J. Semicond. > 2013, Volume 34 > Issue 1 > 012001, doi: 10.1088/1674-4926/34/1/012001

SEMICONDUCTOR PHYSICS

Properties of a polaron in a quantum dot:a squeezed-state variational approach

Jiwen Yin, Weiping Li and Yifu Yu

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 Corresponding author: Yin Jiwen, Email:ji-wenyin@163.com

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Abstract: The ground-state energy and the average number of virtual phonons around the electron in a parabolic quantum dot for the entire range of the electron-phonon coupling constant are obtained using the single-mode squeezed-state variational approach. The variational approach we applied is based on two successive canonical transformations and using a displaced-oscillator type unitary transformation to deal with the bilinear terms which are usually neglected. In order to study the relationship between the ground-state energy and the average number of virtual phonons around the electron of a polaron in a parabolic quantum dot with the electron-LO-phonon coupling constant and the confinement length, numerical calculations are carried out in the electron-LO-phonon strong-and weak-coupling regions.

Key words: squeezed-state, quantum dot, polaron



[1]
Haupt D, Wendler L. Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. Z Phys B, 1994, 94:49 doi: 10.1007/BF01307653
[2]
Ercelebi A, Senger R T. Strong coupling characterisation of quasi-1D polarons in cylindrical QW-wires. Solid State Commun, 1995, 97:509
[3]
Chen Q H, Wang Z B, Wu F L, et al. Variational path-integral study on bound polarons in parabolic quantum dots and wires. Chin Phys Lett, 2001, 18:668 doi: 10.1088/0256-307X/18/5/315
[4]
De Liberato S, CIuti C. Quantum theory of intersubband polarons. Phys Rev B, 2012, 85:125302 doi: 10.1103/PhysRevB.85.125302
[5]
Kandemir B S. Polaronic effects on the energy spectrum of two anyons in a parabolic quantum dot. Phys Rev B, 2006, 73:115301 doi: 10.1103/PhysRevB.73.115301
[6]
Chen Q H, Ren Y H, Jiao Z K, et al. Polaronic effect on the binding energy of an impurity with varying position in parabolic quantum dots. Phys Lett A, 1999, 252:251 doi: 10.1016/S0375-9601(98)00949-9
[7]
Zhang Y, Ong W, Arakelyan I, et al. Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas. Phys Rev Lett, 2012, 108:235302 doi: 10.1103/PhysRevLett.108.235302
[8]
Devreese J T, Alexandrov A. Frohlich polaron and bipolaron:recent developments. Rep Prog Phys, 2009, 72:066501 doi: 10.1088/0034-4885/72/6/066501
[9]
Yin J W, Yu Y F, Xiao J L. Influence of the interaction between phonons and Coulomb potential on the properties of a bound polaron in a quantum dot. Chinese Journal of Semiconductors, 2007, 28:71
[10]
Lamouche G, Fishman G. Two interacting electrons in a three-dimensional parabolic quantum dot:a simple solution. J Phys:Condens Matter, 1998, 10:7857 doi: 10.1088/0953-8984/10/35/018
[11]
Li W P, Xiao J L. Influence of Coulomb potential on the properties of a polaron in a quantum dot. Chinese Journal of Semiconductors, 2007, 28:1187
[12]
Vasilevskiy M I, Anda E V, Makler S S. Electron-phonon interaction effects in semiconductor quantum dots:a non-perturbative approach. Phys Rev B, 2004, 70:035318 doi: 10.1103/PhysRevB.70.035318
[13]
Chen Q H, Ren Y H, Jiao Z K, et al. Feynman-Haken path-integral approach for polarons in parabolic quantum wires and dots. Phys Rev B, 1998, 58:16340 doi: 10.1103/PhysRevB.58.16340
[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]
Kervan N, Altanhan T, Chatterjee A. A variational approach with squeezed-states for the polaronic effects in quantum dots. Phys Lett A, 2003, 315:280 doi: 10.1016/S0375-9601(03)01011-9
[16]
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
Fig. 1.  The strong-coupling polaron ground-state energy $E_0$ in a parabolic quantum dot as a function of the confinement length $l_0$ for (a) $\alpha$ $=$ 3, (b) 4 and (c) 5 using the FH path-integral approach, the LLPH variational approach and the SQS variational approach (in Feynman units).

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Fig. 2.  The weak-coupling polaron ground-state energy $E_0$ in a parabolic quantum dot as a function of the confinement length $l_0$ for (a) $\alpha$ $=$ 0.01, (b) 0.1 and (c) 0.9 using the FH path-integral approach, the LLPH variational approach and the SQS variational approach (in Feynman units).

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Fig. 3.  (a) The average number of virtual phonons $N$ around the electron in the ground-state in a parabolic quantum dot as a function of the confinement length of the strong-coupling limit using the LLPH variational approach and the SQS variational approach (in Feynman units). (b) The average number of virtual phonons $N$ around the electron in the ground-state in a parabolic quantum dot as a function of the electron–LO-phonon coupling constant of weak-coupling limit using the LLPH variational approach and the SQS variational approach (in Feynman units).

DownLoad: Full-Size Img PowerPoint
[1]
Haupt D, Wendler L. Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. Z Phys B, 1994, 94:49 doi: 10.1007/BF01307653
[2]
Ercelebi A, Senger R T. Strong coupling characterisation of quasi-1D polarons in cylindrical QW-wires. Solid State Commun, 1995, 97:509
[3]
Chen Q H, Wang Z B, Wu F L, et al. Variational path-integral study on bound polarons in parabolic quantum dots and wires. Chin Phys Lett, 2001, 18:668 doi: 10.1088/0256-307X/18/5/315
[4]
De Liberato S, CIuti C. Quantum theory of intersubband polarons. Phys Rev B, 2012, 85:125302 doi: 10.1103/PhysRevB.85.125302
[5]
Kandemir B S. Polaronic effects on the energy spectrum of two anyons in a parabolic quantum dot. Phys Rev B, 2006, 73:115301 doi: 10.1103/PhysRevB.73.115301
[6]
Chen Q H, Ren Y H, Jiao Z K, et al. Polaronic effect on the binding energy of an impurity with varying position in parabolic quantum dots. Phys Lett A, 1999, 252:251 doi: 10.1016/S0375-9601(98)00949-9
[7]
Zhang Y, Ong W, Arakelyan I, et al. Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas. Phys Rev Lett, 2012, 108:235302 doi: 10.1103/PhysRevLett.108.235302
[8]
Devreese J T, Alexandrov A. Frohlich polaron and bipolaron:recent developments. Rep Prog Phys, 2009, 72:066501 doi: 10.1088/0034-4885/72/6/066501
[9]
Yin J W, Yu Y F, Xiao J L. Influence of the interaction between phonons and Coulomb potential on the properties of a bound polaron in a quantum dot. Chinese Journal of Semiconductors, 2007, 28:71
[10]
Lamouche G, Fishman G. Two interacting electrons in a three-dimensional parabolic quantum dot:a simple solution. J Phys:Condens Matter, 1998, 10:7857 doi: 10.1088/0953-8984/10/35/018
[11]
Li W P, Xiao J L. Influence of Coulomb potential on the properties of a polaron in a quantum dot. Chinese Journal of Semiconductors, 2007, 28:1187
[12]
Vasilevskiy M I, Anda E V, Makler S S. Electron-phonon interaction effects in semiconductor quantum dots:a non-perturbative approach. Phys Rev B, 2004, 70:035318 doi: 10.1103/PhysRevB.70.035318
[13]
Chen Q H, Ren Y H, Jiao Z K, et al. Feynman-Haken path-integral approach for polarons in parabolic quantum wires and dots. Phys Rev B, 1998, 58:16340 doi: 10.1103/PhysRevB.58.16340
[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]
Kervan N, Altanhan T, Chatterjee A. A variational approach with squeezed-states for the polaronic effects in quantum dots. Phys Lett A, 2003, 315:280 doi: 10.1016/S0375-9601(03)01011-9
[16]
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

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    Received: 06 July 2012 Revised: 06 August 2012 Online: Published: 01 January 2013

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      Article Navigation >  Journal of Semiconductors  > 2013  >  34(1): 012001
      Jiwen Yin, Weiping Li, Yifu Yu. Properties of a polaron in a quantum dot:a squeezed-state variational approach[J]. Journal of Semiconductors, 2013, 34(1): 012001. doi: 10.1088/1674-4926/34/1/012001 J W Yin, W P Li, Y F Yu. Properties of a polaron in a quantum dot:a squeezed-state variational approach[J]. J. Semicond., 2013, 34(1): 012001. doi: 10.1088/1674-4926/34/1/012001.Export: BibTex EndNote
      Citation:
      Jiwen Yin, Weiping Li, Yifu Yu. Properties of a polaron in a quantum dot:a squeezed-state variational approach[J]. Journal of Semiconductors, 2013, 34(1): 012001. doi: 10.1088/1674-4926/34/1/012001

      J W Yin, W P Li, Y F Yu. Properties of a polaron in a quantum dot:a squeezed-state variational approach[J]. J. Semicond., 2013, 34(1): 012001. doi: 10.1088/1674-4926/34/1/012001.
      Export: BibTex EndNote
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      Properties of a polaron in a quantum dot:a squeezed-state variational approach

      doi: 10.1088/1674-4926/34/1/012001

      • Department of Physics and Electronic Informational Engineering, Inner Mongolia Chifeng College, Chifeng 024000, China

      Funds:

      the Research Science Project for the Natural Science Foundation of Inner Mongolia 2011MS0102

      the National Natural Science Foundation of China 11264001

      Project supported by the Research Science Project for the Natural Science Foundation of Inner Mongolia (Nos.2011MS0102, 2012MS0116) and the National Natural Science Foundation of China (No.11264001)

      the Research Science Project for the Natural Science Foundation of Inner Mongolia 2012MS0116

      More Information
      • Corresponding author: Yin Jiwen, Email:ji-wenyin@163.com
      • Received Date: 2012-07-06
      • Revised Date: 2012-08-06
      • Published Date: 2013-01-01

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