Journal ArticleDOI

# Electron and hole states in diluted magnetic semiconductor quantum dots

17 Jun 2004-Physical Review B (American Physical Society)-Vol. 69, Iss: 23, pp 235203

Abstract: The electronic structure of a diluted magnetic semiconductor (DMS) quantum dot (QD) is studied within the framework of the effective-mass theory. We find that the energies of the electron with different spin orientation exhibit different behavior as a function of magnetic field at small magnetic fields. The energies of the hole decreases rapidly at low magnetic fields and saturate at higher magnetic field due to the sp-d exchange interaction between the carriers and the magnetic ions. The mixing effect of the hole states in the DMS QD can be tuned by changing the external magnetic field. An interesting crossing behavior of the hole ground state between the heavy-hole state and the light-hole state is found with variation of the QD radius. The strength of the interband optical transition for different circular polarization exhibts quite different behavior with increasing magnetic field and QD radius.
Topics: Paramagnetism (64%), Magnetization (61%), Magnetic field (58%), Quantum dot (57%)

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Electron and hole states in diluted magnetic semiconductor quantum dots
Kai Chang,
*
S. S. Li, and J. B. Xia
NLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
F. M. Peeters
Department of Physics, University of Antwerp (Campus Drie Eiken), B-2610 Antwerpen, Belgium
(Received 15 December 2003; published 17 June 2004
)
The electronic structure of a diluted magnetic semiconductor (DMS) quantum dot (QD) is studied within the
framework of the effective-mass theory. We ﬁnd that the energies of the electron with different spin orientation
exhibit different behavior as a function of magnetic ﬁeld at small magnetic ﬁelds. The energies of the hole
decreases rapidly at low magnetic ﬁelds and saturate at higher magnetic ﬁeld due to the spd exchange
interaction between the carriers and the magnetic ions. The mixing effect of the hole states in the DMS QD can
be tuned by changing the external magnetic ﬁeld. An interesting crossing behavior of the hole ground state
between the heavy-hole state and the light-hole state is found with variation of the QD radius. The strength of
the interband optical transition for different circular polarization exhibts quite different behavior with increas-
ing magnetic ﬁeld and QD radius.
DOI: 10.1103/PhysRevB.69.235203 PACS number(s): 78.20.Ls, 78.67.Hc, 78.55.Cr
I. INTRODUCTION
The interest in the spin dynamics of carriers in semicon-
ductor structures has increased remarkably because of its im-
portance for basic physics as well as for its potential appli-
cation in spintronic devices. Several proposals
1,2
for quantum
information storage and processing using (electron or
nuclear) spins in semiconductor quantum dots (QD) have
been put forward due to the long spin-coherence time in
semiconductors. Quantum information processing should
preserve the entanglement while the quantum information is
transferred from the photon system to the spin of the electron
in the semiconductor. This process is closely related to the
spin splitting of carriers in semiconductors, i.e., the effective
g factor of the carrier or the exciton. Due to the strong spd
interaction between the carriers and the magnetic ions, di-
luted magnetic semiconductor (DMS) structures
3,4
provides
us with a unique ﬂexibility to tailor the spin splitting of
carriers in DMS systems via the external magnetic ﬁeld.
5
The
external magnetic ﬁeld induces a magnetization of the mag-
netic ions in the DMS which gives rise to a giant spin split-
ting of the electron and hole band structure via the exchange
interaction. Very recently, incorporation of Mn ions into the
crystal matrix of different II-VI semiconductors, successful
approaches to fabricate DMS quantum dot and magnet/DMS
hybrid structures has been reported.
6–8
Photoluminescence
(PL) signals clearly demonstrated the transition of quasi-
zero-dimensional electron-hole pairs bound to these nanos-
tuctures. Due to the requirement of a quantitative under-
standing of the optical properties of DMS QD, there arises a
fundamental interest in the electronic structure of DMS
quantum dots.
In the case of semiconductor nanostructures, the elec-
tronic structure varies signiﬁcantly with decreasing size of
the semiconductor nanostructures, especially for the hole
states. In the zinc-blende bulk material, the heavy- and light-
hole are degenerate with vanishing momentum since the Lut-
tinger Hamiltonian describing the hole states becomes diag-
onal with vanishing momentum. In the quantum well case,
the heavy- and light-hole are nondegenerate due to the con-
ﬁnement along the growth direction. But the projection of
the angular momentum of the band-edge Bloch state on the
growth direction J
z
is still a constant of motion. In quantum
dot structures, the situation is very different due to the three-
dimensional quantum conﬁnement. J
z
is no longer a good
quantum number due to the band mixing effect: the hole
eigenstates become mixtures of the heavy- and light- hole
states. In a DMS QD, an external magnetic ﬁeld induces a
magnetization of the magnetic ions, and the strong exchange
interaction between carriers and the magnetic ions provides
us with a unique and interesting ﬂexibility to tailor the elec-
tronic structure of the DMS QD, consequently changing the
optical property of the DMS QD, i.e., the polarization and
energy position of the PL signals. In this paper, we investi-
gate theoretically the electronic structure of a DMS
Cd
1−x
Mn
x
Te/Cd
1−y
Mg
y
Te QD. We show the energies of the
lowest hole states as function of the magnetic ﬁeld and the
conﬁnement. The energy of the hole decreases rapidly at low
magnetic ﬁelds and saturates at high magnetic ﬁeld. An in-
teresting crossing behavior between the heavy-hole and
light-hole is found with variation of the in-plane conﬁne-
ment. The strength of the interband optical transition for dif-
ferent circular polarization exhibits quite different behavior
with increasing magnetic ﬁeld.
The paper is organized as follows: the model and formal-
ism are presented in Sec. II, in Sec. III we show the numeri-
cal results along with the discussions. A brief conclusion is
given in Sec. IV.
II. MODEL AND FORMALISM
The DMS quantum dot is constructed from a DMS
Cd
1−x
Mn
x
Te/Cd
1−y
Mg
y
Te quantum well with a lateral con-
ﬁnement of the carriers through a parabolic well where the z
axis will be taken along the growth direction. The electron
Hamiltonian is
PHYSICAL REVIEW B 69, 235203 (2004)

19 citations

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