our data are consistent with recent theories developed within the framework of the Luttinger-liquid model, in the limit of weakly disordered wires. We show that, for the relatively low level of disorder in our quantum wires, the value of the interaction parameter g congruent with 0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Fitting such data with perturbation-theory models leads inevitably to wrong (lower) values of g.

Magnetic response of disordered metallic rings: large contribution of far levels.

We calculate the orbital linear magnetic response of disordered metallic rings to an Aharonov-Bohm flux using the BCS model for attractive electron-electron interaction. The contribution of all levels including those up to a high energy cutoff results in a much larger value than previously obtained using the local interaction model. The possible relevance of our results to the resolution of the discrepancy between the experimental and theoretical values for the ensemble-averaged persistent currents in these systems is discussed.

Spin-orbit effects in a GaAs quantum dot in a parallel magnetic field.

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. Counterintuitively we argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B( parallel), even if they are negligible for B( parallel) = 0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B( parallel). Our picture is consistent with the experimental observations of Folk et al.

Transmission phase shift of a quantum dot with kondo correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage, and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin- 1 / 2 impurity that is screened into a singlet.

Spin configurations of a carbon nanotube in a nonuniform external potential

We study, theoretically, the ground state spin of a carbon nanotube in the presence of an external potential. We find that when the external potential is applied to a part of the nanotube, its variation changes the single electron spectrum significantly. This, in combination with Coulomb repulsion and the symmetry properties of a finite length armchair nanotube, induces spin flips in the ground state when the external potential is varied. We discuss the possible application of our theory to recent measurements of Coulomb-blocked peaks and their dependence on a weak magnetic field in armchair carbon nanotubes.