Chern–Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix

In temporal gauge A₀=0$A_0=0$ the 3d Chern–Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the contours projection on the xy plane contribute. Though the theory is quadratic, P-exponents remain non-trivial operators and R  -factors are easier to guess then derive. We show that the topological invariants arise if additional flag structure R³⊃R²⊃R¹${\mathbb{R}}^3\supset {\mathbb{R}}^2\supset {\mathbb{R}}^1$ (xy plane and a y line in it) is introduced, R is the universal quantum R  -matrix and turning points contribute the “enhancement” factors qρ$q^{\rho }$.     

Composite fermion picture for multi-component plasmas in 2D electron–hole systems in a strong magnetic field

Low-lying states of a 2D electron–hole system contain electrons and one or more types of charged excitonic complexes. Binding energies and angular momenta of these excitonic ions, and the pseudopotentials describing their interactions with electrons and with one another are obtained from numerical studies of small systems. Incompressible fluid ground states of such multi-component plasmas are found in exact numerical diagonalizations. A generalized composite fermion (CF) picture involving Chern–Simons charges and fluxes of different types is proposed and shown to predict the low-lying states at any value of the magnetic field.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

In-plane magnetic field-induced anisotropy and orientation energy of stripe phases at half-filled high Landau levels

We report on detailed Hartree–Fock calculations of the unidirectional charge density wave orientation energy induced by a tilted magnetic field. We find that for current experimental samples stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider two-dimensional electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.     

Strong bulk-edge coupling in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of electrons. We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.     

Experimental evidence for a metal–insulator transition and geometric effect in a half-filled Landau level

We have measured the low-temperature transport properties of a high-mobility front-gated GaAs/Al Ga As heterostructure. By changing the applied gate voltage, we can vary the amount of disorder within the system. At a Landau level filling factor , where the system can be described by the composite fermion picture, we observe a crossover from metallic to insulating behaviour as the disorder is increased, in agreement with theory. We also report experimental evidence of geometric effect for composite fermions induced by an effective magnetic field.     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

Exchange interaction effects in the crossing of spin-polarized Landau levels in a silicon-germanium heterostructure: transition into a ferromagnetic state

The crossing of spin-split Landau levels in a Si/SiGe heterostructure is investigated by means of magneto-transport experiments in tilted magnetic fields. We observe a transition from a paramagnetic into a fully spin polarized state. During the transition strongly enhanced maxima in the transverse resistivity ρ_xx appear when the parallel field component is oriented along the Hall bar. We assign this effect to an energy level structure strongly modified by exchange interaction effects between different Landau levels. Surprisingly the maximum in ρ_xx totally disappears when the parallel field component is perpendicular to the Hall bar.     

Ballistic phonon studies in the lowest Landau level

We report time-resolved studies of ballistic phonon absorption in the fractional quantum Hall regime at Landau level filling factors of and . The technique used can resolve the interaction of the two-dimensional electron system with LA and TA phonons and has been used to measure the temperature variation of the heat capacity of a single layer of electrons at . The energy gaps at have also been measured and found to be in good agreement with theory. The roles of compressible and incompressible regions in the phonon absorption process are discussed. Angle resolved measurements at are also in good agreement with theory.     

Coulomb drag in the quantum Hall state: Role of disorder

We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being . We find to be very large, as compared to the zero magnetic field case. We attribute this enhancement to the slow decay of density fluctuations in a strong magnetic field. For a clean system, the linear -dependence of the longitudinal conductivity, characteristic of the state, leads a unique temperature dependence – . Within a semiclassical approximation, disorder leads to a decrease of the transresistivity as compared to the clean case, and a temperature dependence of at low temperatures.     

Korringa-like nuclear spin–lattice relaxation in a 2DES at

Via a resistively detected NMR technique, the nuclear spin–lattice relaxation time T₁ of ⁷¹Ga has been measured in a GaAs/AlGaAs heterostructure containing two weakly coupled 2D electron systems (2DES) at low temperatures, each at Landau level filling . Incomplete electronic spin polarization, which has been reported previously for low density 2DESs at , should facilitate hyperfine-coupled nuclear spin relaxation owing to the presence of both electron spin states at the Fermi level. Composite fermion theory suggests a Korringa-law temperature dependence: T₁T=constant is expected for temperatures . Our measurements show that for temperatures in the range , T₁ rises less rapidly with falling temperature than this law predicts. This may suggest the existence of alternate nuclear spin relaxation mechanisms in this system. Also, our data allows for an estimate of the composite fermion mass.     

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Inter-layer edge tunneling and transport properties in separately contacted double-layer quantum-Hall systems

A theory of transport in the quantum-Hall regime is developed for separately contacted double-layer electron systems. Inter-layer tunneling provides a channel for equilibration of the distribution functions in the two layers at the edge states. Resistances and transresistances for various configurations of the electrodes are calculated as functions of the inter-layer tunneling amplitude. Induced current in one of the layer by a current in the other is also calculated. It is shown that reflection at the leads causes change in the results for some electrode configurations. The results obtained in this work is consistent with recent experiments.     

Correlated electron states at level crossings of bilayer two-dimensional electron systems in tilted magnetic fields

We have measured the energy-level structure of high mobility, strongly coupled bilayer two-dimensional electron systems in tilted magnetic fields by means of magnetotransport experiments. At tilt angles where single-particle levels with opposite spin and symmetry cross, we observe a surprising sudden broadening of the quantum Hall plateaus and a deepening of the Shubnikov–de Haas minima. This observation is explained by an interaction-induced rearrangement of the energy level structure which strongly increases the energetic splitting of two (anti-)crossing levels.