J. Semicond. > 2016, Volume 37 > Issue 9 > 092004
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SEMICONDUCTOR PHYSICS

Magnetopolaron effects on the optical absorptions in a parabolic quantum dot

Shihua Chen

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 Corresponding author: Chen Shihua, hzchenshihua@126.com

DOI: 10.1088/1674-4926/37/9/092004

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Abstract: We investigate the influence of magnetic field on the linear and nonlinear optical absorptions in a parabolic quantum dot (QD) through electron-LO-phonon interaction by using the Lee-Low-Pines-Huybrecht variational calculation for all coupling strengths. We apply our calculations to GaAs which is a good candidate in Ⅲ-V group semiconductors. We find that all the absorption spectra are strongly affected by the electron-LO-phonon interaction, the applied magnetic field, and the Coulomb binding potential. Furthermore, due to the Zeeman splitting, the response of all the absorption values in transition (+1→0) and (-1→0) closely depends on the magnetic field increasing.

Key words: quantum dot, magnetopolaron, optical absorption



[1]
Bondarenko V, Zhao Y. Resonant photoionization absorption spectra of spherical quantum dots. J Phys Condens Matter, 2003, 15: 1377 doi: 10.1088/0953-8984/15/9/301
[2]
Yilmaz S, Safak H. Oscillator strengths for the intersubband transitions in a CdS-SiO2 quantum dot with hydrogenic impurity. Physica E, 2007, 36: 40 doi: 10.1016/j.physe.2006.07.040
[3]
Lu L L, Xie W F, Hassanabadi H. Linear and nonlinear optical absorption coefficients and refractive index changes in a two-electron quantum dot. J Appl Phys, 2011, 109: 063108 doi: 10.1063/1.3560541
[4]
Sahin M. Photoionization cross section and intersublevel transitions in a one- and two-electron spherical quantum dot with a hydrogenic impurity. Phys Rev B, 2008, 77: 045317 doi: 10.1103/PhysRevB.77.045317
[5]
Karabulut I, Baskoutas S. Linear and nonlinear optical absorption coefficients and refractive index changes in spherical quantum dots: effects of impurities, electric field, size, and optical intensity. J Appl Phys, 2008, 103: 073512 doi: 10.1063/1.2904860
[6]
Xie W F. Optical properties of an off-center hydrogenic impurity in a spherical quantum dot with Gaussian potential. Superlatt Microstruct, 2010, 48: 239 doi: 10.1016/j.spmi.2010.04.015
[7]
Schmitt-Rink S, Miller D A B, Chemla D S. Theory of the linear and nonlinear optical properties of semiconductor microcrystallites. Phys Rev B, 1987, 35: 8113 doi: 10.1103/PhysRevB.35.8113
[8]
Li Yali, Shan Shuping. Properties of the magnetopolaron in a triangular quantum well. Journal of Semiconductors, 2015, 36(8): 082005 doi: 10.1088/1674-4926/36/8/082005
[9]
Ma Xinjun, Xiao Boyu, Sun Yong, et al. Effects of magnetic field on the polaron in an asymmetrical Gaussian confinement potential quantum well. Journal of Semiconductors, 2015, 36(10): 102004 doi: 10.1088/1674-4926/36/10/102004
[10]
Zhang Hairui, Sun Yong. Properties of polaron in a triangular quantum well induced by the Rashba effect. Journal of Semiconductors, 2014, 35(10): 102001 doi: 10.1088/1674-4926/35/10/102001
[11]
Mukhopadhyay S, Chatterjee A. Suppression of Zeeman splitting in a GaAs quantum dot. Phys Rev B, 1999, 59: R7833 doi: 10.1103/PhysRevB.59.R7833
[12]
Jacak L, Krasnyj J, Jacak D, et al. Magnetopolaron in a weakly elliptical InAs/GaAs quantum dot. Phys Rev B, 2003, 67: 035303 doi: 10.1103/PhysRevB.67.035303
[13]
Kandemir B S, Cetin A. Impurity magnetopolaron in a parabolic quantum dot: the squeezed-state variational approach. J Phys Condens Matter, 2005, 17: 667 doi: 10.1088/0953-8984/17/4/009
[14]
Mukhopadhyay S, Chatterjee A. The ground and the first excited states of an electron in a multidimensional polar semiconductor quantum dot: an all-coupling variational approach. J Phys Condens Matter, 1999, 11: 2071 doi: 10.1088/0953-8984/11/9/005
[15]
Chen Shihua. The cyclotron resonance of impurity magnetopolarons in two-dimensional quantum dots for all coupling strengths. Physica E, 2011, 43: 1007 doi: 10.1016/j.physe.2010.12.002
[16]
Xie Wenfang. Optical properties of impurity-bound polaron in a parabolic quantum dot. Superlatt Microstruct, 2011, 50(2): 91 doi: 10.1016/j.spmi.2011.05.002
[17]
Sahin M. Third-order nonlinear optical properties of a one- and two-electron spherical quantum dot with and without a hydrogenic impurity. J Appl Phys, 2009, 106: 063710 doi: 10.1063/1.3225100
[18]
Li N, Guo K X, Shao S. Polaron effects on the optical absorptions in cylindrical quantum dots with parabolic potential. Opt Commun, 2012, 285: 2734 doi: 10.1016/j.optcom.2012.01.047
[19]
Chen Shihua. Properties of the two- and three-dimensional quantum dot qubit. Journal of Semiconductors, 2010, 31: 052001 doi: 10.1088/1674-4926/31/5/052001
[20]
Chen S H. Optical absorptions of impurity-bound polaron in a GaAs quantum dot with parabolic potential. J Low Temp Phys, 2014, 177: 40 doi: 10.1007/s10909-014-1186-5
[21]
Peeters F M, Wu X G, Devreese J T. Ground-state energy of a polaron in n dimensions. Phys Rev B, 1986, 33: 3926 doi: 10.1103/PhysRevB.33.3926
[22]
Vahdani M R K, Rezaei G. Linear and nonlinear optical properties of a hydrogenic donor in lens-shaped quantum dots. Phys Lett A, 2009, 373: 3079 doi: 10.1016/j.physleta.2009.06.042
[23]
Mukhopadhyay S, Chatterjee A. Polaronic enhancement in the ground-state energy of an electron bound to a Coulomb impurity in a parabolic quantum dot. Phys Rev B, 1997, 55: 9279 doi: 10.1103/PhysRevB.55.9279
Fig. 1.  The total optical absorption coefficient associated with the transitions (+1 $\to $ 0) in a parabolic QD as a function of incident photon energy $h\omega $ at fixed magnetic field $B=$ 5 T with different electron-phonon coupling constants and Coulomb binding potential,and for $\omega_{0} =5\times 10^{12}\,{\rm s}^{-1}$ .

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Fig. 2.  The energy level spacing between the GS and the first ES (in meV) as a function of the confinement length $l_{0} $ (in Å) in a GaAs QD for a fixed value of magnetic field,i.e. $B=$ 10 T. As a comparison the solid line for $B=$ 0 T is plotted in the same figure.

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Fig. 3.  The linear,third order nonlinear and total change in the absorption coefficient associated with the transitions ( $\pm$ 1 $\to $ 0) in a GaAs QD as a function of incident photon energy $h\omega $ ,respectively,for two different values of the applied magnetic field B,0 and 10 T,with a fixed parabolic potential $\omega_{0} =5\times 10^{12} \,{\rm s}^{-1}$ .

DownLoad: Full-Size Img PowerPoint
[1]
Bondarenko V, Zhao Y. Resonant photoionization absorption spectra of spherical quantum dots. J Phys Condens Matter, 2003, 15: 1377 doi: 10.1088/0953-8984/15/9/301
[2]
Yilmaz S, Safak H. Oscillator strengths for the intersubband transitions in a CdS-SiO2 quantum dot with hydrogenic impurity. Physica E, 2007, 36: 40 doi: 10.1016/j.physe.2006.07.040
[3]
Lu L L, Xie W F, Hassanabadi H. Linear and nonlinear optical absorption coefficients and refractive index changes in a two-electron quantum dot. J Appl Phys, 2011, 109: 063108 doi: 10.1063/1.3560541
[4]
Sahin M. Photoionization cross section and intersublevel transitions in a one- and two-electron spherical quantum dot with a hydrogenic impurity. Phys Rev B, 2008, 77: 045317 doi: 10.1103/PhysRevB.77.045317
[5]
Karabulut I, Baskoutas S. Linear and nonlinear optical absorption coefficients and refractive index changes in spherical quantum dots: effects of impurities, electric field, size, and optical intensity. J Appl Phys, 2008, 103: 073512 doi: 10.1063/1.2904860
[6]
Xie W F. Optical properties of an off-center hydrogenic impurity in a spherical quantum dot with Gaussian potential. Superlatt Microstruct, 2010, 48: 239 doi: 10.1016/j.spmi.2010.04.015
[7]
Schmitt-Rink S, Miller D A B, Chemla D S. Theory of the linear and nonlinear optical properties of semiconductor microcrystallites. Phys Rev B, 1987, 35: 8113 doi: 10.1103/PhysRevB.35.8113
[8]
Li Yali, Shan Shuping. Properties of the magnetopolaron in a triangular quantum well. Journal of Semiconductors, 2015, 36(8): 082005 doi: 10.1088/1674-4926/36/8/082005
[9]
Ma Xinjun, Xiao Boyu, Sun Yong, et al. Effects of magnetic field on the polaron in an asymmetrical Gaussian confinement potential quantum well. Journal of Semiconductors, 2015, 36(10): 102004 doi: 10.1088/1674-4926/36/10/102004
[10]
Zhang Hairui, Sun Yong. Properties of polaron in a triangular quantum well induced by the Rashba effect. Journal of Semiconductors, 2014, 35(10): 102001 doi: 10.1088/1674-4926/35/10/102001
[11]
Mukhopadhyay S, Chatterjee A. Suppression of Zeeman splitting in a GaAs quantum dot. Phys Rev B, 1999, 59: R7833 doi: 10.1103/PhysRevB.59.R7833
[12]
Jacak L, Krasnyj J, Jacak D, et al. Magnetopolaron in a weakly elliptical InAs/GaAs quantum dot. Phys Rev B, 2003, 67: 035303 doi: 10.1103/PhysRevB.67.035303
[13]
Kandemir B S, Cetin A. Impurity magnetopolaron in a parabolic quantum dot: the squeezed-state variational approach. J Phys Condens Matter, 2005, 17: 667 doi: 10.1088/0953-8984/17/4/009
[14]
Mukhopadhyay S, Chatterjee A. The ground and the first excited states of an electron in a multidimensional polar semiconductor quantum dot: an all-coupling variational approach. J Phys Condens Matter, 1999, 11: 2071 doi: 10.1088/0953-8984/11/9/005
[15]
Chen Shihua. The cyclotron resonance of impurity magnetopolarons in two-dimensional quantum dots for all coupling strengths. Physica E, 2011, 43: 1007 doi: 10.1016/j.physe.2010.12.002
[16]
Xie Wenfang. Optical properties of impurity-bound polaron in a parabolic quantum dot. Superlatt Microstruct, 2011, 50(2): 91 doi: 10.1016/j.spmi.2011.05.002
[17]
Sahin M. Third-order nonlinear optical properties of a one- and two-electron spherical quantum dot with and without a hydrogenic impurity. J Appl Phys, 2009, 106: 063710 doi: 10.1063/1.3225100
[18]
Li N, Guo K X, Shao S. Polaron effects on the optical absorptions in cylindrical quantum dots with parabolic potential. Opt Commun, 2012, 285: 2734 doi: 10.1016/j.optcom.2012.01.047
[19]
Chen Shihua. Properties of the two- and three-dimensional quantum dot qubit. Journal of Semiconductors, 2010, 31: 052001 doi: 10.1088/1674-4926/31/5/052001
[20]
Chen S H. Optical absorptions of impurity-bound polaron in a GaAs quantum dot with parabolic potential. J Low Temp Phys, 2014, 177: 40 doi: 10.1007/s10909-014-1186-5
[21]
Peeters F M, Wu X G, Devreese J T. Ground-state energy of a polaron in n dimensions. Phys Rev B, 1986, 33: 3926 doi: 10.1103/PhysRevB.33.3926
[22]
Vahdani M R K, Rezaei G. Linear and nonlinear optical properties of a hydrogenic donor in lens-shaped quantum dots. Phys Lett A, 2009, 373: 3079 doi: 10.1016/j.physleta.2009.06.042
[23]
Mukhopadhyay S, Chatterjee A. Polaronic enhancement in the ground-state energy of an electron bound to a Coulomb impurity in a parabolic quantum dot. Phys Rev B, 1997, 55: 9279 doi: 10.1103/PhysRevB.55.9279

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    Received: 23 October 2015 Revised: 30 March 2016 Online: Published: 01 September 2016

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      Article Navigation >  Journal of Semiconductors  > 2016  >  37(9): 092004
      Shihua Chen. Magnetopolaron effects on the optical absorptions in a parabolic quantum dot[J]. Journal of Semiconductors, 2016, 37(9): 092004. doi: 10.1088/1674-4926/37/9/092004 ****S H Chen. Magnetopolaron effects on the optical absorptions in a parabolic quantum dot[J]. J. Semicond., 2016, 37(9): 092004. doi: 10.1088/1674-4926/37/9/092004.
      Citation:
      Shihua Chen. Magnetopolaron effects on the optical absorptions in a parabolic quantum dot[J]. Journal of Semiconductors, 2016, 37(9): 092004. doi: 10.1088/1674-4926/37/9/092004 ****
      S H Chen. Magnetopolaron effects on the optical absorptions in a parabolic quantum dot[J]. J. Semicond., 2016, 37(9): 092004. doi: 10.1088/1674-4926/37/9/092004.
      shu

      Magnetopolaron effects on the optical absorptions in a parabolic quantum dot

      DOI: 10.1088/1674-4926/37/9/092004

      • Department of Electrical Engineering, Huzhou Vocational Technology College, Huzhou 313000, China

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      • Corresponding author: Chen Shihua, hzchenshihua@126.com
      • Received Date: 2015-10-23
      • Revised Date: 2016-03-30
      • Published Date: 2016-09-01

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