Temperature Dependence of Strong-Coupled Polaron in a Triangular Potential Quantum Dot

The effect of temperature on the ground-state energy of polaron was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekar type in triangular potential quantum dot (QD). The ground-state energy was expressed as functions of the confinement length of QD, the coupling strength, the polar angle and the temperature. It is found that the ground-state energy decreases with increasing the confinement length of QD and the electron-phonon coupling strength and increases with enhancing the temperature.     

The Rashba Effect of Polaron in a Parabolic Quantum Dot

The condition of electric-LO phonon strong coupling in a parabolic quantum dot (QD) is studied in detail. We obtain the polaron ground state energy by the variational method of Pekar, considering the influence of the Rashba SO interaction. The relations on the polaron ground state energy with the parallel confinement length, the electron-LO phonon coupling constant and the perpendicular confinement length are derived for a parabolic quantum dot.     

The Rashba Effect on the Bound Polaron in a Parabolic Quantum Dot

The bound polaron ground state energy is calculated by the variational method of Pekar considering the influence of the Rashba SO interaction on the condition of electric?CLO phonon strong coupling in a parabolic quantum dot (QD). The relations on the bound polaron ground state energy with the parallel confinement length, the electron?CLO phonon coupling constant, the perpendicular confinement length and the Coulomb binding parameter are derived for a parabolic quantum dot.     

Rashba Effect on the Bound Polaron in an Asymmetric Quantum Dot

By using LLP variational method, the Rashba effect on the bound polaron in an asymmetric quantum dot is investigated and the expression of the bound polaron ground state energy is derived. Considering different Coulomb bound potentials, we discuss the relations between the ground state energy and the electron–phonon coupling strength, the wave vector, the transverse effective confinement length and the longitudsinal effective confinement length, respectively. The results show that the ground state energy is a decreasing function of the Coulomb bound potential, the electron–phonon coupling strength, the transverse effective confinement length and the longitudinal effective confinement length. On the contrary, it is an increasing function of the wave vector. Due to the Rashba effect, the ground state energy splits into two branches.     

The Polar Optical Phonon Confinement Effect on the Binding Energy of a Hydrogenic Impurity in Quantum Wires Under Applied Electric and Magnetic Fields

The impurity bound polaron in a cylindrical quantum wire with a parabolic confining potential was studied by the variational approach. The polaron effects on the ground-state binding energy in electric and magnetic fields are investigated by means of Pekar-Landau variation technique by taking into account optical phonon confinement within the wire region and localization at its boundaries. It is shown that not only electron confinement, but also polar optical phonon confinement leads to a considerable enhancement of the polaron effect. The results for the binding energy as well as polaronic correction are obtained as a function of the applied fields.     

The Effective Mass of Impurity–bound Polaron in a Two- and Three-Dimensional Quantum Dot

Within the framework of the Landau–Pekar variational method we have derived an analytical expression for the ground-state binding energies and the effective mass of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. We have also calculated the number of phonons in the cloud of this bound polaron. It is found that the effective mass increase with increasing the Coulomb binding parameter and increase with the decrease in size of the QD. The results also indicate that this effect becomes much more pronounced with decreasing dimensionality.     

The Properties of the Polaron Ground State in a Parabolic Quantum Dot and Ring

The polaron ground state energy is obtained by using variational method of Pekar type on the condition of electric-LO phonon strong coupling in a quantum dot and ring. The relations of the polaron ground state energy on the inner confinement strength, the outer confinement strength, the inner and outer radius of quantum dot and ring are derived.     

The Effects of Electric Field on a Triangular Bound Potential Quantum Dot Qubit

On the condition of electron-LO-phonon strong coupling in a triangular bound potential quantum dot, we obtain the eigenenergy and eigenfuctions of the ground state and the first-excited state by using the Pekar type of variational method. This two-level system in a quantum dot can be employed as a qubit, which is a basic unit for quantum information operation and storage. Our numerical results indicate that the oscillation period of this qubit is an increasing function of the confinement length and the electric field. The influence of electric field on the period of oscillation becomes greater when the confinement length is increased. The electron probability density of the qubit is an increasing function of the electron-LO-phonon coupling constant. On the contrary, it is a decreasing function of the electric field. Meanwhile, the electron probability density varies periodically with the polar angle.     

Impurity Effect of a Bound Polaron in Quantum Rods

Based on a coordinate transformation, we first change the boundary potential of a quantum rod from the ellipsoidal form into a spherical one. And then the properties of the vibrational frequency and the ground state binding energy of a strongly-coupled impurity bound polaron in it are studied. The effects of the ellipsoid aspect ratio, the electron-phonon coupling strength, the Coulomb bound potential and the transverse and longitudinal effective confinement lengths are taken into consideration by using the linear combination operator method. It is found that the vibrational frequency and the ground state binding energy will increase with increasing Coulomb bound potential and the electron-phonon coupling strength. They are decreasing functions of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths.     

The Triangular and Coulomb Bound Potential Quantum Dot Qubit

Under the condition of electron-LO-phonon strong coupling in a triangular and Coulomb bound potential quantum dot (QD) qubit, the eigenenergies and eigenfunctions of the ground-state and the first-excited state are obtained by using a variational method of the Pekar type. This system in QD may be employed as a quantum system-qubit and the numerical calculations are performed, meanwhile the relations of the period of oscillation on the electron-LO-phonon coupling strength, the Coulomb binding parameter, the polar angle and the confinement length are derived.     

Effects of Magnetic Field on the Coherence Time of a Parabolic Quantum Dot Qubit

We obtain the eigenenergies and eigenfunctions (EE) of the ground and first excited states of an electron strongly coupled to LO-phonon in a parabolic quantum dot. The effect of an applied magnetic field is considered by using variational method of Pekar type. This system may be regarded as a two-level qubit. Spontaneous phonon emission arouses the qubit’s decoherence. Relations between the coherence time (CT) and the magnetic field, the effective confinement length (ECL) and the polaron radius (PR) are numerically calculated. It is found that the CT is an increasing function of the ECL, whereas it is a decreasing one of the cyclotron frequency and PR. We can extend the CT by changing these parameters in the correlated quantum functional devices.     

Loosening quantum confinement: observation of real conductivity caused by hole polarons in semiconductor nanocrystals smaller than the bohr radius

We report on the gradual evolution of the conductivity of spherical CdTe nanocrystals of increasing size from the regime of strong quantum confinement with truly discrete energy levels to the regime of weak confinement with closely spaced hole states. We use the high-frequency (terahertz) real and imaginary conductivities of optically injected carriers in the nanocrystals to report on the degree of quantum confinement. For the smaller CdTe nanocrystals (3 nm < radius < 5 nm), the complex terahertz conductivity is purely imaginary. For nanocrystals with radii exceeding 5 nm, we observe the onset of real conductivity, which is attributed to the increasingly smaller separation between the hole states. Remarkably, this onset occurs for a nanocrystal radius significantly smaller than the bulk exciton Bohr radius a(B) ～ 7 nm and cannot be explained by purely electronic transitions between hole states, as evidenced by tight-binding calculations. The real-valued conductivity observed in the larger nanocrystals can be explained by the emergence of mixed carrier-phonon, that is, polaron, states due to hole transitions that become resonant with, and couple strongly to, optical phonon modes for larger QDs. These polaron states possess larger oscillator strengths and broader absorption, and thereby give rise to enhanced real conductivity within the nanocrystals despite the confinement.     

Transition from two-dimensional to three-dimensional quantum confinement in semiconductor quantum wires/quantum dots

We report the photoluminescence (PL) and polarization-resolved PL characteristics of a novel GaAs/AlGaAs quantum wire/dot semiconductor system, realized by metalorganic vapor-phase epitaxy of site-controlled, self-assembled nanostructures in inverted tetrahedral pyramids. By systematically changing the length of the quantum wires, we implement a continuous transition between the regimes of two-dimensional and three-dimensional quantum confinement. The two main evidences for this transition are observed experimentally and confirmed theoretically: (i) strongly blue-shifted ground-state emission, accompanied by increase separation of ground and excited transition energies; and (ii) change in the orientation of the main axis of linear polarization of the photoluminescence, from parallel to perpendicular with respect to the wire axis. This latter effect, whose origin is shown to be purely due to quantum confinement and valence band mixing, sets in at wire lengths of only approximately 30 nm.     

Hydrogenic Impurity Bound Magnetopolaron in a Two-dimensional Quantum Dot for All Coupling Strengths

The ground-state (GS) binding energies of a magnetopolaron bound to a Coulomb impurity in a two-dimensional parabolic quantum dot (QD) are studied within a variational calculation for all coupling strengths. The Lee-Low-Pines-Huybrecht variational technique that is developed previously for all coupling strength has been extended for polarons in a magnetic field. The dependence of the GS binding energies on the magnetic field, the confinement length, and the Coulomb binding parameter is investigated.     

The Effects of Hydrogen-Like Impurity and Temperature on State Energies and Transition Frequency of Strong-Coupling Bound Polaron in an Asymmetric Gaussian Potential Quantum Well

In the present work, we study the ground state energy, the first excited state energy and the transition frequency (TF) between the two states of the strong-coupling impurity bound polaron in an asymmetric Gaussian potential quantum well (AGPQW) by using the variational method of the Pekar type. By employing quantum statistics theory, the temperature effect on the state energies (SEs) and the TF are also calculated with a hydrogen-like impurity at the coordinate origin of the AGPQW. According to the obtained results, we found that the SEs and the TF are increasing functions of the temperature, whereas they are decreasing ones of the Coulombic impurity potential.     

Electric Field Effect on State Energies and Transition Frequency of a Strong-Coupling Polaron in an Asymmetric Quantum Dot

We study the ground and the first excited states’ energies and the corresponding transition frequency of a strong-coupling polaron in an asymmetric quantum dot (AQD). The effects of the electric field, the transverse and the longitudinal effective confinement lengths and the electron-phonon coupling strength are taken into account by using a variational method of the Pekar type. It is found that the ground and the first excited states’ energies and the transition frequency are decreasing functions of the electric field. They will increase rapidly with decreasing the transverse and longitudinal effective confinement lengths. The transition frequency is an increasing function of the electron-phonon coupling strength, whereas the energies are decreasing ones of it.     

The application of hartree approximation in exciton recombination energy for conical InAs/GaAs quantum dots

Under the framework of the Hartree approximation, the ground state exciton binding energy and the interband transition energy are calculated by solving the coupled Schrodinger equations taking into account the coulomb interaction. The self-consistent effective confining potentials are obtained using a fast three-dimensional Fourier transform in every step of the reduced Schrodinger equations. The exciton binding energy increases at first, and then goes through the process of the decline with the increment of the size of conical InAs/GaAs quantum dot. The ground-state exciton oscillator strength becomes larger when the size of the quantum dots increases. It indicates that the radiative lifetime of the exciton will become shorter. The temperature will affect the interband transition energy, but the exciton binding energy is almost temperature-independent.     

Temperature Effect of Strong-Coupling Magnetopolaron in Quantum Rods

We study the temperature effect on the vibrational frequency and the ground state binding energy of a strong-coupling magnetopolaron in the quantum rods. The vibrational frequency and the ground state binding energy are expressed as a functions of the aspect ratio of the ellipsoid, the magnetic field cyclotron frequency,the transverse effective confinement lengths, the temperature and the electron-phonon coupling strength by using a linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase with decreasing the transverse effective confinement lengths. They are increasing functions of the cyclotron frequency and electron-phonon coupling strength. However, they become decreasing ones of the temperature and aspect ratio.     

The Effects of Electric Field on Oscillation Period of Triangular Bound Potential Quantum Dot Qubit

This paper calculates the oscillation period of an electron by using variational method of Pekar type on the condition of electric-LO-phonon strong coupling in a triangular bound potential quantum dot. It obtains the eigenenergies of the ground state and the first excited state, the eigenfunctions of the ground state and the first excited state. This system in a quantum dot may be employed as a two-level quantum system qubit. The superposition state electron density oscillates in the quantum dot with a period when the electron is in the superposition state of the ground and the first-excited state. It studies the influence of the electric field on the period of oscillation at different electron-LO-phonon coupling strength, different polar angle and different confinement length.     

The Temperature Effects on the Parabolic Quantum Dot Qubit in the Electric Field

The temperature effects on the parabolic quantum dot qubit in the electric field have been studied under the condition of electric-LO-phonon strong coupling using the variational method of Pekar type. The numerical results lead us to formulate the derivative relationships of the oscillation period of the electron in the superposition state of the ground state and the first-excited state with the electric field, the electron-LO-phonon coupling constant and the confinement length at different temperatures, respectively.