to -12pt [-12pt]to 16ptRapid Note Wavefunctions for the Luttinger liquid

Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the Gaussian boson LL Hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL Hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions. Received 26 January 1999 and Received in final form 21 April 1999     

Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene

We investigate electronic transport in dual-gated twisted-bilayer graphene. Despite the subnanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite interlayer screening and extract the capacitance between the atomically spaced layers. At zero filling factor, we observe an insulating state at large displacement fields, which can be explained by the presence of counterpropagating edge states with interlayer coupling.     

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two-dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at and .     

Thickness-induced violation of de Haas-van Alphen effect through exact analytical solutions at a one-electron and a one-composite fermion level

A systematic study of the energetics of electrons in an interface in a magnetic field is reported with exact analytical calculations based on a Landau level (LL) picture, by serious consideration of the finite thickness of the quantum well (QW). The approach is physically transparent and subtly different in its line of reasoning from standard methods avoiding any semi-classical approximation. We find “internal” phase transitions (at partial LL filling) for magnetisation and susceptibility that are not captured by other approaches and that give rise to nontrivial violations of the standard de Haas-van Alphen periods, in a manner that reproduces the exact quantal astrophysical behaviours in the limit of full three-dimensional (3D) space. Upon inclusion of Zeeman splitting, additional features are also found, such as global energy minima originating from the interplay of QW, Zeeman and LL Physics, while a corresponding calculation in a composite fermion picture with Λ-levels, leads to new predictions on magnetic properties of an interacting electron liquid. By pursuing the same line of reasoning for a topologically nontrivial system with a relativistic spectrum, we find evidence that similar effects might be operative in the dimensionality crossover of 3D strong topological insulators to 2D topological insulator quantum wells.     

Oscillatory magnetization of two-dimensional electron gas

Diamagnetic moment of the two-dimensional electron gas is calculated for finite temperature using a simple energy band model and assuming no collisional broadening of Landau levels. Numerical results are presented for GaAs band parameters. The diamagnetic moment oscillates around zero value as a function of magnetic field strength and tends to zero at low fields. It is concluded that both the diamagnetic and the paramagnetic susceptibilities of the 2D electron gas vanish in the low field limit.     

Energy Momentum of Marder Universe in Teleparallel Gravity

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of cylindrically-symmetric Marder universe, we consider the Møller, Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum definitions in the teleparallel gravity (TG). The energy-momentum distributions are found to be zero. These results are the same as a previous works of Aygün et al., they investigated the same problem in general relativity (GR) by using the Einstein, Møller, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Qadir–Sharif and Weinberg’s definitions. These results support the viewpoints of Banerjee–Sen, Xulu, Radinschi and Aydo?du–Salt?. Another point is that our study agree with previous works of Cooperstock–Israelit, Rosen, Johri et al. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in teleparallel gravity. It is also independent of the teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.     

Manipulation of Dirac points in graphene-like crystals

We review different scenarios for the motion and merging of Dirac points in 2D crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels.     

Infrared spectroscopy of Landau levels of graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.     

Quantum Hall effect in a system with an electron reservoir

Precise measurements of the magnetic-field and gate-voltage dependences of the capacitance of a field-effect transistor with an electron system in a wide GaAs quantum well have been carried out. It has been found that the capacitance minima caused by the gaps in the Landau spectrum of the electron system become anomalously wide when two size-quantization subbands are occupied. The effect is explained by retention of the chemical potential in the gap between the Landau levels of one of the subbands owing to redistribution of electrons between the subbands under a change in the magnetic field. The calculation taking into account this redistribution has been performed in a model of the electron system formed by two two-dimensional electron layers. The calculation results describe both the wide capacitance features and the observed disappearance of certain quantum Hall effect states.     

Anticrossing of spin-split subbands in quasi-one-dimensional wires

In quantum Hall systems, both anticrossings and magnetic phase transitions can occur when opposite-spin Landau levels coincide. Our results indicate that both processes are also possible in quasi-1D quantum wires in an in-plane B field, Bparallel. Crossings of opposite-spin 1D subbands resemble magnetic phase transitions at zero dc source-drain bias, but display anticrossings at high dc bias. Our data also imply that the well-known 0.7 structure may evolve into a spin-hybridized state in finite dc bias.     

Broken-symmetry states of Dirac fermions in graphene with a partially filled high Landau level

We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wave vectors +/-q*. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against perturbation from disorder scattering. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wave functions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state of the Dirac fermions in graphene with lower filling factors in the N=3 LL.     

Magnetic field studies of the frictional drag between coupled two-dimensional electronic systems – Coulomb versus phonon coupling

The coupling between systems of two spatially separated two-dimensional (2D) electron gases and between systems of a separated 2D electron gas and a 2D hole gas is studied as a function of magnetic field . The small barrier (30 nm) separated coupled electron gases showed a transition from a phonon dominated interaction at to a Coulomb dominated one at quantising fields. For large barriers (190 nm) phonons have been found to be the dominant coupling mechanism both at zero and finite fields. However, for all barriers investigated we could observe novel screening effects manifested in a suppression of the coupling at half-filled Landau levels. For the coupled electron–hole gases we have investigated samples with large barriers ( ) so that the coupling is both in zero and finite fields dominated by phonon mediated processes. The enhanced screening effects could not be observed in those samples possibly due to the less pronounced quantisation of the hole gas.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Direct measurement of the Fermi energy in graphene using a double-layer heterostructure

We describe a technique which allows a direct measurement of the relative Fermi energy in an electron system by employing a double-layer heterostructure. We illustrate this method by using a graphene double layer to probe the Fermi energy as a function of carrier density in monolayer graphene, at zero and in high magnetic fields. This technique allows us to determine the Fermi velocity, Landau level spacing, and Landau level broadening. We find that the N=0 Landau level broadening is larger by comparison to the broadening of upper and lower Landau levels.     

Energy Distributions of the Szekeres Universes in Teleparallel Gravity

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy definitions in the teleparallel gravity (the tetrad theory of gravitation (TG)). We have found that Einstein and Bergmann–Thomson energy distributions give the same results, Landau–Lifshitz distribution is disagree in TG with these definitions. These results are the same as a previous works of Aygün et al., they investigated the same problem by using Einstein, Bergmann–Thomson, Landau–Lifshitz (LL) and Møller energy-momentum complexes in GR. However, both GR and TG are equivalent theories that is the energy densities are the same using different energy-momentum complexes in both theories. Also, our results are support the Cooperstock’s hypothesis.     

Anomalous robustness of the ν=5/2 fractional quantum Hall state near a sharp phase boundary

We report magnetotransport measurements in wide GaAs quantum wells with a tunable density to probe the stability of the fractional quantum Hall effect at a filling factor of ν=5/2 in the vicinity of the crossing between Landau levels (LLs) belonging to the different (symmetric and antisymmetric) electric subbands. When the Fermi energy (E(F)) lies in the excited-state LL of the symmetric subband, the 5/2 quantum Hall state is surprisingly stable and gets even stronger near this crossing, and then suddenly disappears and turns into a metallic state once E(F) moves to the ground-state LL of the antisymmetric subband. The sharpness of this disappearance suggests a first-order transition.     

Landau theory of magnetic phase diagrams and first order magnetisation processes

The Landau free energy expansion up to sixth order in the magnetisation has been used to study ferro- and paramagnetic phases in zero and finite applied magnetic fields. Magnetic phase diagrams are determined in terms of Landau coefficient ratios which indicate first order and metamagnetic phase transitions. In addition the critical magnetic field and specific magnetisations corresponding to first order magnetisation processes are calculated in terms of these coefficients. A method of evaluating Landau coefficients is also demonstrated.