Resonant tunneling of electrons between two-dimensional systems of different densities in a quantizing magnetic field

The results of experimental investigation of the vertical electron transport in a GaAs/Al_0.3Ga_0.7As/GaAs single-barrier tunneling heterostructure with a doped barrier are presented. Two-dimensional accumulation layers appear on different sides of the barrier as a result of the ionization of Si donors in the barrier layer. The nonmonotonic shift of the current peak is found in the I–V curve of the tunneling diode in a magnetic field perpendicular to the planes of two-dimensional layers. Such a behavior is shown to be successfully explained in the model of appearing the Coulomb pseudogap and the pinning of the spin-split Landau levels at the Fermi levels of the contacts. In this explanation, it is necessary to assume that the Landé factor is independent of the filling factors of the Landau levels and is g* = 7.5 for both layers.     

Incompressible paired hall state, stripe order, and the composite fermion liquid phase in half-filled landau levels

We consider the two lowest Landau levels at half filling. In the higher Landau level (nu = 5/2), we find a first-order phase transition separating a compressible striped phase from a paired quantum Hall state, which is identified as the Moore-Read state. The critical point is very near the Coulomb potential and the transition can be driven by increasing the width of the electron layer. We find a much weaker transition (either second-order or a crossover) from pairing to the composite fermion Fermi-liquid behavior. A very similar picture is obtained for the lowest Landau level, but the transition point is not near the Coulomb potential.     

Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript>

Exact analytical representation for the Coulomb matrix elements by means of Appell’s double series F₂ is derived. The finite sum obtained for the Appell function F₂ allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.     

A non-singular spherically symmetric separable copy of the vacuum in SU(2) Landau gauge

We give a new non-singular spherically symmetric and separable copy of the vacuum in Landau gauge for SU(2) Yang-Mills theories. The solution can be considered as a generalization of Gribov's solution in Coulomb gauge and thus it demonstrates the similarity between vacua in Coulomb and Landau gauges.     

Calculation of electric transport close to a Lifshitz transition in a high magnetic field

The effects of the Landau quantization and interactions on a Lifshitz transition are studied. The Landau quantization leads to a quasi-one-dimensional behavior for the direction parallel to the field. The repulsive Coulomb interactions give rise to a gas of strongly correlated carriers. Consequently, in the ground state, an electron pocket is emptied in a discontinuous fashion as a function of the chemical potential or magnetic field. This discontinuity is gradually smeared by temperature, in agreement with experiments for CeIn₃. We further calculate the conductivity and the Hall conductivity in the presence of nonmagnetic impurities, the Landau quantization and interactions.     

FULLY RELATIVISTIC CALCULATIONS OF THE ENERGIES, OSCILLATOR STRENGTHS AND EINSTEIN COEFFICENTS OF THE FORBIDDEN TRANSITIONS FOR Ne-LIKE SEQUENCES

We provide systematic calculations about the energy levels, Einstein coefficients and oscillator strengths for electric quadrupole (E2) and magnetic quadrupole (M2) transitions between n=3 and n=2 of Ne-like systems by using the fully relativistic multi-configuration Dirac-Fock method. The oscillator strengths of the E2 transitions under Coulomb and Babshkin gauges are compared with each other and show the differences from 1.2 to 12 percent. We also found that the M2 line (0.37429 nm) with the biggest oscillator strengths in Ne-like Ag³⁷⁺ mixes with the line (2p⁵_3/23s_1/23d_5/2)_3/2→gs (0.37427 nm) emitted by the Na-like Ag³⁶⁺.     

Magneto-absorption in CdS

We have investigated the 2°K absorption spectra of CdS between 4700 Å and 4860 Å for magnetic fields up to 100 kG. We find that excitonic effects are important for the two lowest Landau levels but not for the third or higher Landau levels. The most interesting feature of the data is that the higher excited states (n ? 3) of the exciton are associated with the two lowest Landau levels. These results are discussed and compared with those in other materials. A reduced effective mass of 0.18m₀ has been deduced.     

A Mathematical Representation of Quantizing the Motion of Relativistic Electrons in a Magnetic Field

It is shown that the quadratic component of the kinetic energy of continuous longitudinal motion of relativistic electrons in the external magnetic field is varied continuously between 0 and 2(2m _e c ²_B H) within each Landau energy level, undergoing an abrupt change at the boundaries of the levels. This results in the fact that in the quantum limit of a superstrong magnetic field where all electrons are at the zero Landau level, the maximum quadratic component of the kinetic energy of free longitudinal electron motion along the direction of the magnetic field is twice as high as the maximum quadratic component of the kinetic energy of its bound transverse motion.     

Shake-up processes in intersubband magneto-photoabsorption of a two-dimensional electron gas

I theoretically study shake-up processes in photoabsorption of an interacting low-density two-dimensional electron gas (2DEG) in magnetic fields. Such processes, in which an incident photon creates an electron–hole pair and simultaneously excites one electron to one of the higher Landau levels, were observed experimentally [Phys. Rev. Lett. 79 (1997) 3974] and were called combined exciton-cyclotron resonance (ExCR). The recently developed theory of ExCR [Phys. Rev. B 64 (2001) 241101] allows for a consistent treatment of the Coulomb correlations, establishes the exact ExCR selection rules, and predicts the high-field features of ExCR. In this work, I generalize the existing theory of high-field ExCR in the 2DEG to the case when the hole is excited to higher hole Landau levels.     

Nonequilibrium Green's Function Approach to Resonant Magnetotunneling Through a Quantum Dot

Keldysh's nonequilibrium Green's function is applied to studying resonant magnetotunneling through a quantum dot. We propose a microscopic Anderson-impurity-like Hamiltonian in which two kinds of the on-site Coulomb interactions are introduced:the interaction of two electrons at the same Landau level with different spins, U₁ and the interaction for the electrons between different Landau levels, U₁. I-V curves are obtained under different magnetic fields in asymmetrical structures which can display both the energy quantization and singleelectron charging effect. The theoretical results are in good agreement with the experiments qualitatively. The linear-response conductance is also discussed.     

Mesoscopic fluctuations of the Coulomb drag at nu = 1/2

We consider mesoscopic fluctuations of Coulomb drag transresistivity between two layers at a Landau level filling factor nu = 1/2 each. We find that, at low temperatures, sample to sample fluctuations exceed both the ensemble average and the corresponding fluctuations at B = 0. At the experimentally relevant temperatures, the variance of the transresistivity is proportional to T(-1/2). We find the dependence of this variance on density and magnetic field to reflect the attachment of two flux quanta to each electron.     

Far-infrared laser oscillation due to cyclotron emission in p-type germanium

Far-infrared laser oscillation due to cyclotron emission in the light hole band of p-type germanium was observed under crossed electric and magnetic fields. The wavelength is inversely proportional to magnetic fields with a cyclotron mass ofm _c =0.048m _c . Numerical calculations based on Luttinger Hamiltonian show that mixing of wavefunctions between the light and heavy hole bands causes population inversion betweenn=0 andn=1 light-hole Landau levels. It is also shown that non-equidistant energy spacing of light-hole Landau levels is essential to yield net amplification.     

Resonantly enhanced tunneling in a double layer quantum hall ferromagnet

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling nuT=1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed.     

Fractional quantum Hall States of Dirac electrons in graphene

We have investigated the fractional quantum Hall states of Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of electrons in graphene significantly modifies the interelectron interactions. This results in a specific dependence of the ground state energy and the energy gaps for electrons on the Landau-level index. For the valley-polarized states, i.e., at nu=1/m, m being an odd integer, the energy gaps have the largest values in the n=1 Landau level. For the valley-unpolarized states, e.g., for the 2/3 state, the energy gaps are suppressed for n=1 as compared to those at n=0. For both n=1 and n=0, the ground state of the 2/3 system is fully valley-unpolarized.     

On the vacuum structure in the Coulomb and Landau gauges

Vacuum structure in the SU(N) Coulomb and Landau gauges is studied by using the methods of harmonic maps. A systematic way for solving the Gribov vacuum copy equation is presented and many examples are discussed in both the Coulomb and Landau gauges as applications of the method. Finally, the physical interpretation of Gribov ambiguities is shortly reviewed from a topological point of view.     

Fractionalization into merons in quantum dots

We study by exact diagonalization, in the lowest Landau level approximation, the Coulomb interaction problem of N=4 and N=6 quantum dots in the limit of zero Zeeman coupling. We find that meron excitations constitute the lowest lying states of the quantum dots. This is based on a mapping between the excitations of the dot and states of the Haldane-Shastry spin chain.     

Magneto-optics and strain effects in GaInAsAlInAs and GaInAsInP quantum wells

Transitions between the Landau levels of the lowest electron and hole sub-bands have been observed in the inter-band optical absorption of a modulation doped Ga_.47In_.53AsAl_0.48In_.52As superlattice and a Ga_0.3In_.7AsInP strained layer superlattice, in magnetic fields up to 16T. In the unstrained sample, the energies of transitions up to 250 meV above the GaInAs band gap were found to be well described by a parabolic model for the heavy hole band and the model of Bowers and Yafet for the conduction band. In contrast to previous work on undoped quantum wells, no Coulomb binding effects were observed in this lightly doped sample, and this is attributed to screening of the exciton. In the strained sample, the heavy hole sub-band was found to show highly non-parabolic structure, and this is believed to be due to the effects of biaxial strain on the valence band.     

Quantum-Hall activation gaps in graphene

We have measured the quantum-Hall activation gaps in graphene at filling factors nu=2 and nu=6 for magnetic fields up to 32 T and temperatures from 4 to 300 K. The nu=6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at nu=2 is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields B>20 T and temperatures T>100 K. We explain this surprising behavior by a narrowing of the lowest Landau level.     

Two-dimensional electron gas in a strong magnetic field. II

The quantum mechanical problem on the motion of electrons in a strong (quantizing the motion) magnetic field is considered, taking into account the Coulomb interaction between charges. It is shown how, on the basis of the solutions found, it is possible to obtain the fractional filling factor of the Landau levels that enters into the expression for the Hall conductivity of a two-dimensional electron gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 25–29, March, 1990.