Henini M. Handbook of Self Assembled Semiconductor Nanostructures for Novel devices in Photonics and Electronics

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(a)

2087

2086

Det. energy (meV)

2100

Phonon replica

Ground state

PL intensity (arb. units)

2105 2110 2115 21202095 2125

2110 212021002090

Energy (meV)

Exct. energy (meV)

exct

 2117.95

exct

 2117.74

2085.0 2086.0 2087.0 2088.0

Energy (meV)

PL intensity (arb. units)

2118.4

2118.2

2118.0

2117.8

2117.6

2117.4

2118.4

2118.2

2118.0

2117.8

2117.6

2117.4

2085.5 2086.0 2086.5 2087.0 2087.5

Detection ener

y (meV)

2086.0 2086.5 2087.02085.5 2087.5

Detection energy (meV)(b)

Excitation energy (meV)

Figure 14.9 (a) Experimental PL and PLE spectra of an Mn-doped quantum dot exciton. The inset shows the

contour plot of the multichannel PLE. (b) and (c) PLE contour plots for excited state e

obtained for co-polarized

(b) and cross-polarized (c) circular excitation and detection. (d) Resonant PL spectra obtained in co-polarized circular

excitation and detection for two different excitation wavelengths on e

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460 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

strongly depends on both the wavelength and on the polarization of the excitation laser. This

dependence shows that under resonant excitation there is no complete spin relaxation of the

exciton–Mn complex during the lifetime of the exciton. As shown in Fig. 14.9d , this long spin

relaxation time combined with the ﬁ ne structure of the excited states permits the selective cre-

ation of a given spin conﬁ guration of the exciton–Mn complex by tuning the polarization and

wavelength of the excitation laser.

14.4 Geometrical effects on the optical properties of quantum dots doped with

a single magnetic atom

14.4.1 Inﬂ uence of an anisotropic strain distribution

Several phenomena can lead to the mixing between light and heavy holes in QDs. First, the sym-

metry reduction due to the conﬁ nement geometry of the dot has to be considered. In this case, a

hole band mixing appears through the non-diagonal terms of the Luttinger–Kohn Hamiltonian.

This mixing is responsible for the linear polarization rate observed in strongly conﬁ ned quantum

wires [77] . A large wave function anisotropy is needed to reproduce the observed linear polariza-

tion [78] . Such anisotropy can only be obtained in a very elongated conﬁ ning potential for the

holes with large barriers. This is inconsistent with the observation of huge linear polarization

rates in shallow CdTe/ZnTe QDs presenting a quite weak in-plane asymmetry as revealed by AFM

measurements [55] . Another origin of hh–lh mixing is the coupling of the X and Y valence band

states produced by the microscopic arrangement of chemical bonds at heterointerfaces [79] . This

contribution is expected to be weak in ﬂ at self-assembled QDs with almost symmetric interfaces.

As we will see in the following, an efﬁ cient mixing can arise from the anisotropic relaxation

of strains in the QDs plane. Inﬂ uence of strains on hole states has been intensively studied in

quantum wells. Two main effects have been demonstrated, namely the variation of the gap due

to hydrostatic strains and the hh–lh degeneracy lift due to biaxial strains. We will show that in

QDs the strain distribution can also be responsible for a strong lh–hh mixing. This mixing has

striking effects on the hole spin anisotropy.

In bulk semiconductors, the spin orbit interaction is responsible for splitting the hole states. We

only consider here the lowest energy holes with angular momentum j  3 / 2. These  j , j



states

can be simply deﬁ ned using orbital ( X , Y , Z ) and spin ( ↑ , ↓ ) eigenvectors:

|3 / 2 , 3 / 2

|3 / 2 , 1 / 2





 



 

〉↑

〉↑↓

〉↓↑

XiY







XiY

|3 / 2 , 3 / 2

〉↓

(14.3)

Using these notations, the Bir–Pikus Hamiltonian describing the inﬂ uence of the strain on the

valence band structure is written:

Ha bj j

jj jj

BP v ii

ixy

xy yx

   



εε ε

∑∑

⎛

⎝

⎜

(1/3)

⎞⎞

⎠

⎟

(14.4)

where the abbreviation c.p. is used for circular permutation over x , y and z corresponding to the

crystal axes. The matrices of the angular momentum operator



can be found in [69] .

denotes the ij component of the strain tensor and a

, b and d are the deformation potentials for

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Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 461

the valence band. Using the hole formalism, J. Allègre et al. found a

 0 . 9 1 e V, b  0.99 eV and

d  2.76 eV for CdTe [73] .

While growing CdTe on ZnTe, CdTe is compressed in the growth plane and distended in the

growth direction. CdTe QDs form by deformation of a two-dimensional layer induced by strain

relaxation [45] . In this formation mechanism, both elastic and inelastic strain relaxations are

involved and one expects each QD to probe a different local in-plane strain distribution. When

studying a particular QD, one has to consider a particular set of values for ε

. In the following, we

will mainly consider the effects of strain anisotropy in the growth plane and describe the strain

on each QD by an average value of ε

and ε

 ε

. A non-zero value of the volume average ε

can result from a local deformation of the lattice induced by neighbouring QDs or dislocations.

In this approximation, the Bir and Pikus Himiltonian is reduced to a block-diagonal matrix in the

(  3 / 2 ,  1 / 2 ,  1 / 2 ,  3 / 2) basis:

PQ R

RPQ

PQ R

RPQ









†

⎛

⎝

⎜

⎞

⎠

⎟

(14.5)

with

Rid b

vii

xx yy

xy xx yy







 

εε

εεε

∑

⎛

⎝

⎜

⎞

⎠

⎟

()

(14.6)

Using the hh band as the origin of the energies in the valence band, the strain Hamiltonian can

be rewritten as:





−

′

⎛

⎝

⎜

⎜⎜

⎜

⎞

⎠

⎟

(14.7)

This notation allows us to introduce useful parameters to describe the strain effects, namely the

light–heavy hole splitting Δ

, the strain coupling amplitude ρ

and the strain-induced anisotropy

axis in the QD plane deﬁ ned by the angle θ 

with respect to the x (100) axis. In the following, we

will deﬁ ne angles relative to the (110) axis corresponding to the cleaved edge of the sample. We

thus introduce the new angle θ

 θ

 45º. Because of the strain-induced VBM described by the

Hamiltonian (Eq. 14.7), the general form for the lowest energy hole states is:

| ( )| 3/2 ( )| 1/2ϕχ χ

hhh



〉∝ 〉 〉





(14.8)

where w

lh(hh)

is the probability of the hole being light (heavy) and

lh hh()

()



its envelope function.

Considering now single Mn-doped QDs, the sp–d exchange interactions between the conﬁ ned

carriers and the single Mn atom are responsible for a peculiar ﬁ ne structure of the emission [4] .

It has been demonstrated that the hole–Mn spin interaction is of prime importance in this ﬁ ne

structure, because of its energy range and above all because of the spin anisotropy of the hole

[67, 68] . It appears clearly that a valence band mixing will have dramatic consequences on the

emission ﬁ ne structures of Mn-doped QDs. In the heavy-hole approximation, a hole acts on the

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462 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

Mn spin as an effective magnetic ﬁ eld applied along the growth axis, lifting its spin degeneracy. If

a mixing of heavy and light holes is introduced, one has to consider a system of coupled spins in

which hole–Mn spin ﬂ ips become possible.

One can ﬁ nd a signature of the valence band mixing in the emission spectra of neutral

single Mn-doped QDs [69] . In an Mn-doped QD, the ground state of the exciton is composed of six

bright energy levels and six dark energy levels resulting from the coupling of bright excitons and

dark excitons with the six projections of the Mn spin. For a given exciton spin (  1 or  2), the six

Mn spin projections have different energies. In this system, the hole spin interacts with both the

Mn spin and the electron spin. The effect of an increasing valence band mixing on the excitonic

emission spectrum of a QD is presented in Fig. 14.10a . Parameters are chosen to reproduce the

features of QD5 emission spectrum plotted on Fig. 14.10b : the e-Mn exchange integral I

e  M n

set to 70 μ eV; the splitting between bright and dark exciton δ

is chosen equal to 550 μ eV, equally

divided among the long range and short range e–h exchange interaction. Other parameters are

the same as in the previous charged exciton calculation.

1.0

0.5

0.0

0.0 0.2 0.4 0.6 0.8 1.0

(a)

p/

Energy (meV)

1.0

Exp.

Calc.

PL intensity (arb. units)

2037 2039 0

Energy (meV) Energy (meV)(c)(b)

11

0.5

Figure 14.10 (a) Dependence of the exciton–Mn energy spectrum on the strength of the valence band mixing

ρ / Δ

. The dotted line corresponds to the situation of QD6 ( ρ / Δ

 0.07). (b) and (c) are the experimental and

calculated emission spectra of QD6.

14.4.2 Inﬂ uence of the shape anisotropy

Let us consider now the inﬂ uence of the electron–hole exchange interaction. We have seen in the

case of non-magnetic QDs that, in ﬁ rst approximation, the only effect of the valence band mixing

on the short range e–h exchange is to couple bright exciton states together. For magnetic QDs,

bright states associated with the same Mn spin projection are thus coupled. This coupling mainly

concerns the energy levels associated with Mn spin projections  1/2 because they are only

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Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 463

slightly split by the exciton–Mn exchange interaction. An increase of the valence band mixing

will thus open a slight gap in the middle of the bright exciton ﬁ ne structure (around 0.25 meV in

Fig. 14.10a ).

Another gap appears on the low energy side of the structure because of the hole–Mn inter action.

As a matter of fact, simultaneous hole–Mn spin ﬂ ips couple bright and dark states associated with

consecutive Mn spin projections. The exciton–Mn exchange interaction induces an overlap of the

bright and dark exciton ﬁ ne structure. States coupled by h–Mn spin ﬂ ips are therefore quite close

to each other and an increase in the VBM, that is to say an increase in the h–Mn spin ﬂ ip efﬁ ciency,

will open a gap between them. This can be observed in Fig. 14.10a around  0.1 meV. Finally, one

may note once again that the overall splitting of the structure decreases as the VBM increases

because of the decrease of the weight of the heavy-hole in the exciton ground state.

Such coupling between bright and dark excitons is observed in the spectrum of QD6 presented

in Fig. 14.10b . In this QD, the valence band mixing is quite weak and the gaps induced by the e–h

exchange and the h–Mn exchange can be hardly resolved in the exciton spectrum. Nevertheless,

the h–Mn spin ﬂ ips-induced bright–dark coupling is large enough to give non-negligible oscillator

strengths to the dark states. Three “ dark ” states are then observed in the emission spectrum. The

value ρ

/ Δ

can be estimated at 0.07. Using this parameter we can calculate the QD6 exciton emis-

sion spectrum. The result is plotted in Fig. 14.10c . It has been shown in previous work [4] that the

exciton–Mn system is partially thermalized during the exciton lifetime. This results in an increase

in the intensity of the lines as their energy decreases. In the calculation we thus consider that the

system has relaxed and that it is characterized by an effective spin temperature T

eff

depending both

on the phonon bath and on the hot carrier gas produced by the laser excitation. In Fig. 14.10c

eff

 15 K. With this effective temperature, “ dark ” states appear in the calculated spectrum but

their intensity is weaker than in the experiment. Moreover, comparing the intensities of the bright

lines in the calculation and in the experiment, we note that we cannot ﬁ t the data with an effective

temperature smaller than 15 K in order to increase the “ dark ” state’s intensity. These features show

that we should not consider a total thermalization in the exciton–Mn system: if the spin relaxation

is partially blocked, it is difﬁ cult to thermalize the system. As bright and dark excitons are created

with the same generation rate, the intensities of the associated transitions can be comparable even

though they have different oscillator strengths. This is particularly the case under weak excitation

conditions where the inﬂ uence of the hot carrier gas spin reservoir is reduced.

We ﬁ nally consider the neutral exciton ﬁ ne structure of a single Mn-doped QD that presents an

anisotropic in-plane shape (QD7 presented in Fig. 14.11 ). Effects of the long range electron–hole

exchange interaction on the emission spectrum of a single Mn-doped QD were discussed in a former

letter [70] . Nevertheless, details of the polarization properties were not analysed. Here, we detail

these polarization features and show that the VBM is once again necessary to explain them. Figure

14.11 presents the linear polarization dependence of the emission spectrum of QD7. The experi-

mental spectrum shows the main characteristics of a quite strong VBM as detailed in Fig. 14.11a .

The spectrum presents an overall linear polarization rate of about 25% orientated at θ

 1 1 0 °

from the cleaved edge of the sample and dark states appear on the low energy side of the structure.

Two gaps can also be observed: one between the two ﬁ rst main lines and the other between the

third and the fourth lines. However, if these peculiarities were only due to the combined effect of

the VBM and short range e–h exchange, one could expect the third and the fourth lines to be polar-

ized parallel and perpendicular to the strain direction (110°). It is not the case and, surprisingly, the

emission spectrum also presents non-orthogonal linear polarization directions.

These polarization directions are the signature of a competition between a valence band mix-

ing and long range electron–hole exchange interaction. The calculation of the emission spec-

trum of QD7 (right panel of Fig 14.11 ) gives a good agreement with the experiment using the

following parameters: I



 6 0 μ eV, I



 1 3 5 μ eV,

δδ

300

lr sr

 μeV

, δ

 4 5 0 μ eV,

 3 0 m e V, ρ

/ Δ

 0.25 and T

eff

 20 K. The strain direction and the dot shape direction

must be roughly perpendicular (80°) to ﬁ t the experiment. The main features of QD7 emission

are well reproduced as presented in Fig. 14.11 .

In anisotropic QDs, the interplay between the electron–hole and exciton–Mn exchange inter-

actions is conﬁ rmed by magneto-optical measurements ( Fig. 14.12 ). The typical Zeeman split-

ting of the six lines is clearly observed in the data at all ﬁ elds, with a strong intensity gradient at

the highest ﬁ elds resulting from a rather strong Mn spin polarization. For this clearly anisotropic

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464 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

dot, the central gap in the emission structure is maintained in both circular polarizations, with

a small quadratic diamagnetic energy shift. This behaviour is explained as follows: the dot ani-

sotropy leads to successive anticrossings of the  1 bright exciton states associated with given

Mn spin projections (  1/2,  3/2 and  5/2) as a function of magnetic ﬁ eld – As B increases,

transitions associated with the J

  1 exciton shift up in energy whereas the J

  1 transi-

tions shift down. The anisotropic part of the electron–hole exchange interaction mixes succes-

sively the J

  1 exciton states associated with S

  1 / 2, then with S

  3 / 2 and ﬁ nally

with S

  5 / 2 at successively higher B. For QD3, these anticrossings are observed successively

at 2.5, 7 and 11 T.

To understand fully the rich magnetic behaviour of these anisotropic QDs, we calculated the

optical transitions under magnetic ﬁ eld by diagonalizing the complete Hamiltonian of the electron-

heavy hole–Mn system (including the exchange, Zeeman and diamagnetism Hamiltonians).

Calculated transitions are presented in Fig. 14.12b . The ﬁ tted Landé factors of the electron

  1.1), the hole (g

 0.3) and the Mn atom (g

 2.0), the splitting between J

  1 and

  2 excitons (  1 meV) and the diamagnetic factor ( γ  2 . 4 5 μ eV  T

 2

) agree well with pre-

vious work [4, 29, 56] . Parameters δ

and δ

were adjusted to ﬁ t the zero ﬁ eld data, as explained

earlier.

Comparison between calculation and data explains most of the details of the magneto-optic

properties. In particular, around 7 T, the central gap is perturbed in both circular polarizations.

In σ  , this is due to anticrossings induced by the mixing of  s

 1/2, j

  3/2, S

 states and

  1/2,  3/2, S

 1  states by the electron – Mn exchange [4] , i.e. corresponding to simultane-

ous spin-ﬂ ips of electron and manganese spins. In σ  polarization, Fig. 14.12b shows that the

line of second lowest energy crosses the central gap as an essentially non-radiative transition.

This implies a mixing of   1 / 2, 3 / 2 ,  3 / 2  and   1 / 2 ,  3 / 2,  1 / 2  . This is a second-order

mixing involving both mixing of   1 / 2,  3 / 2,  1 / 2  and 1/2,  3/2,  3/2  by the e–Mn

160

120

Analysis angle (°)

204520442043

Ener

y (meV)

1.0 0.5 0.0 0.5 1.0

Ener

y (meV)

PL intensity. (arb. units)

20°

130°

Exp. Calc.

Figure 14.11 Experimental and calculated polarization resolved photoluminescence of QD6. The intensity maps

present the dependence of the emission on the analyser angle. The emission spectrum are presented for orthogonal

linear analyser directions (red and black curves).

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Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 465

exchange and mixing of   1 / 2, 3 / 2,  3 / 2  and 1 / 2,  3 / 2,  3 / 2  by the anisotropic e–h

exchange; that is, the e–Mn exchange induces a mixing of states mediated by the anisotropy-

induced coupling.

To summarize these geometrical effects, as for as this study is concerned an anisotropic stain

distribution in the growth plane and a QD-shaped anisotropy induce a valence band mixing

which strongly modiﬁ es the emission spectra of single Mn-doped QDs. The main observed effects

are: (i) the appearance of anticrossings related to possible Mn–hole spin-ﬂ ips, (ii) the separation

of the six line structures into two sets of lines partially polarized, and (iii) the variation of the

linear polarization directions which are no longer perpendicular to the exciton ﬁ ne structure of a

given QD. The last feature clearly evidences the competition between two types of anisotropy, one

coming from the conﬁ nement potential (shape anisotropy) and one coming from the local strain

distribution into the dot.

14.5 Carrier-controlled spin properties of a single magnetic atom

14.5.1 Carrier-induced spin splitting of a single Mn atom in a quantum dot

Investigating both the biexciton and the exciton transitions in the same Mn-doped QD, we ana-

lyse the impact of the Mn–exciton exchange interaction on the ﬁ ne structure of the QD emission.

2046204520442043

Ener

y (meV)

210

12

Ener

y (meV)

10 T

0 T

10 T

QD3

(a)

σ−

σ

2J

1

1

(b)

Figure 14.12 (a) Intensity map of magnetic ﬁ eld dependence of the emission spectrum of an asymmetric

Mn-doped dot QD3, for circular polarization σ  and σ  . (b) Optical transitions obtained from the diagonalization

of the spin  Zeeman  diamagnetism Hamiltonian in the subspace of the 24 heavy-hole exciton and Mn spin

components; line thickness and colour scale for σ  , σ  are proportional to absolute value of the projection of the

exciton state on the J

  1 ,  1 exciton, respectively (green  low intensity, blue  high intensity). The two

transitions which are forbidden at all magnetic ﬁ elds (| J

  2, S

  5 / 2  ) are not plotted.

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466 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

A single electron–hole pair is enough to induce a spontaneous splitting of the exciton–Mn system

and a slight polarization of the Mn spin distribution. The injection of a second electron–hole pair

cancels the exchange interaction with the Mn ion and the Mn spin degeneracy is almost com-

pletely restored.

In the following, we will compare the ﬁ ne structure of the exciton and biexciton in a single Mn-doped

QD. Figure 14.13 shows the emission spectra of one of these Mn-doped QDs for various excitation

4 6 8

2 4 6 8

2 4 6

tot

 I

 I

(arb. units)

αI

tot

αI

tot

X–Mn

–Mn

PL intensity (arb. units)

202820272026

Energy (meV)

203920382037

200

X–Mn

–Mn

 3

PL intensity (arb. units)

203920382037

Energy (meV)

...

–Mn

B  0T

T  5K

700

Figure 14.13 PL spectra of a single Mn-doped QD for different excitation intensity. X–Mn denotes the exciton–Mn

emission while X

–Mn corresponds to the recombination of the two-exciton–Mn (biexciton) states. The insets give a

detail of the X–Mn emission spectra at low excitation density (X

–Mn corresponds to the bright excitons and X

–Mn

corresponds to the dark excitons) and the evolution of the integrated intensities of X–Mn and X

–Mn as a function

of the total emission intensity.

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Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 467

densities. At low excitation, the spectrum is dominated by the six line ﬁ ne structure (labelled

X–Mn) which is attributed to a conﬁ ned exciton interacting with a single Mn atom. The three

additional lines, observed at low excitation intensity in the low energy side of the emission struc-

ture (enlarged view in the inset of Fig. 14.13 ), are due to the interaction of the dark exciton

states ( J

  2) with the Mn

2 

ion [69] . The PL contribution of the dark states is enhanced by

the relaxation of the exciton–Mn system towards the low-energy levels. This relaxation is also

responsible for the asymmetry in the emission intensity distribution of the bright states at low

excitation intensity [4] .

On increasing the excitation intensity, a new structure of six lines, labelled X

–Mn, appears

10.9 meV below the exciton lines. Its intensity increases quadratically with the excitation and its

structure reproduces the spectral pattern of X–Mn. Such intensity dependence has been observed

in various QD systems and is regarded as a ﬁ ngerprint of exciton and biexciton emission [62, 63] .

The energy difference between the X–Mn and the X

–Mn transitions (10.9 meV) corresponds to

the typical binding energy of the biexciton measured in non-magnetic CdTe/ZnTe QDs [62] . We

have also noticed that, as the excitation intensity increases, the contribution of the transitions

associated with the dark exciton states progressively vanishes. This evolution, already observed

in non-magnetic QDs [62] , is due to the longer lifetime of the dark exciton states. Because of

this difference in lifetime, for a given non-resonant excitation intensity, the probability to cre-

ate a biexciton with two dark excitons is larger than with two bright excitons. The formation

of the biexciton acts then as an efﬁ cient recombination channel for the dark exciton states and

decreases their direct PL contribution.

Magneto-optic measurements conﬁ rm that the exciton and the biexciton transitions coming

from the same Mn-doped QD are observed. The magnetic ﬁ eld dependence of the exciton–Mn and

biexciton–Mn transition energies are presented as a contour plot in Figure 14.14 . For X–Mn, six

lines are observed in each circular polarization. Their energy follows the Zeeman and diamagnetic

shift of the exciton in non-magnetic QDs [4] . The excitonic transitions present also a rich ﬁ ne

structure mainly characterized by a series of ﬁ ve anticrossings observed in σ  polarization around

7 T. These anticrossings come from the mixing of the bright and dark exciton states [4] induced

by a simultaneous spin ﬂ ip of the electron and Mn

2 

ion. The ﬁ ne structure of the exciton–

Mn and the biexciton–Mn systems under magnetic ﬁ eld present a perfect mirror symmetry. The

anticrossings observed on the high energy lines of X–Mn in σ  polarization are symmetrically

observed on the low energy lines and in σ  polarization for X

–Mn (circles in Fig. 14.14 ) [70] .

As it appears in the contour plot presented in Fig. 14.14 , the relative intensities of the six emis-

sion lines observed in each circular polarization strongly depend on the applied magnetic ﬁ eld.

The emission intensity, which is almost equally distributed over the six emission lines at zero ﬁ eld,

is concentrated on the high-energy side of the σ  emission and on the low-energy side of the σ 

emission at high magnetic ﬁ eld. The intensity distribution is similar for X–Mn and X

–Mn.

In a QD, the biexciton ground state is a spin-singlet state ( J  0) and cannot be split by the

magnetic ﬁ eld or the spin interaction part of the carriers–Mn Hamiltonian [71] . In this model,

the creation of two excitons in the same QD cancels all the exchange interaction terms with the

2 

ion. Thus, the ﬁ ne structure of the biexciton–Mn transitions is controlled by the ﬁ nal state

of the recombination of the biexciton, i.e. the eigenstates of the exciton–Mn coupled system.

The optical transitions directly reﬂ ect this mirror symmetry of the energy levels. Moreover, the

intensity distribution of the X–Mn and X

–Mn transitions are both controlled by the spin polari-

zation of the Mn

2 

ion. The spin of the Mn

2 

ion is orientated by the applied magnetic ﬁ eld. At

high ﬁ eld, when the biexciton recombines, the probability of leaving in the QD an exciton cou-

pled with a Mn spin component S

  5/2 is enhanced. Therefore, in the two-photon cascade,

occurring during the recombination of a biexciton, the polarization of the Mn spin will enhance

the intensity of the high-energy biexcitonic transition in σ  polarization and the one in the

low-energy single-exciton transition in σ  polarization. Symmetrically, the emission intensity is

concentrated in the low-energy biexcitonic transition in σ  polarization and in the high-energy

single-exciton transition in σ  polarization.

In summary, the analysis of the biexciton ﬁ ne structure shows that the optical injection of a con-

trolled number of carriers in an individual QD allows control of the spin splitting of a single mag-

netic ion. The exchange interaction with a single exciton acts as an effective local magnetic ﬁ eld

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468 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

which splits the Mn levels in zero applied magnetic ﬁ eld. The injection of a second exciton almost

cancels the carriers – Mn exchange interaction and the Mn spin splitting is signiﬁ cantly reduced.

14.5.2 Electrical control of a single Mn atom in a quantum dot

CdTe/ZnTe QDs are p -type modulation doped by the transfer of holes from the p -doped ZnTe sub-

strate and from surface states that act as acceptors [60, 61] . The occupation of the QDs by holes

can be controlled by an external bias voltage V on an aluminium Schottky gate with respect to

a back contact on the p -type substrate. The bias-dependent emission of a non-magnetic QD and

a Mn-doped QD is presented in Fig. 14.15 . For increasing V , the surface level states are shifted

below the ground hole level in the QDs which results in the single hole charging of the dots. The

optically generated excitons then form charged excitons with the bias-induced extra hole in the

QD. At zero bias or negative bias, the Fermi level is above the ground state and the QDs are likely

to be neutral. However, the separated capture of photo-created electron or holes can sometimes

charge the dots so that weak contributions of X



or X



are observed in the zero bias spectra.

2039

20382037

X–Mn

202820272026

–Mn

σ

σ

Energy (meV)Energy (meV)

11 T

Figure 14.14 Intensity contour plot of the magnetic ﬁ eld dependence of the excitonic and biexcitonic transitions

of a single Mn-doped QD. The bright areas correspond to the high PL intensity. The anticrossings observed for the

exciton are symmetrically reproduced on the biexciton transitions.

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