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Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot

## Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot

Eerdunchaolu, Bai Xu-Fang, Han Chao
• #### Abstract

The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied by using the variational method of Pekar type based on the Lee-Low-Pines’ unitary transformation. With the influences of the electronic spin and the external magnetic field taken into consideration, the change law of ground state energy E0, the average number of phonon N0, the first excited state energy E1 and the average number of phonon N1 of the magneto-bipolarons with the confinement strength ω0, the dielectric constant ratio η, the electron-phonon coupling α, and the cyclotron frequency ωc are derived in two-dimensional quantum dot. Numerical results indicate that the ground state energy E0 and the first excited state energy E1 consist of four parts: the single-article energy Ee of two electrons, the Coulomb interaction energy EC between two electrons, the interaction energy Es between the electronic spin and the external magnetic field, and the interaction energy Ee-ph of the electron with the longitudinalo optical phonons. The energy E1 of the first excited state splits into two lines, i.e., E1(1+1) and E1(1-1) due to the interaction between the “orbital” motion of the single-particle and the magnetic field, and each level of the ground-state energy and the first excited state energies set produces three “fine structures” due to the interaction between the electronic spin and the magnetic field. N0 and N1 increase with ω0, α and ωc increasing; Ee-ph is always less than zero, and absolute value |Ee-ph| increases with ω0, α and ωc increasing. The electron-phonon interaction has an important influence on the formation of bound state of the magneto-bipolaron; but the confinement potential and coulomb repulsive energy between electrons are unfavorable for the formation of magneto-bipolaron in the bound state.

#### Authors and contacts

• Funds: Project supported by the National Natural Science Foundation of Hebei Province, China (Grand No. E2013407119) and the Items of Institution of Higher Education Scientific Research of Hebei Province, China (Grand No. ZD20131008).

#### References

 [1] Li W S, Sun B Q 2013 Acta Phys. Sin. 62 047801 (in Chinese) [李文生, 孙宝权 2013 物理学报 62 047801] [2] Yang F, Zheng R S 2007 Solid State Commun. 141 555 [3] Zhu J, Ban S L, Ha S H 2012 Chin. Phys. B 21 097301 [4] Li Y, Zheng R S, Feng Y C, Liu S H, Niu H B 2006 Chin. Phys. B 15 702 [5] Shen M, Bai Y K, An X T, Liu J J 2013 Chin. Phys. B 22 047101 [6] Chen S H Yao Q Z 2011 Modern Phys. Lett. B 25 2419 [7] Kastner M A 1992 Rev. Mod. Phys. 64 849 [8] Loss D, Di Vincenzo D P 1998 Phys. Rev. A 57 120 [9] Burkard G, Loss D, Di Vincenzo D P 1999 Phys. Rev. B 59 2070 [10] Harju A, Siljamäki S, Nieminen R M 2002 Phys. Rev. Lett. 88 226804 [11] Chen Z S, Sun L L, Li S S 2004 J. Semicond. 25 790 (in Chinese) [陈早生, 孙连亮, 李树深 2004 半导体学报 25 790] [12] Eerdunchaolu, Wuyunqimuge, Xiao X, Han C, Win W 2012 Commun. Theor. Phys. 57 157 [13] Emin D 1989 Phys. Rev. Lett. 62 1544 [14] Peng Q M, Sun J X, Li X J, Li M L, Li F 2011 Appl. Phys. Lett. 99 033509 [15] Schellekens A J, Wagemans W, Kersten S P, Bobbert P A, Koopmans B 2011 Phys. Rev. B 84 075204 [16] Pokatilov E P, Crotitoru M D, Fomin V M, Devreese J T 2003 Phys. Stat. Sol. B 237 244 [17] Senger R T, Ercelebi A R T 2002 J. Phys.: Condens Matt. 14 5549 [18] Ruan Y H, Chen Q H, Jiao Z K 2003 Int. J. Modern Phys. B 17 4332 [19] Hohenadler M, Littlewood P B 2007 Phys. Rev. B 76 155122 [20] Fai L C, Fomethe A, Fotue A J, Mborong V B, Domngang S, Issofa N, Tchoffo M 2008 Superlatt. Microstuct. 43 44 [21] Eerdunchaolu, Win W 2011 Physica B 406 358 [22] Xin W, Gao Z M, Wuyunqimuge, Han C, Eerdunchaolu 2012 Superlattice Microst. 52 872 [23] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 97 [24] Yildirim T, Ercelebi A 1999 J. Phys. Condens. Matter. 3 1271 [25] Schiff L 1986 Quantum Mechanics (3nd Ed) (New York: McGraw-Hill, Inc.) p375, p376

#### Cited By

•  [1] Li W S, Sun B Q 2013 Acta Phys. Sin. 62 047801 (in Chinese) [李文生, 孙宝权 2013 物理学报 62 047801] [2] Yang F, Zheng R S 2007 Solid State Commun. 141 555 [3] Zhu J, Ban S L, Ha S H 2012 Chin. Phys. B 21 097301 [4] Li Y, Zheng R S, Feng Y C, Liu S H, Niu H B 2006 Chin. Phys. B 15 702 [5] Shen M, Bai Y K, An X T, Liu J J 2013 Chin. Phys. B 22 047101 [6] Chen S H Yao Q Z 2011 Modern Phys. Lett. B 25 2419 [7] Kastner M A 1992 Rev. Mod. Phys. 64 849 [8] Loss D, Di Vincenzo D P 1998 Phys. Rev. A 57 120 [9] Burkard G, Loss D, Di Vincenzo D P 1999 Phys. Rev. B 59 2070 [10] Harju A, Siljamäki S, Nieminen R M 2002 Phys. Rev. Lett. 88 226804 [11] Chen Z S, Sun L L, Li S S 2004 J. Semicond. 25 790 (in Chinese) [陈早生, 孙连亮, 李树深 2004 半导体学报 25 790] [12] Eerdunchaolu, Wuyunqimuge, Xiao X, Han C, Win W 2012 Commun. Theor. Phys. 57 157 [13] Emin D 1989 Phys. Rev. Lett. 62 1544 [14] Peng Q M, Sun J X, Li X J, Li M L, Li F 2011 Appl. Phys. Lett. 99 033509 [15] Schellekens A J, Wagemans W, Kersten S P, Bobbert P A, Koopmans B 2011 Phys. Rev. B 84 075204 [16] Pokatilov E P, Crotitoru M D, Fomin V M, Devreese J T 2003 Phys. Stat. Sol. B 237 244 [17] Senger R T, Ercelebi A R T 2002 J. Phys.: Condens Matt. 14 5549 [18] Ruan Y H, Chen Q H, Jiao Z K 2003 Int. J. Modern Phys. B 17 4332 [19] Hohenadler M, Littlewood P B 2007 Phys. Rev. B 76 155122 [20] Fai L C, Fomethe A, Fotue A J, Mborong V B, Domngang S, Issofa N, Tchoffo M 2008 Superlatt. Microstuct. 43 44 [21] Eerdunchaolu, Win W 2011 Physica B 406 358 [22] Xin W, Gao Z M, Wuyunqimuge, Han C, Eerdunchaolu 2012 Superlattice Microst. 52 872 [23] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 97 [24] Yildirim T, Ercelebi A 1999 J. Phys. Condens. Matter. 3 1271 [25] Schiff L 1986 Quantum Mechanics (3nd Ed) (New York: McGraw-Hill, Inc.) p375, p376
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##### Publishing process
• Received Date:  06 October 2013
• Accepted Date:  24 October 2013
• Published Online:  20 January 2014

## Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot

• 1. Department of Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China;
• 2. College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043, China
Fund Project:  Project supported by the National Natural Science Foundation of Hebei Province, China (Grand No. E2013407119) and the Items of Institution of Higher Education Scientific Research of Hebei Province, China (Grand No. ZD20131008).

Abstract: The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied by using the variational method of Pekar type based on the Lee-Low-Pines’ unitary transformation. With the influences of the electronic spin and the external magnetic field taken into consideration, the change law of ground state energy E0, the average number of phonon N0, the first excited state energy E1 and the average number of phonon N1 of the magneto-bipolarons with the confinement strength ω0, the dielectric constant ratio η, the electron-phonon coupling α, and the cyclotron frequency ωc are derived in two-dimensional quantum dot. Numerical results indicate that the ground state energy E0 and the first excited state energy E1 consist of four parts: the single-article energy Ee of two electrons, the Coulomb interaction energy EC between two electrons, the interaction energy Es between the electronic spin and the external magnetic field, and the interaction energy Ee-ph of the electron with the longitudinalo optical phonons. The energy E1 of the first excited state splits into two lines, i.e., E1(1+1) and E1(1-1) due to the interaction between the “orbital” motion of the single-particle and the magnetic field, and each level of the ground-state energy and the first excited state energies set produces three “fine structures” due to the interaction between the electronic spin and the magnetic field. N0 and N1 increase with ω0, α and ωc increasing; Ee-ph is always less than zero, and absolute value |Ee-ph| increases with ω0, α and ωc increasing. The electron-phonon interaction has an important influence on the formation of bound state of the magneto-bipolaron; but the confinement potential and coulomb repulsive energy between electrons are unfavorable for the formation of magneto-bipolaron in the bound state.

Reference (25)

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