We present high spectral resolution photoluminescence measurements of individual InAs/GaAs quantu... more We present high spectral resolution photoluminescence measurements of individual InAs/GaAs quantum dots for different excitation power densities and temperatures. The experimental results are compared with k.p calculations that include direct and exchange interactions for systems with up to three excitons in the dot. We have been able to assign most of the many peaks observed to various few-particle states. In
The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-... more The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-band strain dependent k· p Hamiltonian. The influence of strain on band energies and the conduction-band effective mass are examined. Single particle bound-state energies and exciton binding energies are computed as functions of island size. The eight-band results are compared with those for one, four and six bands, and with results from a one-band approximation in which m(r) is determined by the local value of the strain. The eight-band model predicts a lower ground state energy and a larger number of excited states than the other approximations.
We calculate the electronic structure of nm scale InP islands embedded in Ga_0.51In_0.49P. The ca... more We calculate the electronic structure of nm scale InP islands embedded in Ga_0.51In_0.49P. The calculations are done in the envelope approximation and include the effects of strain, piezoelectric polarization, and mixing among 6 valence bands. The electrons are confined within the entire island, while the holes are confined to strain induced pockets. One pocket forms a ring at the bottom of the island near the substrate interface, while the other is above the island in the GaInP. The two sets of hole states are decoupled. Polarization dependent dipole matrix elements are calculated for both types of hole states.
Pseudopotentials, tight-binding models, and k· p theory have stood for many years as the standard... more Pseudopotentials, tight-binding models, and k· p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here we present the first new method in decades, which we call atomistic k· p theory. In its usual formulation, k· p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however it is insensitive to the locations of individual atoms. We construct an atomistic k· p theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or ab initio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamon...
The electronic structure of an infinite 1D array of vertically coupled InAs/GaAs strained quantum... more The electronic structure of an infinite 1D array of vertically coupled InAs/GaAs strained quantum dots is calculated using an eight-band strain-dependent k-dot-p Hamiltonian. The coupled dots form a unique quantum wire structure in which the miniband widths and effective masses are controlled by the distance between the islands, d. The miniband structure is calculated as a function of d, and it is shown that for d>4 nm the miniband is narrower than the optical phonon energy, while the gap between the first and second minibands is greater than the optical phonon energy. This leads to decreased optical phonon scattering, providing improved quantum wire behavior at high temperatures. These miniband properties are also ideal for Bloch oscillation.
Calculating the electronic structure of systems involving very different length scales presents a... more Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with an energy close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation ...
First-principle ultrasoft pseudo potential approach of the plane wave based on density functional... more First-principle ultrasoft pseudo potential approach of the plane wave based on density functional theory (DFT) has been used for studying the electronic characterization and optical properties of ZnO and Fe, Co doped ZnO. The results show that the doping impurities change the lattice parameters a little, but bring more changes in the electronic structures. The band gaps are broadened by doping, and the Fermi level accesses to the conduction band which will lead the system to show the character of metallic properties. The dielectric function and absorption peaks are identified and the changes compared to pure ZnO are analyzed in detail.
The integer quantum Hall effect with a superconducting contact is analyzed. It is shown that the ... more The integer quantum Hall effect with a superconducting contact is analyzed. It is shown that the conductance plateaus occur at σxy = 2ne /h which is double the usual value. Non-Andreev scattering at the interface and flux penetration into the superconductor are shown to not affect the result. The effect should be observable in InAs quantum wells with Nb a contact. Typeset using REVTEX 1 This paper will examine the integer quantum Hall effect (IQHE) [1] in the presence of a superconductor-normal (SN) junction [2,3] at one of the leads. The IQHE occurs in a two dimensional electron gas (2DEG) in a strong magnetic field as quantized conductance plateaus with the value σxy = ne /h where n is the number of filled Landau levels. SN junctions have received considerable attention because of the transport properties caused by Andreev reflection, which takes place when an electron (hole) incident from the normal side has an energy lying within the superconducting gap of the superconductor. Because current is carried in the superconductor as Cooper pairs, a single electron (hole) at the Fermi level cannot enter the superconductor. For a Cooper pair to be injected into the superconductor a hole (electron) must be reflected back into the normal region. SN junctions in magnetic fields have been studied previously [4], although the magnetic field has usually been assumed small enough that Landau quantization is not significant. The system to be analyzed is a non-interacting Lx × Ly 2D electron gas (2DEG) that is periodic in the ŷ direction, with a uniform perpendicular magnetic field B = Bẑ. At x = Lx there is an infinite barrier, and the semi-infinite superconductor is located at x < 0. The superconductor is placed on only one side of the 2DEG to avoid the Josephson effect and to simplify some of the later analysis. The magnetic field and superconducting gap are assumed to change abruptly at the SN interface and are otherwise constant throughout the two different regions. Let us first briefly review Laughlin’s derivation of the IQHE without a superconductor [5,6] in which the periodic 2DEG encircles a magnetic flux Φ. The flux is adiabatically increased from 0 to one flux quantum, Φ0 = hc/e, and then removed by a gauge transformation. The addition of ∆Φ = Φ0 increases the energy of the 2DEG, but the gauge transformation returns the Hamiltonian to its original form. Therefore, the net result is an excited state of the original system. Examination of the electron wave functions in the Landau gauge shows that adding one flux quantum transfers a single electron per Landau level from one edge of the sample to the other. Since the current is related to the change in energy of the 2DEG by Iy = c∆U/∆Φ, we may equate ∆U to the energy for transporting 2 one electron per Landau level across a potential difference V to obtain Iy = ne V/h. Now consider what happens when the superconductor is present. Assume Φ0 is added such that the electrons in the 2DEG are shifted towards the superconductor. (Φ0 corresponds to two flux quanta for the superconductor, so it may still be gauge transformed away.) To be removed from the sample, an electron must enter the superconductor. However at the Fermi level there are no quasiparticle states available in the superconductor and therefore another charge is needed to make a Cooper pair. This extra charge comes from an Andreev reflected hole which, because of its charge, is shifted in the opposite direction, away from the superconductor. Hence, adiabatic addition of one flux quantum transports a charge 2e across the sample leading to Iy = 2ne V/h, (1) or the double quantum Hall effect (2QHE). Clearly the superconductor does not change the role of impurities in providing localized states that lead to the conductance plateaus [5,6]. To examine the 2QHE in more detail, we will compute the states of the system, and explicitly compute Iy using the edges states. The system will be described by the Bogoluibovde Genne (BdG) equation [7], Hψ(r) = Eψ(r) (2) H =
ABSTRACTWe use Raman scattering to study the spatially-resolved strain and stress in a complex zi... more ABSTRACTWe use Raman scattering to study the spatially-resolved strain and stress in a complex zinc blende GaAs/GaP heterostructured nanowire which contains both axial and radial interfaces. The nanowires are grown by metal-organic chemical vapor deposition in the [111] direction with Au nano particles as catalysts, High spatial resolution Raman scans along the nanowires show the GaAs/GaP interface is clearly identifiable. We interpret the phonon energy shifts in each material as one approaches the interface.
... Neave, PJ Dobson, BA Joyce, and J. Zhang, AppI. Phys. Lett. 47, 100 (1983); PR Pukite, JM Van... more ... Neave, PJ Dobson, BA Joyce, and J. Zhang, AppI. Phys. Lett. 47, 100 (1983); PR Pukite, JM Van Hove, and P. 1. Cohen, J. Vac. Sci. Technol. B 2, 243 (1984). [201 MD Pashley, KW Haberern, and JM Gaines, AppI. Phys. Lett. 58, 406 (1991). [211 MS Miller, CE Pryor, H. Weman ...
We present high spectral resolution photoluminescence measurements of individual InAs/GaAs quantu... more We present high spectral resolution photoluminescence measurements of individual InAs/GaAs quantum dots for different excitation power densities and temperatures. The experimental results are compared with k.p calculations that include direct and exchange interactions for systems with up to three excitons in the dot. We have been able to assign most of the many peaks observed to various few-particle states. In
The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-... more The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-band strain dependent k· p Hamiltonian. The influence of strain on band energies and the conduction-band effective mass are examined. Single particle bound-state energies and exciton binding energies are computed as functions of island size. The eight-band results are compared with those for one, four and six bands, and with results from a one-band approximation in which m(r) is determined by the local value of the strain. The eight-band model predicts a lower ground state energy and a larger number of excited states than the other approximations.
We calculate the electronic structure of nm scale InP islands embedded in Ga_0.51In_0.49P. The ca... more We calculate the electronic structure of nm scale InP islands embedded in Ga_0.51In_0.49P. The calculations are done in the envelope approximation and include the effects of strain, piezoelectric polarization, and mixing among 6 valence bands. The electrons are confined within the entire island, while the holes are confined to strain induced pockets. One pocket forms a ring at the bottom of the island near the substrate interface, while the other is above the island in the GaInP. The two sets of hole states are decoupled. Polarization dependent dipole matrix elements are calculated for both types of hole states.
Pseudopotentials, tight-binding models, and k· p theory have stood for many years as the standard... more Pseudopotentials, tight-binding models, and k· p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here we present the first new method in decades, which we call atomistic k· p theory. In its usual formulation, k· p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however it is insensitive to the locations of individual atoms. We construct an atomistic k· p theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or ab initio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamon...
The electronic structure of an infinite 1D array of vertically coupled InAs/GaAs strained quantum... more The electronic structure of an infinite 1D array of vertically coupled InAs/GaAs strained quantum dots is calculated using an eight-band strain-dependent k-dot-p Hamiltonian. The coupled dots form a unique quantum wire structure in which the miniband widths and effective masses are controlled by the distance between the islands, d. The miniband structure is calculated as a function of d, and it is shown that for d>4 nm the miniband is narrower than the optical phonon energy, while the gap between the first and second minibands is greater than the optical phonon energy. This leads to decreased optical phonon scattering, providing improved quantum wire behavior at high temperatures. These miniband properties are also ideal for Bloch oscillation.
Calculating the electronic structure of systems involving very different length scales presents a... more Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with an energy close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation ...
First-principle ultrasoft pseudo potential approach of the plane wave based on density functional... more First-principle ultrasoft pseudo potential approach of the plane wave based on density functional theory (DFT) has been used for studying the electronic characterization and optical properties of ZnO and Fe, Co doped ZnO. The results show that the doping impurities change the lattice parameters a little, but bring more changes in the electronic structures. The band gaps are broadened by doping, and the Fermi level accesses to the conduction band which will lead the system to show the character of metallic properties. The dielectric function and absorption peaks are identified and the changes compared to pure ZnO are analyzed in detail.
The integer quantum Hall effect with a superconducting contact is analyzed. It is shown that the ... more The integer quantum Hall effect with a superconducting contact is analyzed. It is shown that the conductance plateaus occur at σxy = 2ne /h which is double the usual value. Non-Andreev scattering at the interface and flux penetration into the superconductor are shown to not affect the result. The effect should be observable in InAs quantum wells with Nb a contact. Typeset using REVTEX 1 This paper will examine the integer quantum Hall effect (IQHE) [1] in the presence of a superconductor-normal (SN) junction [2,3] at one of the leads. The IQHE occurs in a two dimensional electron gas (2DEG) in a strong magnetic field as quantized conductance plateaus with the value σxy = ne /h where n is the number of filled Landau levels. SN junctions have received considerable attention because of the transport properties caused by Andreev reflection, which takes place when an electron (hole) incident from the normal side has an energy lying within the superconducting gap of the superconductor. Because current is carried in the superconductor as Cooper pairs, a single electron (hole) at the Fermi level cannot enter the superconductor. For a Cooper pair to be injected into the superconductor a hole (electron) must be reflected back into the normal region. SN junctions in magnetic fields have been studied previously [4], although the magnetic field has usually been assumed small enough that Landau quantization is not significant. The system to be analyzed is a non-interacting Lx × Ly 2D electron gas (2DEG) that is periodic in the ŷ direction, with a uniform perpendicular magnetic field B = Bẑ. At x = Lx there is an infinite barrier, and the semi-infinite superconductor is located at x < 0. The superconductor is placed on only one side of the 2DEG to avoid the Josephson effect and to simplify some of the later analysis. The magnetic field and superconducting gap are assumed to change abruptly at the SN interface and are otherwise constant throughout the two different regions. Let us first briefly review Laughlin’s derivation of the IQHE without a superconductor [5,6] in which the periodic 2DEG encircles a magnetic flux Φ. The flux is adiabatically increased from 0 to one flux quantum, Φ0 = hc/e, and then removed by a gauge transformation. The addition of ∆Φ = Φ0 increases the energy of the 2DEG, but the gauge transformation returns the Hamiltonian to its original form. Therefore, the net result is an excited state of the original system. Examination of the electron wave functions in the Landau gauge shows that adding one flux quantum transfers a single electron per Landau level from one edge of the sample to the other. Since the current is related to the change in energy of the 2DEG by Iy = c∆U/∆Φ, we may equate ∆U to the energy for transporting 2 one electron per Landau level across a potential difference V to obtain Iy = ne V/h. Now consider what happens when the superconductor is present. Assume Φ0 is added such that the electrons in the 2DEG are shifted towards the superconductor. (Φ0 corresponds to two flux quanta for the superconductor, so it may still be gauge transformed away.) To be removed from the sample, an electron must enter the superconductor. However at the Fermi level there are no quasiparticle states available in the superconductor and therefore another charge is needed to make a Cooper pair. This extra charge comes from an Andreev reflected hole which, because of its charge, is shifted in the opposite direction, away from the superconductor. Hence, adiabatic addition of one flux quantum transports a charge 2e across the sample leading to Iy = 2ne V/h, (1) or the double quantum Hall effect (2QHE). Clearly the superconductor does not change the role of impurities in providing localized states that lead to the conductance plateaus [5,6]. To examine the 2QHE in more detail, we will compute the states of the system, and explicitly compute Iy using the edges states. The system will be described by the Bogoluibovde Genne (BdG) equation [7], Hψ(r) = Eψ(r) (2) H =
ABSTRACTWe use Raman scattering to study the spatially-resolved strain and stress in a complex zi... more ABSTRACTWe use Raman scattering to study the spatially-resolved strain and stress in a complex zinc blende GaAs/GaP heterostructured nanowire which contains both axial and radial interfaces. The nanowires are grown by metal-organic chemical vapor deposition in the [111] direction with Au nano particles as catalysts, High spatial resolution Raman scans along the nanowires show the GaAs/GaP interface is clearly identifiable. We interpret the phonon energy shifts in each material as one approaches the interface.
... Neave, PJ Dobson, BA Joyce, and J. Zhang, AppI. Phys. Lett. 47, 100 (1983); PR Pukite, JM Van... more ... Neave, PJ Dobson, BA Joyce, and J. Zhang, AppI. Phys. Lett. 47, 100 (1983); PR Pukite, JM Van Hove, and P. 1. Cohen, J. Vac. Sci. Technol. B 2, 243 (1984). [201 MD Pashley, KW Haberern, and JM Gaines, AppI. Phys. Lett. 58, 406 (1991). [211 MS Miller, CE Pryor, H. Weman ...
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