Exchange interaction effects in electron spin resonance: Larmor theorem violation in narrow-gap quantum well heterostructures

We report a theoretical study of the exchange interaction effects in the electron spin resonance (ESR) in n-type narrow-gap quantum well (QW) heterostructures. Using the Hartree-Fock approximation, based on the eight-band k?p Hamiltonian, the many-body correction to the ESR energy is found to be nonzero, providing theoretical evidence of Larmor theorem violation in symmetric narrow-gap QWs. We predict the exchange enhancement of the ESR g-factor and its divergence in low magnetic fields. The 'enhanced' ESR g-factor and quasiparticle g-factor, measured in magnetotransport, coincide at even-valued filling factors of the Landau levels in moderate and quantizing magnetic fields.     

Theory of g-factor enhancement in narrow-gap quantum well heterostructures

We report on the study of the exchange enhancement of the g-factor in the two-dimensional (2D) electron gas in n-type narrow-gap semiconductor heterostructures. Our approach is based on the eight-band k?p Hamiltonian and takes into account the band nonparabolicity, the lattice deformation, the spin-orbit coupling and the Landau level broadening in the δ-correlated random potential model. Using the 'screened' Hartree-Fock approximation we demonstrate that the exchange g-factor enhancement not only shows maxima at odd values of Landau level filling factors but, due to the conduction band nonparabolicity, persists at even filling factor values as well. The magnitude of the exchange enhancement, the amplitude and the shape of the g-factor oscillations are determined by both the screening of the electron-electron interaction and the Landau level width. The 'enhanced' g-factor values calculated for the 2D electron gas in InAs/AlSb quantum well heterostructures are compared with our earlier experimental data and with those obtained by Mendez et?al (1993 Phys.?Rev.?B 47 13937) in magnetic fields up to 30?T.     

Experimental demonstration of Fermi surface effects at filling factor 5/2

Using small wavelength surface acoustic waves (SAW) on ultrahigh mobility heterostructures, Fermi surface properties are detected at 5/2 filling factor at temperatures higher than those at which the quantum Hall state forms. An enhanced conductivity is observed at 5/2 by employing sub-0.5-microm SAW, indicating a quasiparticle mean-free path substantially smaller than that in the lowest Landau level. These findings are consistent with the presence of a filled Fermi sea of composite fermions, which may pair at lower temperatures to form the 5/2 ground state.     

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role.     

Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.     

Landau-level spectroscopy of a two-dimensional electron system by tunneling through a quantum dot

A single InAs self-assembled quantum dot is incorporated in the barrier of a tunnel diode and used as a spectroscopic probe of an adjacent two-dimensional electron system from the Fermi energy to the subband edge. We obtain quantitative information about the energy dependence of the quasiparticle lifetime. For magnetic field B, applied parallel to the current, we observe peaks in the current-voltage characteristics I(V) corresponding to the formation of Landau levels. Close to filling factor nu=1 we observe directly the exchange enhancement of the Lande g factor.     

Point impurities remove degeneracy of the Landau levels in a two-dimensional electron gas

The density of states of a two-dimensional electron gas in a magnetic field has been studied taking into account the scattering on point impurities. It is demonstrated that allowance for the electron-impurity interaction completely removes degeneracy of the Landau levels even for a small volume density of these point defects. The density of states is calculated in a self-consistent approximation taking into account all diagrams without intersections of the impurity lines. The electron density of states ρ is determined by the contribution from a cut of the one-particle Green’s function rather than from a pole. In a wide range of the electron energies ω (measured from each Landau level), the value of ρ(ω) is inversely proportional to the energy |ω| and proportional to the impurity concentration. The obtained results are applicable to various two-dimensional electron systems such as inversion layers, heterostructures, and electrons on the surface of liquid helium.     

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.     

On the Possibility of Superconductivity in Bilayer Heterostructures

A model is created for bilayer heterostructures in a strong magnetic field which makes it possible to neglect the Coulomb interaction. The thermodynamic instability of states of the electron system in a strong magnetic field leads to the formation of a periodic vortex lattice. The case is considered where the electron density is close to the density of the half-filled Landau level. An electron spectrum is found and an analog of the Cooper effect appearing under the Bogoliubov canonical transformation for electron Fermi operators is studied.     

Study of hopping in two dimensional electron gas in InGaAs/InP heterostructures with two subbands

Shubnikov de Haas, quantum Hall effect and direct measurements of the diagonal conductivity on InGaAs/InP heterostructures have been performed on a quasi Corbino disk combining Hall bar and Corbino geometry. The temperature dependence of is studied at several minima of the magnetoresistance . A hopping conduction is observed when the Fermi level is between two Landau levels. And a low magnetic field intersubband scattering has been also noticed.The study of the transient time after illumination shows that the photoconductivity is mainly due to localized states.     

Density of states of the two-dimensional electron system at Si-MOS and Si-MNOS devices in the quantum Hall regime

The measurement of activation energies for various positions of the Fermi level between two Landau levels provides an opportunity to evaluate the density of states (DOS) in the quantum Hall regime. We present results of measurements of the temperature dependence of the magnetoresistivity _xx at filling factors ν = 2 and ν = 4 for several Si-MOS and MNOS samples with the same layout but different insulator layers of SiO₂ or SiO₂/Si₃N₄, respectively. The Hall mobility of the MNOS structures is noticeably higher than that of the MOS structures, whereas the DOS determined from activation energy measurements is lower. The measured DOS is higher than the simple overlap of two adjacent Gaussian-shaped Landau bands with broadening parameters taken from the Hall mobility data. This can be explained by a constant background contribution to the DOS. For the i = 2 plateau an estimate of the effective Landé-factor can be given.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Composite-fermion spin excitations as nu approaches 1/2: interactions in the Fermi sea

Measurements of low-lying spin excitations by inelastic light scattering unveil a delicate balance between spin reversal and Fermi energies in the Fermi sea of composite fermions that emerges in the limit of nu --> 1/2. The interplays between these two fundamental quasiparticle interactions are uncovered in lowest spin-flip excitations in which the spin orientation and Landau level index of composite fermions change simultaneously. A collapse of the spin-flip excitation gap as nu --> 1/2 is linked to vanishing quasiparticle energy level spacings and loss of full spin polarization.     

STM/STS measurements of two-dimensional electronic states trapped around surface defects in magnetic fields

The local density of states (LDOS) near point defects on a surface of highly oriented pyrolytic graphite (HOPG) was studied at very low temperatures in magnetic fields up to 6 T. We observed localized electronic states over a distance of the magnetic length around the defects in differential tunnel conductance images at the valley energies of the Landau levels (LLs) as well as relatively extended states at the peak ones of LLs. These states appear mainly at energies above the Fermi energy corresponding to the electron LL bands. The data suggest that the quantum Hall state is realized in the quasi two dimensional electron system in HOPG. At the peak energy associated with the n=0 (electron) and -1 (hole) LLs characteristic of the graphite structure, a reduced LDOS around the defects is observed. The spatial distribution is almost field independent, which indicates that it represents the potential shape produced by the defects.     

Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.     

Opening an energy gap in an electron double layer system at the integer filling factor in a tilted magnetic field

We employ magnetocapacitance measurements to study the spectrum of a double layer system with gate-voltage-tuned electron density distributions in tilted magnetic fields. For the dissipative state in normal magnetic fields at filling factor v=3 and 4, a parallel magnetic field component is found to give rise to the opening of a gap at the Fermi level. We account for the effect in terms of parallel-field-caused orthogonality breaking of the Landau wave functions with different quantum numbers for two subbands.     

Hartree-Fock solution of CDW of two-dimensional electron gas in magnetic field

Temperature dependence of the amplitude of the charge density wave of two-dimensional electron gas in strong magnetic field is calculated within Hartree-Fock approxiimation. The density of states is investigated, too, and it is shown that there is not an energy gap at Fermi level when the lowest Landau level is half filled.     

Supersymmetric approach to heavy-fermion systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes n _c + 1 states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.     

Spin-dependent transport in a magnetic two-dimensional electron gas

Magneto-transport and magneto-optical probes are used to interrogate spin-dependent transport in magnetic heterostructures wherein a two dimensional electron gas (2DEG) is exchange-coupled to local moments. At low temperatures, the significant s–d exchange-enhanced spin splitting in these “magnetic” 2DEGs is responsible for the observation of unusual transport properties such as a complete spin polarization of the gas at large Landau level filling factors and a pronounced, non-monotonic background magneto-resistance. Magneto-transport measurements of gated samples performed in a parallel field geometry are used to systematically study the variation of the magneto-resistance with sheet concentration, yielding new insights into the dependence of spin transport on the Fermi energy of the majority spin carriers.