Electro-magnetic weak coupling optical polaron and temperature effect in quantum dot

Abstract: We investigate the influence of the electric field and magnetic fields on the ground state energy of a polaron in a spherical semiconductor quantum dot (QD) using the modified Lee Low Pines (LLP) method.The numerical results show the increase of the ground state energy with the increase of the electric field and the electron-phonon coupling constant, and the decrease with the magnetic field and the longitudinal confinement length.It is also seen that the temperature is an increasing function of the cyclotron frequency and the coupling constant whereas it decreases with the electric field strength.The modulation of the electric field, the magnetic field and the confinement length leads to the control of decoherence in the system.

Key words: electric field, magnetic field, modified LLP, polaron energy, quantum dot, temperature

References:

[1]	Senger R T, Erçelebi A. Q1D-polaron in rigid boundary cylindrical wires:mixed coupling approximation[J]. Solid State Phys, 1998, 22: 169.
[2]	Yu Y B, Zhu S N, Guo K X. Polaron effects on third-harmonic generation in cylindrical quantum-well wire[J]. Solid State Commun, 2004, 132(10): 689.
[3]	Liang X X, Gu S W, Lin D L. Polaronic states in a slab of a polar crystal[J]. Phys Rev B, 1986, 34(4): 2807.
[4]	Zhu K D, Kobayashi T. Resonant shallow donor magnetopolaron effect in a GaAs/AlGaAs quantum dot in high magnetic fields[J]. Solid State Commun, 1994, 92(4): 353.
[5]	Licari J J, Evrard R. Electron-phonon interaction in a dielectric slab:effect of the electronic polarizability[J]. Phys Rev B, 1977, 15(4): 2254.
[6]	Das Sarma S, Mason B A. Optical phonon interaction effect in layered semiconductor structures[J]. Ann Phys NY, 1985, 163(1): 78.
[7]	Licari J J. Polaron self-energy in a dielectric slab[J]. Solid State Commun, 1979, 29(8): 625.
[8]	Comas F, Trallero-Inner C, Riera R. LO-phonon confinement and polaron effect in a quantum well[J]. Phys Rev B, 1989, 39(9): 5907.
[9]	Yu Y F, Xiao J L, Yin J W. Influence of the interaction between phonons and Coulomb potential on the properties of a bound polaron in a quantum dot[J]. Chinese Physics B, 2007, 17(6): 2236.
[10]	Roussignol P, Ricard D, Flytzanis C. Phonon broadening and spectral hole burning in very small semiconductor particles[J]. Phys Rev Lett, 1989, 62: 312.
[11]	Zhu K D, Gu S W. The polaron self-energy due to phonon confinement in quantum boxes and wires[J]. J Phys:Condens Matter, 1992, 4: 1291.
[12]	Mukhopadhyay S, Chatterjee A. Formation and stability of a singlet optical bipolaron in a parabolic quantum dot[J]. J Phys:Condens Matter, 1996, 8(22): 4017.
[13]	Lee T D, Low F E, Pine D. The motion of slow electron in polar crystals[J]. Phys Rev, 1953, 90(2): 297.
[14]	Zhu K D, Gu S W. Polaronic states in a harmonic quantum dot[J]. Phys Lett A, 1992, 163(5/6): 435.
[15]	Chatterjee A, Mukhopadhyay S. Polaronic effects in quantum dots[J]. Acta Phys Polon B, 2001, 32(2): 473.
[16]	Hameau S, Guldner Y, Verzelen O. Strong electron-phonon coupling regime in quantum dots:evidence for everlasting resonant polarons[J]. Phys Rev Lett, 1999, 83(20): 4152.
[17]	Zher S, Bassam S. The optical polaron in spherical quantum dot confinement[J]. An-Najah Univ J Res (N Sc), 2009, 23: 15.
[18]	Zher S, Bassam S. The optical polaron versus the effective dimensionality in quantum well systems[J]. An-Najah Univ J Res (N Sc), 2010, 24: 55.
[19]	Stauber T, Zimmermann R, Castella H. Electron-phonon interaction in quantum dots:a solvable model[J]. Phys Rev B, 2000, 62(11): 7336.
[20]	Fai L C, Fomethe A, Mborong V B. Screening effect on the polaron by plasmons in the field of self-action potential in a planar nanocrystal[J]. Superlattices and Microstructures, 2010, 47: 631.
[21]	Inoshita T, Sakaki H. Electron relaxation in a quantum dot:significance of multiphonon processes[J]. Phys Rev B, 1992, 46(11): 7260.
[22]	Sahoo S. Energy levels of the Fröhlich polaron in a spherical quantum dot[J]. Phys Lett A, 1998, 238(6): 390.
[23]	Yin Jiwen, Xiao Jinglin, Yu Yifu. The influence of electric field on a parabolic quantum dot qubit[J]. Chinese Physics B, 2009, 18(2): 446.
[24]	Fotue A J, Kenfack S C, Fotsin H. Modified Lee-Low-Pines Polaron in spherical quantum dot in an electric field[J]. Science International Journal, 2015, 6(1): 15.
[25]	Morales-Bayuelo A, Vivas-Reyes R. Theoretical model for the polarization molecular and Huckel treatment of phosphocyclopentadiene in an external electric field:hirschfeld study[J]. J Math Chem, 2013, 7: 1835.
[26]	Morales-Bayuelo A, Vivas-Reyes R. Theoretical calculations and modeling for the molecular polarization of furan and thiophene under the action of an electric field using quantum similarity[J]. J Quant Chem, 2014, 2014: 585394.
[27]	Tchoffo M, Fai L C, Issofa N. Magnetopolaron in a cylindrical quantum dot[J]. International Journal of Nanoscience, 2009, 8.
[28]	Erçelebi A, Senger R T. Energy and mass of 3D and 2D polarons in the overall range of the electron-phonon coupling strengths[J]. J Phys:Condens Matter, 1994, 6(28): 5455.
[29]	Senger R T, Erçelebi A. Q1D-polaron in rigid boundary cylindrical wires:mixed coupling approximation[J]. Solid State Phys, 1998, 22: 169.
[30]	Xiao J L. Electric field effect on state energies and transition frequency of a strong-coupling polaron in an asymmetric quantum dot[J]. J Low Temp Phys, 2013, 172: 122.
[31]	Xiao J L. The effect of temperature and electric field on a quantum rod qubit[J]. J Low Temp Phys, 2012, 168: 297.
[32]	Zhao C L, Xiao J L. Temperature effect of strong coupling magnetopolaron in quantum rods[J]. J Low Temp Phys, 2010, 160: 209.
[33]	Kandemir B S, Cetin A. Impurity magnetopolaron in a parabolic quantum dot:the squeezed-state variational approach[J]. J Phys Condens Matter, 2003, 17(4): 667.
[34]	Nguyen V L, Nguyen M T, Nguyen T D. Magnetic field effects on the binding energy of hydrogen impurities in quantum dots with parabolic confinements[J]. Physica B, 2000, 292(1): 153.
[35]	Wang C S, Xiao J L. Transition frequency of weak-coupling impurity bound magnetopolaron in an anisotropic quantum dot[J]. Mod Phys Lett B, 2012, 26: 1150003.
[36]	Chatterjee A. Strong-coupling theory for the multidimensional free optical polaron[J]. Phys Rev B, 1990, 41: 1668.
[37]	Li W, Zhu K. Strong electron-phonon interaction effect in quantum dots[J]. Commun Theor Phys, 1998, 29: 343.

[1]	Senger R T, Erçelebi A. Q1D-polaron in rigid boundary cylindrical wires:mixed coupling approximation[J]. Solid State Phys, 1998, 22: 169.
[2]	Yu Y B, Zhu S N, Guo K X. Polaron effects on third-harmonic generation in cylindrical quantum-well wire[J]. Solid State Commun, 2004, 132(10): 689.
[3]	Liang X X, Gu S W, Lin D L. Polaronic states in a slab of a polar crystal[J]. Phys Rev B, 1986, 34(4): 2807.
[4]	Zhu K D, Kobayashi T. Resonant shallow donor magnetopolaron effect in a GaAs/AlGaAs quantum dot in high magnetic fields[J]. Solid State Commun, 1994, 92(4): 353.
[5]	Licari J J, Evrard R. Electron-phonon interaction in a dielectric slab:effect of the electronic polarizability[J]. Phys Rev B, 1977, 15(4): 2254.
[6]	Das Sarma S, Mason B A. Optical phonon interaction effect in layered semiconductor structures[J]. Ann Phys NY, 1985, 163(1): 78.
[7]	Licari J J. Polaron self-energy in a dielectric slab[J]. Solid State Commun, 1979, 29(8): 625.
[8]	Comas F, Trallero-Inner C, Riera R. LO-phonon confinement and polaron effect in a quantum well[J]. Phys Rev B, 1989, 39(9): 5907.
[9]	Yu Y F, Xiao J L, Yin J W. Influence of the interaction between phonons and Coulomb potential on the properties of a bound polaron in a quantum dot[J]. Chinese Physics B, 2007, 17(6): 2236.
[10]	Roussignol P, Ricard D, Flytzanis C. Phonon broadening and spectral hole burning in very small semiconductor particles[J]. Phys Rev Lett, 1989, 62: 312.
[11]	Zhu K D, Gu S W. The polaron self-energy due to phonon confinement in quantum boxes and wires[J]. J Phys:Condens Matter, 1992, 4: 1291.
[12]	Mukhopadhyay S, Chatterjee A. Formation and stability of a singlet optical bipolaron in a parabolic quantum dot[J]. J Phys:Condens Matter, 1996, 8(22): 4017.
[13]	Lee T D, Low F E, Pine D. The motion of slow electron in polar crystals[J]. Phys Rev, 1953, 90(2): 297.
[14]	Zhu K D, Gu S W. Polaronic states in a harmonic quantum dot[J]. Phys Lett A, 1992, 163(5/6): 435.
[15]	Chatterjee A, Mukhopadhyay S. Polaronic effects in quantum dots[J]. Acta Phys Polon B, 2001, 32(2): 473.
[16]	Hameau S, Guldner Y, Verzelen O. Strong electron-phonon coupling regime in quantum dots:evidence for everlasting resonant polarons[J]. Phys Rev Lett, 1999, 83(20): 4152.
[17]	Zher S, Bassam S. The optical polaron in spherical quantum dot confinement[J]. An-Najah Univ J Res (N Sc), 2009, 23: 15.
[18]	Zher S, Bassam S. The optical polaron versus the effective dimensionality in quantum well systems[J]. An-Najah Univ J Res (N Sc), 2010, 24: 55.
[19]	Stauber T, Zimmermann R, Castella H. Electron-phonon interaction in quantum dots:a solvable model[J]. Phys Rev B, 2000, 62(11): 7336.
[20]	Fai L C, Fomethe A, Mborong V B. Screening effect on the polaron by plasmons in the field of self-action potential in a planar nanocrystal[J]. Superlattices and Microstructures, 2010, 47: 631.
[21]	Inoshita T, Sakaki H. Electron relaxation in a quantum dot:significance of multiphonon processes[J]. Phys Rev B, 1992, 46(11): 7260.
[22]	Sahoo S. Energy levels of the Fröhlich polaron in a spherical quantum dot[J]. Phys Lett A, 1998, 238(6): 390.
[23]	Yin Jiwen, Xiao Jinglin, Yu Yifu. The influence of electric field on a parabolic quantum dot qubit[J]. Chinese Physics B, 2009, 18(2): 446.
[24]	Fotue A J, Kenfack S C, Fotsin H. Modified Lee-Low-Pines Polaron in spherical quantum dot in an electric field[J]. Science International Journal, 2015, 6(1): 15.
[25]	Morales-Bayuelo A, Vivas-Reyes R. Theoretical model for the polarization molecular and Huckel treatment of phosphocyclopentadiene in an external electric field:hirschfeld study[J]. J Math Chem, 2013, 7: 1835.
[26]	Morales-Bayuelo A, Vivas-Reyes R. Theoretical calculations and modeling for the molecular polarization of furan and thiophene under the action of an electric field using quantum similarity[J]. J Quant Chem, 2014, 2014: 585394.
[27]	Tchoffo M, Fai L C, Issofa N. Magnetopolaron in a cylindrical quantum dot[J]. International Journal of Nanoscience, 2009, 8.
[28]	Erçelebi A, Senger R T. Energy and mass of 3D and 2D polarons in the overall range of the electron-phonon coupling strengths[J]. J Phys:Condens Matter, 1994, 6(28): 5455.
[29]	Senger R T, Erçelebi A. Q1D-polaron in rigid boundary cylindrical wires:mixed coupling approximation[J]. Solid State Phys, 1998, 22: 169.
[30]	Xiao J L. Electric field effect on state energies and transition frequency of a strong-coupling polaron in an asymmetric quantum dot[J]. J Low Temp Phys, 2013, 172: 122.
[31]	Xiao J L. The effect of temperature and electric field on a quantum rod qubit[J]. J Low Temp Phys, 2012, 168: 297.
[32]	Zhao C L, Xiao J L. Temperature effect of strong coupling magnetopolaron in quantum rods[J]. J Low Temp Phys, 2010, 160: 209.
[33]	Kandemir B S, Cetin A. Impurity magnetopolaron in a parabolic quantum dot:the squeezed-state variational approach[J]. J Phys Condens Matter, 2003, 17(4): 667.
[34]	Nguyen V L, Nguyen M T, Nguyen T D. Magnetic field effects on the binding energy of hydrogen impurities in quantum dots with parabolic confinements[J]. Physica B, 2000, 292(1): 153.
[35]	Wang C S, Xiao J L. Transition frequency of weak-coupling impurity bound magnetopolaron in an anisotropic quantum dot[J]. Mod Phys Lett B, 2012, 26: 1150003.
[36]	Chatterjee A. Strong-coupling theory for the multidimensional free optical polaron[J]. Phys Rev B, 1990, 41: 1668.
[37]	Li W, Zhu K. Strong electron-phonon interaction effect in quantum dots[J]. Commun Theor Phys, 1998, 29: 343.

Electro-magnetic weak coupling optical polaron and temperature effect in quantum dot

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