Effect of external magnetic field on electron spin dephasing induced by hyperfine interaction in quantum dots

We investigate the influence of an external magnetic field on spin phase relaxation of single electrons in semiconductor quantum dots induced by the hyperfine interaction. The basic decay mechanism is attributed to the dispersion of local effective nuclear fields over the ensemble of quantum dots. The characteristics of electron spin dephasing is analyzed by taking an average over the nuclear spin distribution. We find that the dephasing rate can be estimated as a spin precession frequency caused primarily by the mean value of the local nuclear magnetic field. Furthermore, it is shown that the hyperfine interaction does not fully depolarize electron spin. The loss of initial spin polarization during the dephasing process depends strongly on the external magnetic field, leading to the possibility of effective suppression of this mechanism. Typeset using REVTEX 1 The spin state of an electron confined in a semiconductor quantum dot (QD) is considered one of the most promising candidates for realizing the basic building block (i.e., qubit) of a quantum information system. Since the fundamental concept of this new paradigm relies on quantum mechanical entanglement of qubits, it is quite crucial to control spin relaxation processes that destroy the coherence of spin quantum state. So far, most of the attention has been devoted to the relaxation processes that result in irreversible loss of wave function phase due to spin-phonon interaction caused by spin-orbital coupling in solids or hyperfine interaction (HFI) in crystals with non-zero nuclei spin moments (see Refs. 1 and 2 as well as the references therein). The common feature of these spin-lattice mechanisms is that their relaxation rates are very small in QDs at low temperatures. On the other hand, the HFI can be considered as a source of a local magnetic field −→ H HF acting on the electron spin that does not disappear at low (or even zero) temperature. This particularity makes the HFI a potentially dominant mehchanism at sufficiently low temperatures. In typical QDs, a sum of the contributions from a great number of nuclei spins forms this field. Thus, the strength and the direction of the −→ H HF are the random variables, which vary from one QD to the next. Obviously, this dispersion can be damaging to quantum computation since electron spin precession occurs with a random phase and frequency. Nevertheless, it appears from a qualitative speculation that the role of −→ H HF dispersion diminishes progressively with an increasing strength of the homogeneous external magnetic field −→ B applied to the array of QDs. In this paper, we provide a quantitative analysis of electron spin evolution under the presence of an external magnetic field −→ B as well as the local hyperfine field −→ H HF . Note, that a theory of electron spin relaxation caused by HFI in a QD was recently presented in Ref. 4. The main interest of Khaetskii et al. lies on the electron spin decoherence process inside a single QD when the external magnetic field is zero. It also contains a brief discussion of spin dephasing time. On the other hand, the present study concentrates on the important process of electron spin dephasing induced by HFI in an ensemble of QDs and explicitly considers the effect of external magnetic fields. 2 The Hamiltonian of electron spin S in a QD containing N nuclear spins Ij (j = 1, ..., N) takes the form (h̄ = 1) H = ωeSz + ωn N