Strongly coupled edge states in a graphene quantum Hall interferometer.

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into quasiparticles.

Hunting for Majoranas.

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes.

Crossover between strongly coupled and weakly coupled exciton superfluids.

In fermionic systems, superconductivity and superfluidity occur through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, which is challenging in electronic systems. We studied graphene double layers separated by an atomically thin insulator.

s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1.

We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length.

Fractional charge and fractional statistics in the quantum Hall effects.

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area.

Topological superconductivity in a phase-controlled Josephson junction.

Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states.

Electrical generation and detection of spin waves in a quantum Hall ferromagnet.

Spin waves are collective excitations of magnetic systems. An attractive setting for studying long-lived spin-wave physics is the quantum Hall (QH) ferromagnet, which forms spontaneously in clean two-dimensional electron systems at low temperature and in a perpendicular magnetic field. We used out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves in magnetically ordered QH states.

Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene.

Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogs of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference.

Thermal Transport Signatures of Broken-Symmetry Phases in Graphene.

In the half filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end, we calculate the spectrum of spin and valley waves in the ν=0 quantum Hall state of bilayer graphene.

Spin Superfluidity in the ν=0 Quantum Hall State of Graphene.

Strong electron interactions can lead to a variety of broken-symmetry phases in monolayer graphene. In the quantum Hall regime, the interaction effect are enhanced by the formation of highly degenerate Landau levels, catalyzing the emergence of such phases. Recent magnetotransport studies show evidence that the ν=0 quantum Hall state of graphene is in an insulating canted antiferromagnetic phase with the Néel vector lying within the graphene plane.

Current Correlations from a Mesoscopic Anyon Collider.

Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially.

Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots.

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood.

Transport in two-dimensional disordered semimetals.

We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the electron-hole liquid subject to zero and finite perpendicular magnetic fields using an effective medium approximation and a complementary mapping on resistor networks.

Fractional quantum Hall phase transitions and four-flux states in graphene.

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization.

Superfluidity and dimerization in a multilayered system of fermionic polar molecules.

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer.

Spin order in paired quantum Hall states.

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism.

Particle-hole symmetry and the Pfaffian state.

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing.

Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots.

We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots.

Out-of-plane spin polarization from in-plane electric and magnetic fields.

We show that the joint effect of spin-orbit and magnetic fields leads to a spin polarization perpendicular to the plane of a homogeneous two-dimensional electron system with Rashba spin-orbit coupling and in-plane parallel dc magnetic and electric fields, for angle-dependent impurity scattering or nonparabolic energy spectrum, while only in-plane polarization persists for simplified models. We derive Bloch equations, describing the main features of recent experiments, including the magnetic field dependence of static and dynamic responses.

Proposed experiments to probe the non-Abelian nu = 5/2 quantum hall state.

We propose several experiments to test the non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2. In a simplified version of the experiment suggested by [S. Das Sarma, M.

Theory of spin hall conductivity in n-doped GaAs.

We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew-scattering and side-jump contributions to the spin-Hall conductivity. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with experiments by Kato et al. [Science 306, 1910 (2004)].

Steady states of a microwave-irradiated quantum-Hall gas.

We consider effects of a long-wavelength disorder potential on the zero conductance state (ZCS) of the microwave-irradiated 2D electron gas. Assuming a uniform Hall conductivity, we construct a Lyapunov functional and derive stability conditions on the domain structure of the photogenerated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find nonzero conductances, photovoltages, and circulating dissipative currents.

Dynamic ferromagnetic proximity effect in photoexcited semiconductors.

The spin dynamics of photoexcited carriers in semiconductors in contact with a ferromagnet is treated theoretically and compared with time-dependent Faraday rotation experiments. The long-time response of the system is found to be governed by the first tens of picoseconds in which the excited plasma interacts strongly with the intrinsic interface between the semiconductor and the ferromagnet in spite of the existence of a Schottky barrier in equilibrium.

Finite-size effects in tunneling between parallel quantum wires.

We present theoretical calculations and experimental measurements which reveal finite-size effects in the tunneling between two parallel quantum wires, fabricated at the cleaved edge of a GaAs/AlGaAs bilayer heterostructure. Observed oscillations in the differential conductance, as a function of bias voltage and applied magnetic field, provide direct information on the shape of the confining potential. Superimposed modulations indicate the existence of two distinct excitation velocities, as expected from spin-charge separation.