V. M. Apalkov

Random resonators and prelocalized modes in disordered dielectric films.

We calculate the areal density of disorder-induced resonators with a high quality factor, Q>>1, in a film with fluctuating refraction index. We demonstrate that, for a given kl>1, where k is the light wave vector and l is the transport mean-free path, when on average the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of most probable resonators as functions of Q and kl are found.

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.

Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms

We investigate the Fock-Darwin states of the massless chiral fermions confined in a graphitic parabolic quantum dot. In light of Klein tunneling, we analyze the condition for confinement of the Dirac fermions in a cylindrically symmetric potential. New features of the energy levels of the Dirac electrons as compared to the conventional electronic systems are discussed. We also evaluate the dipole-allowed transitions in the energy levels of the dots. We propose that in the high magnetic field limit, the band parameters can be accurately determined from the dipole-allowed transitions.

Bias-selectable tricolor tunneling quantum dot infrared photodetector for atmospheric windows

A tricolor infrared detector with bias-selectable peaks based on tunneling quantum dot infrared photodetector (T-QDIP) architecture is demonstrated. Photoabsorption takes place in In0.4Ga0.6As quantum dots (QDs) and the excited electrons are collected by resonant tunneling across an Al0.2Ga0.8As∕In0.1Ga0.9As∕Al0.2Ga0.8As double barrier coupled to the QDs. The field dependent tunneling for excited carriers in T-QDIP is used to select the operating wavelength. This T-QDIP detector exhibits three distinct response peaks at 4.5∕4.9±0.05, 9.5±0.05, and 16.9±0.1μm up to 80K. The peak detectivity is in the range of (1.0–6.0)×1012Jones at 50K. Bias polarity allows the selection of either the 9.5μm or the 16.9μm peak.

Stable Pfaffian state in bilayer graphene.

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.

Two-phonon scattering of magnetorotons in fractional quantum Hall liquids

mechanism of magnetoroton dissociation. Understanding this mechanism is essential for the interpretation of the phonon absorption spectroscopy data, and for the prediction of the possible outcome of experiments at different filling factors. We show that the phonon-pulse-induced dissociation of the magnetoroton occurs as a second-order process in the electron-phonon interaction. It is a common feature for all systems containing dispersionless particles that two-phonon processes provide the main contribution to the transport

Tuning gaps and phases of a two-subband system in a quantizing magnetic field

In this work we study the properties of a two-subband quasi-two-dimensional electron system in a strong magnetic field when the electron filling factor is equal to 4. When the cyclotron energy is close to the intersubbandsplitting the system can be mapped onto a four-level electron system with an effective filling factor of 2. The ground state is either a ferromagnetic state or a spin-singlet state, depending on the values of the interlevel splitting and Zeeman energy. The boundaries between these phases are strongly influenced by the interelectron interaction. A significant exchange-mediated enhancement of the excitation gap results in the suppression of the electron-phonon interaction. The rate of absorption of nonequilibrium phonons is calculated as a function of Zeeman energy and intersubband splitting. The phonon absorption rate has two peaks as a function of intersubband splitting and has a steplike structure as a function of Zeeman energy.

Controllable driven phase transitions in fractional quantum Hall states in bilayer graphene.

Here we report from our theoretical studies that, in biased bilayer graphene, one can induce phase transitions from an incompressible fractional quantum Hall state to a compressible state by tuning the band gap at a given electron density. The nature of such phase transitions is different for weak and strong interlayer coupling. Although for strong coupling more levels interact there is a lesser number of transitions than for the weak coupling case. The intriguing scenario of tunable phase transitions in the fractional quantum Hall states is unique to bilayer graphene and has never before existed in conventional semiconductor systems.

Quantum cascade transitions in nanostructures

In this article we review the physical characteristics of quantum cascade transitions (QCTs) in various nanoscopic systems. The quantum cascade laser which utilizes such transitions in quantum wells is a brilliant outcome of quantum engineering that has already demonstrated its usefulness in various real-world applications. After a brief introduction to the background of this transition process, we discuss the physics behind these transitions in an externally applied magnetic field. This has unravelled many intricate phenomena related to intersubband resonance and electron relaxation modes in these systems. We then discuss QCTs in a situation where the quantum wells in the active regions of a quantum cascade structure are replaced by quantum dots. The physics of quantum dots is a rapidly developing field with its roots in fundamental quantum mechanics, but at the same time, quantum dots have tremendous potential applications. We first present a brief review of those aspects of quantum dots that are likely to be reflected in a quantum-dot cascade structure. We then go on to demonstrate how the calculated emission peaks of a quantum-dot cascade structure with or without an external magnetic field are correlated with the properties of quantum dots, such as the choice of confinement potentials, shape, size and the low-lying energy spectra of the dots. Contents PAGE 1 Introduction 456 2 Intersubband transitions in quantum wells 458 3 Quantum cascade transitions 462 3.1. Basic principles 462 3.1.1. Minibands and minigaps 464 3.1.2. Vertical transitions 464 3.1.3. GaAs/AlGaAs quantum cascade lasers 464 3.1.4. QCLs based on superlattice structures 465 3.1.5. Type-II quantum cascade lasers 466 3.1.6. Recent developments 466 3.2. Applications: sense-ability and other qualities 466 4 Quantum cascade transitions in novel situations 467 4.1. External magnetic field 467 4.1.1. Parallel magnetic field 468 4.1.2. Many-body effects: depolarization shift 470 4.1.3. The role of disorder 471 4.1.4. Tilted magnetic field 475 4.2. Magneto-transport experiments and phonon relaxation 479 4.3. Magneto-optics experiment and phonon relaxation 484 5 A brief review of quantum dots 485 5.1. From three- to zero-dimensional systems 485 5.2. Making the dots 487 5.2.1. Lithographic patterning 487 5.2.2. Self-assembled quantum dots 488 5.3. Shell filling in quantum dots 489 5.4. Electron correlations: spin states 490 5.5. Anisotropic dots 491 5.6. Influence of an external magnetic field 491 5.6.1. The Fock diagram 491 5.6.2. The no-correlation theorem 492 5.6.3. Correlation effects and magic numbers 492 5.6.4. Spin transitions 493 5.7. Quantum dots in novel systems 494 5.8. Potential applications of quantum dots 494 5.8.1. Single-electron transistors (SETs) 494 5.8.2. Single-photon detectors 494 5.8.3. Single-photon emitters 495 5.8.4. Quantum-dot lasers 495 6 Quantum cascade transitions in quantum-dot structures 496 6.1. Quantum dots versus quantum wells 496 6.2. QCT with rectangular dots 497 6.2.1. Vertical transitions 500 6.2.2. Diagonal transitions 501 6.3. QCT in a parabolic dot 504 6.4. Magnetic field effects on intersubband transitions 506 6.5. Mid-IR luminescence from a QD cascade device 512 7 Summary and open questions 513 Acknowledgements 515 References 515

Luminescence spectra of a quantum-dot cascade laser

A quantum cascade laser in which the quantum wells in the active regions are replaced by quantum dots with their atom-like discrete energy levels is an interesting system with which to study novel features in optical spectroscopy. We study structures suitable for diagonal lasing transitions in coupled dots, and vertical transitions in a single dot. The luminescence spectra as a function of electron number and dot size show that for diagonal transitions a significant amount of blueshift in the emission spectra can be achieved by increasing the electron population in the quantum dots as well as by decreasing the size of the dots.