S.-R. Eric Yang

Character of states near the Fermi level in (Ga,Mn)as : Impurity to valence band crossover

We discuss the character of states near the Fermi level in Mn doped GaAs, as revealed by a survey of dc transport and optical studies over a wide range of Mn concentrations. A thermally activated valence band contribution to dc transport, a mid-infrared peak at energy hbar omega approx 200 meV in the ac- conductivity, and the hot photoluminescence spectra indicate the presence of an impurity band in low doped ( 2% doping, no traces of Mn-related activated contribution can be identified in dc-transport, suggesting that the impurity band has merged with the valence band. No discrepancies with this perception are found when analyzing optical measurements in the high-doped GaAs:Mn. A higher energy (hbar omega approx 250 meV) mid-infrared feature which appears in the metallic samples is associated with inter-valence band transitions. Its red-shift with increased doping can be interpreted as a consequence of increased screening which narrows the localized-state valence-band tails and weakens higher energy transition amplitudes. Our examination of the dc and ac transport characteristics of GaAs:Mn is accompanied by comparisons with its shallow acceptor counterparts, confirming the disordered valence band picture of high-doped metallic GaAs:Mn material.

Addition spectra of quantum dots in strong magnetic fields.

We consider the magnetic field dependence of the chemical potential for parabolically confined quantum dots in a strong magnetic field. Approximate expressions based on the notion that the size of a dot is determined by a competition between confinement and interaction energies are shown to be consistent with exact diagonalization studies for small quantum dots. Fine structure is present in the magnetic field dependence which cannot be explained without a full many-body description and is associated with ground-state level crossings as a function of confinement strength or Zeeman interaction strength. Some of this fine structure is associated with precursors of the bulk incompressible states responsible for the fractional quantum Hall effect

Quantum dots in strong magnetic fields: stability criteria for the maximum density droplet

In this article we discuss the ground state of a parabolically confined quantum dot in the limit of very strong magnetic fields where the electron system is completely spin-polarised and all electrons are in the lowest Landau level. Without electron-electron interactions the ground state is a single Slater determinant corresponding to a droplet centred on the minimum of the confinement potential and occupying the minimum area allowed by the Pauli exclusion principle. Electron-electron interactions favour droplets of larger area. We derive exact criteria for the stability of the maximum density droplet against edge excitations and against the introduction of holes in the interior of the droplet. The possibility of obtaining exact results in the strong magnetic field case is related to important simplifications associated with broken time-reversal symmetry in a strong magnetic field.

Infrared conductivity of metallic (III,Mn)V ferromagnets

We present a theory of the infrared conductivity and absorption coefficients of metallic ~III,Mn!V ferromagnetic semiconductors. We find that the conductivity is dominated by intervalence-band transitions that produce peaks at \v;220 meV and obscure the broadened Drude peak. We demonstrate that transverse f-sum rule measurements can be used to extract accurate values for the free-carrier density, bypassing the severe characterization difficulties that have till now been created by the large anomalous Hall effect in these materials.

Interactions, localization, and the integer quantum hall effect

We report on numerical studies of the influence of Coulomb interactions on the localization of electronic wave functions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that interactions have no effect on the critical exponent characterizing the diverging localization length, no effect on the fractal dimension of the second moment of the extended wave functions, and no effect on Thouless number estimates of the maximum dissipative conductivity.

Disorder and ferromagnetism in diluted magnetic semiconductors

We have investigated the interplay between disorder and ferromagnetism in III 1 - x Mn x V semiconductors. Our study is based on a model in which S=5/2 Mn local moments are exchange coupled to valence-band holes that interact via Coulomb interactions with each other, with ionized Mn acceptors, and with the antisite defects present in these materials. We find quasiparticle participation ratios consistent with a metal-insulator transition that occurs in the ferromagnetic state near x∼0.01. By evaluating the distribution of exchange mean fields at Mn moment sites, we provide evidence in favor of the applicability of impurity-band magnetic-polaron and hole-fluid models on insulating and metallic sides of the phase transition, respectively.

States near Dirac points of a rectangular graphene dot in a magnetic field

In neutral graphene dots, the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped graphene dot with two zigzag and two armchair edges. We find that a quasidegenerate level forms near zero energy and the number of states in this level can be tuned by the magnetic field. The wave functions of states in this level are all peaked on the zigzag edges with or without some weight inside the dot. Some of these states are magnetic field-independent surface states while the others are field-dependent. We have found a scaling result from which the number of magnetic field-dependent states of large dots can be inferred from those of smaller dots.

Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetry in the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.

Non-drude optical conductivity of (III, Mn)V ferromagnetic semiconductors

We present a numerical model study of the zero-temperature infrared optical properties of (III,Mn)V diluted magnetic semiconductors. Our calculations demonstrate the importance of treating disorder and interaction effects simultaneously in modelling these materials. We find that the conductivity has no clear Drude peak, that it has a broadened inter-band peak near 220 meV, and that oscillator weight is shifted to higher frequencies by stronger disorder. These results are in good qualitative agreement with recent thin film absorption measurements. We use our numerical findings to discuss the use of f-sum rules evaluated by integrating optical absorption data for accurate carrier-density estimates.

Quantum-Hall quantum bits

Bilayer quantum-Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level systems that have potential advantages as quantum bits.