Physics Letters A 360 (2007) 655–658 www.elsevier.com/locate/pla Bipolaronic phase in polar semiconductor quantum dots: An all-coupling approach Phani Murali Krishna a , Soma Mukhopadhyay b,1 , Ashok Chatterjee b,∗,2 a School of Physics, University of Hyderabad, Hyderabad 500046, India b Department of Physics, Bilkent University, Ankara, Turkey Received 24 April 2004; accepted 1 September 2006 Available online 22 September 2006 Communicated by J. Flouquet Abstract An all-coupling variational calculation has been performed to explore the formation and stability of a bipolaron in a polar semiconductor quantum dot. It has been shown that quantum confinement in general leads to a broadening of the bipolaron stability region. It has been furthermore shown for the first time that stable bipolarons can exist in realistic parabolic quantum dots of polar semiconductors like GaAs, CdS, CdTe and CdSe if they are fabricated in certain range of sizes.  2006 Elsevier B.V. All rights reserved. PACS: 71.38.-k; 63.20.Kr; 73.21.Hb Keywords: Quantum dot; Polaronic effects; Bipolaron Much effort has lately gone into exploring the polaronic ef- fects in quantum dots (see [1] and references therein). It has been shown that electron-longitudinal-optical (LO) phonon in- teraction has pronounced effects on the electronic properties of quantum dots. Several investigations have also been made to study the formation and stability of bipolarons in a quantum dot. A bipolaron is a bound pair of two polarons with a common cloud of virtual phonons. Bipolarons are known to be impor- tant in semiconducting glasses in which diamagnetism is a rule rather than an exception [2]. The discovery of high temperature superconductivity in CuO 2 based layered ceramic materials [3] and subsequent proposal of bipolaronic mechanism [4] for pair- ing has made the bipolaron problem most fascinating in recent years. In the case of quantum dots, the bipolaron problem was first investigated by Mukhopadhyay and Chatterjee [5] and it * Corresponding author. E-mail address: ashok@fen.bilkent.edu.tr (A. Chatterjee). 1 On leave from Department of Physics, Shadan Institute of P. G. Studies, Kharatabad, Hyderabad, India. 2 On leave from School of Physics, University of Hyderabad, Hyderabad 500 046, India. was shown that in the strong coupling limit the confining po- tential of the quantum dot reduces the stability of the bipolaron. Essentially similar results were also observed in [6]. Pokatilov et al. [7] have investigated the stability of bipolarons in a spher- ical quantum dot with parabolic confinement by applying Feyn- man’s variational principle and calculated the bipolaron binding energy, number of phonons in a bipolaron cloud and the bipo- laron radius. They have shown that in a quantum dot bipolaron states are possible even for intermediate values of the electron- phonon coupling constant, α (α ∼ 2). They have also shown that the binding energy passes through a maximum for a certain value of the confinement length. Recently, Senger and Ercelebi [8] have made a very interesting investigation on the stability of a bipolaron in spherical quantum dots using a single Hamil- tonian and a variational method and have obtained a broader range of stability than shown in [5]. Because of the conflicting conclusions obtained by different groups, the bipolaron prob- lem in a quantum dot has of late become a very interesting problem and has thrown up a new challenge to the theorists. It is therefore worthwhile to take up this problem and make a thor- ough investigation. The purpose of the present Letter is to make an attempt in this direction. Furthermore, to our knowledge, no 0375-9601/$ – see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.09.020