Optical control of spin coherence in singly charged (In,Ga)As/GaAs quantum dots

(2) Washington; 3); (3) St. Petersburg; (4) Bochum; A. Greilich (1); Al. L. Efros (2); A. Shabaev (2); A. Wieck (4) ((1) Dortmund; D. Reuter (4); D. R. Yakovlev (1

REVIEW

Optical control of spin coherence in singly charged (In,Ga)As/GaAs quantum dots

Optics · Submitted 3 Mar 2006 · 26 references

Pith's verdict: A credible demonstration of pulse-area-dependent spin coherence in singly charged quantum dots, but the quantitative pi-pulse assignment rests on an uncalibrated axis and a single-dot model.

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arXiv IDphysics/0603020 (version 1)

Pith IDUXPBEGVR, Pith's permanent record of this paper and its review

Citation(2) Washington, 3), (3) St. Petersburg, (4) Bochum, A. Greilich (1), Al. L. Efros (2), A. Shabaev (2), A. Wieck (4) ((1) Dortmund, D. Reuter (4), D. R. Yakovlev (1, E. A. Zhukov (1), Germany, Germany), I. A. Merkulov (3), I. A. Yugova (1), M. Bayer (1), R. Oulton (1), Russia, USA, V. Stavarache (4). "Optical control of spin coherence in singly charged (In,Ga)As/GaAs quantum dots." arXiv:physics/0603020 (2006). https://pith.science/paper/UXPBEGVR

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Editor's note

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Read this one for the data, not for the pi-pulse calibration. The new thing is real: the Dortmund/Bochum/NRL group shows that in self-assembled (In,Ga)As/GaAs dots with one resident electron per dot, the Faraday-rotation amplitude oscillates as you increase the pump power, and the long-lived spin beats survive to nanoseconds. That is the first time coherent control of electron spin coherence has been shown in self-assembled singly charged dots, extending the low-power interface-dot work of Dutt et al. The g-factor measurements, hole g-factor dispersion, and dephasing-vs-field analysis are careful and consistent. The paper does what it claims experimentally.

The soft spot is exactly the stress-test concern, and it lands. The pulse area axis is arbitrary units (Theta proportional to sqrt(P), dipole moment unknown), so the power at which Theta = pi is not known. The assignment of the first FR maximum to pi is an inference from the Rabi model, not a calibration. Worse, the model calculation in Fig. 3 and Eq. (2) is for a single dot at resonance, while the sample has a 10 meV inhomogeneous line and the laser bandwidth is about 2 meV. For detuned dots the inversion is not cos^2(Theta/2); the optimal pulse area shifts with detuning, and ensemble averaging over the measured inhomogeneous distribution can move and damp the extrema. So the observed first maximum need not correspond to Theta = pi. The damping of the second oscillation is attributed to dipole-moment inhomogeneity, but detuning inhomogeneity would do that too.

I also note the key dynamical equations (1)-(2) are attributed to an unpublished manuscript [17]. That may be normal in a Letter, but it makes the theoretical prediction uncheckable from the paper. Even without the derivation, the qualitative period-2pi oscillation of the spin components follows from the standard two-level model, so this is a minor issue for the central experiment.

Bottom line: the qualitative observation of power-dependent, long-lived spin beats is solid and publishable. The quantitative claim "(2n+1)pi-pulses are most efficient" is not established by the evidence as presented. The authors could fix this by calibrating the pulse area (e.g., single-dot Rabi oscillations or an independent measurement of d) or by computing the ensemble average over detuning and showing the extrema are robust. This deserves a serious referee; I would send it out with a request for clarification rather than desk-reject. The paper is useful for anyone working on spin-based quantum dots; the data and g-factor values are a good reference, but the pi-pulse claim should be read as a hypothesis until the calibration is addressed.

Referee report

Significance

If fully established, the result is significant: it demonstrates resonant all-optical coherent control of electron spin coherence in singly charged quantum dots and proposes a spin-echo-like refocusing mechanism. The experimental observation of a damped, oscillatory FR amplitude as a function of pulse power is a valuable result in its own right and is plausibly attributed to Rabi physics. The extraction of electron and hole g-factors and the analysis of g-factor dispersion and dephasing are also useful. The time-domain model in Fig. 4 reproduces the qualitative features of the measured FR traces using experimental parameters. However, the quantitative claim that coherence generation is most efficient for (2n+1)π pulses is not fully supported by the presented evidence, because the pulse-area axis is uncalibrated and the comparison between theory and experiment does not include the inhomogeneous ensemble of the sample.

Major objections (3)

[Fig. 2(b) and main text after Eq. (2)] The pulse-area axis in Fig. 2(b) is explicitly in arbitrary units, and no independent calibration of the transition dipole moment d or of the absolute pulse area is provided. The text nevertheless states that the FR amplitude 'becomes maximum when applying a π-pulse' and 'becomes minimum for a 2π-pulse.' This identification of the first maximum and first minimum with Θ=π and Θ=2π is an assumption rather than a measured result. Since the abstract and conclusion make the quantitative statement that spin coherence is 'most efficient for (2n+1)π-pulses,' this load-bearing point needs either an independent pulse-area calibration or a rephrasing of the claim as qualitative consistency with a two-level Rabi model.
[Eq. (1), Eq. (2), and Fig. 2 comparison] The analytical state |ψ_ET⟩ = α0 cos(Θ/2)|↑⟩ + β0|↓⟩ - i α0 sin(Θ/2)|↑↓⇑⟩ and the spin-vector equations (1) describe a single dot at exact resonance. The experiment, however, excites an ensemble with a 10 meV FWHM emission line using a laser with ~2 meV bandwidth (Fig. 1 inset). For a dot detuned by δ, the inversion is (Ω²/(Ω²+δ²)) sin²(√(Ω²+δ²)t/2), so the pulse area at which the maximum occurs shifts with detuning. The paper does not present an ensemble average of the FR amplitude versus pulse area; Fig. 4 is a time-domain calculation at fixed parameters. Consequently, the agreement between the first maximum of the measured FR amplitude and Θ=π is not quantitatively justified, and the observed damping of the oscillation cannot be attributed solely to dipole-moment inhomogeneities without additional calculation.
[Theoretical foundation (Eqs. (1)-(2), Ref. [17])] The central spin-dynamics equations, Eq. (1) and Eq. (2), are attributed to the unpublished manuscript [17], and their derivation is not included. Because the quantitative pulse-area predictions follow from these equations, the reader cannot verify the result from the paper alone. The authors should either include the derivation in an appendix or supplemental material, or state explicitly which steps are taken from [17] and which are standard two-level Rabi physics. This is particularly important given that the pulse-area calibration in the experiment is inferred from the theoretical model.

Minor objections (5)

[Fig. 2(b)] The axis label 'pulse area (arb. units)' combined with the text's identification of the first maximum as a π-pulse would be much clearer if the corresponding pump power values or an independently calibrated Θ scale were shown; otherwise the reader cannot connect the data points to the claimed π and 2π positions.
[Eq. (1)] The first term on the right-hand side of the second equation should be written as a cross product, e.g., [(Ωe + ΩN) × S], to avoid ambiguity in the vector equation.
[Fig. 3 caption] The initial conditions for panels (a)-(d) are stated in a compressed form; please spell them out explicitly (for example, (a),(b): Sz0 = Sy0 = 0, Sx0 = 0.29; (c),(d): Sz0 = Sy0 = 0, Sx0 = 0.5) so that the reader can follow which panel corresponds to which curve.
[Main text, final paragraph] The sentence 'The long trion lifetimes in our QDs could enable realization of regime' is missing an article; it should read 'realization of a regime.'
[Fig. 1 caption] The caption contains corrupted character sequences (e.g., '/s48 /s53 /s49/s48 ...') that should be removed in the final published version.

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The paper

The paper claims

Circularly polarized laser pulses can write, flip, and refocus electron spin coherence in singly charged quantum dots, with the effect strongest for odd multiples of a π pulse.

The reading

Resonant pulses of circularly polarized light write a controllable electron spin coherence into semiconductor quantum dots that contain on average a single resident electron. The pulse creates a transient coherent superposition of the electron and a charged-exciton (trion) state; when the trion recombines, a long-lived electron spin precession remains. The efficiency of this writing depends on the laser pulse area, defined as the time-integrated electric-field–dipole product: it is largest for $(2n+1)\pi$ pulses and essentially zero for $2\pi$ pulses. This matters because it turns a simple optical pulse into a coherent spin rotation, a primitive operation for spin-based quantum information processing.

What carries the argument

The central mechanism is the electron–trion coherent superposition produced by a short resonant pulse. The pulse area, $\Theta = 2\int dE(t)\,dt/\hbar$, determines the state: for a $\sigma^+$ pulse, the initial electron state $\alpha_0|\!\uparrow\rangle + \beta_0|\!\downarrow\rangle$ becomes $\alpha_0\cos(\Theta/2)|\!\uparrow\rangle + \beta_0|\!\downarrow\rangle - i\alpha_0\sin(\Theta/2)|\!\uparrow\downarrow\Uparrow\rangle$. This makes the in-plane spin components $S_{x,y}$ oscillate as $\cos(\Theta/2)$ while the out-of-plane component $S_z$ oscillates with period $2\pi$, so that odd multiples of $\pi$ give maximal polarization transfer and even multiples give sign reversal of the precessing in-plane spin. The spin dynamics after the pulse are governed by two coupled vector equations for the electron spin $\mathbf{S}$ and trion spin $\mathbf{J}$ (Eq. 1), in which trion radiative decay acts as a source that repopulates electron spin coherence once the trion has recombined.

Extended reading notes

Core claim

The paper reports that in n-type modulation-doped (In,Ga)As/GaAs quantum dots with one resident electron per dot, resonant circularly polarized picosecond pulses produce electron spin coherence through a transient electron–trion superposition. Pump–probe Faraday rotation shows that the amplitude of the long-lived spin beats oscillates with pulse area: it rises to a first maximum at a $\pi$ pulse, falls to about 60% at $2\pi$, and then shows further damped oscillations, behaviour the paper identifies with Rabi oscillations of the electron Bloch vector. From the field dependence the paper extracts the electron g-factor magnitude $|g_e| = 0.57$ and, from the enhanced dephasing at high field, a g-factor spread $\Delta g_e = 0.004$. The accompanying theory uses vector equations of motion for the electron and trion spin polarizations to show that odd multiples of $\pi$ maximize the transferred $z$-polarization, while even multiples of $\pi$ reverse the sign of the in-plane spin components, a property the paper proposes for refocusing precessing spins.

Load-bearing premise

The paper assumes the quantum dots contain on average one resident electron each, so the optical excitation creates an electron–trion superposition rather than a neutral-exciton state; if the charge occupation differs, the pulse-area resonance and the whole trion-based interpretation would not hold.

Editorial extensions

If this is right

The spin state written by a pulse is set by the pulse area, so one laser can prepare, flip, or leave unchanged the electron spin depending only on intensity.
Because in-plane spin components reverse sign at $2n\pi$ pulses, such pulses can refocus a precessing spin ensemble, giving an all-optical analog of spin echo.
The observed pulse-area oscillation calibrates the dot–light coupling (transition dipole moment) and its inhomogeneity across the ensemble.
The measured g-factor spread $\Delta g_e = 0.004$ implies ensemble dephasing at high fields is dominated by g-factor dispersion, so more homogeneous dot ensembles would extend $T_2^*$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the same pulse-area control holds in a single dot, $\pi/2$ and $\pi$ pulses would act as single-qubit rotations for a dot-based spin qubit; the paper demonstrates the effect on an ensemble, so a single-dot verification is the natural next step.
The predicted refocusing at $2n\pi$ could be tested with a three-pulse Faraday-rotation experiment: a $\pi/2$ pulse to start precession, a $2\pi$ pulse at a delay, and a probe to see the echo.
The quantitative prediction $S_z((2n+1)\pi) = -0.25$ for an initially unpolarized spin ensemble could be checked by measuring the absolute Faraday-rotation amplitude against a calibrated reference.
Because the same electron–trion superposition underlies many optical spin-initialization and readout schemes, the pulse-area dependence implies that excitation powers must be calibrated carefully to avoid inadvertently returning a spin to its starting state.

Original abstract

Electron spin coherence has been generated optically in n-type modulation doped (In,Ga)As/GaAs quantum dots (QDs) which contain on average a single electron per dot. The coherence arises from resonant excitation of the QDs by circularly-polarized laser pulses, creating a coherent superposition of an electron and a trion state. Time dependent Faraday rotation is used to probe the spin precession of the optically oriented electrons about a transverse magnetic field. Spin coherence generation can be controlled by pulse intensity, being most efficient for (2n+1)pi-pulses.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,638 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Electron spin coherence has been generated optically in n-type modulation doped (In,Ga)As/GaAs quantum dots (QDs) which contain on average a single electron per dot. The coherence arises from resonant excitation of the QDs by circularly-polarized laser pulses, creating a coherent superposition of an electron and a trion state. Time dependent Faraday rotation is used to probe the spin precession of the optically oriented electrons about a transverse magnetic field. Spin coherence generation can be controlled by pulse intensity, being most efficient for (2n+1)pi-pulses.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Electron spin coherence has been generated optically in n-type modulation doped (In,Ga)As/GaAs quantum dots (QDs) which contain on average a single electron per dot.	result 0.54	0.88	0.27	asserted 1.00
s1	The coherence arises from resonant excitation of the QDs by circularly-polarized laser pulses, creating a coherent superposition of an electron and a trion state.	method 0.49	0.81	0.17	asserted 1.00
s2	Time dependent Faraday rotation is used to probe the spin precession of the optically oriented electrons about a transverse magnetic field.	method 1.00	0.85	0.06	asserted 1.00
s3	Spin coherence generation can be controlled by pulse intensity, being most efficient for (2n+1)pi-pulses.	result 0.99	0.85	0.36	asserted 0.99

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 2.** FIG. 2: (a): Closeup of FR rotation signal at

**Figure 3.** FIG. 3: (a) and (c): Reorientation of electron spin polariza

**Figure 4.** FIG. 4: Calculated time dependence of pump-probe FR signal

Figures reproduced from arXiv:physics/0603020 by the authors.

References

Works cited (26)

[17]

A. V. Koudinov et al. , Phys. Rev. B 70, 241305(R) (2004)

View on Pith 2004
[1]

The oscillation frequency increases with magnetic ﬁeld as expected from the spin-splitting of electron states: ℏΩ e =geµ BB , where ge is the electron g -factor and µ B is the Bohr magneton. We have analyzed the FR dynam- ics in Fig. 1(a) by an oscillatory function with exponen- tially damped amplitude, ∝ exp (−t/T ⋆ 2 ) cos (Ω et) . The resulting B -ﬁeld...

View on Pith 2000
[2]

The spin beats become increasingly damped with increasing magnetic ﬁeld, corresponding to a reduction of the ensemble spin dephasing time T ⋆ 2 , plotted in Fig. 1(c). The damping of the spin precession arises from vari- ations of the electron g -factor within the QD ensemble, causing an enhanced spread of Ω e with increasing B , whose impact on the depha...

View on Pith
[3]

The additional modulation of the FR traces at high ﬁelds is observable only during the trion lifetime and therefore can be naturally assigned to the photoexcited holes with a spin-splitting ℏΩ h = ghµ BB , where gh is the hole g -factor. The analysis gives | gh | =0.66 at B =5 T. The decay time of this mode is 170 ps which is signiﬁcantly shorter than the...

View on Pith
[4]

J. M. Kikkawa and D. D. Awschalom, Science 287, 473 (2000)

View on Pith 2000
[5]

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998)

View on Pith 1998
[6]

A. Imamoglu et al. , Phys. Rev. Lett. 83, 4204 (1999)

View on Pith 1999
[7]

Semiconductor Spintronics and Quantum Computation , ed. by D. D. Awschalom, D. Loss, and N. Samarth (Springer-Verlag, Heidelberg 2002)

View on Pith 2002
[8]

In a ﬁrst step, however, electron spin coherence must be established, which recently was addressed in charged GaAs/AlGaAs interface QDs. [9] However, only rather low excitation powers were used in those experiments, so that coherent control of electron spin polarization in form of Rabi oscillations did not occur. In this Letter we demonstrate by pump-prob...

View on Pith
[9]

J. M. Elzerman et al. , Nature 430, 431 (2004]; M. Krout- var et al. , Nature 432, 81 (2004)

View on Pith 2004
[10]

W. A. Coish and D. Loss, Phys. Rev. B 70, 195340 (2004)

View on Pith 2004
[11]

J. R. Petta et al. , Science 309, 2180 (2005)

View on Pith 2005
[12]

P. Chen et al. , Phys. Rev. B 69, 075320 (2003)

View on Pith 2003
[13]

M. V. Gurudev Dutt et al. , Phys. Rev. Lett. 94, 227403 (2005)

View on Pith 2005
[14]

M. O. Scully and M. S. Zubairy, Quantum Optics. , Cam- bridge University Press (1997)

View on Pith 1997
[15]

A. Greilich et al. , cond-mat/0505446 and /0601107

View on Pith Pith review arXiv
[16]

I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B 65, 205309 (2002)

View on Pith 2002
[18]

see, for example, T. H. Stievater et al. , Phys. Rev. Lett. 87, 133603 (2001); A. Zrenner et al. , Nature 418, 612 (2002) and references therein

View on Pith 2001
[19]

P. Borri et al. , Phys. Rev. B 66, 081306(R) (2002)

View on Pith 2002
[20]

J. G. Tischler et al. , Phys. Rev. B 66, 081310(R) (2002)

View on Pith 2002
[21]

A. Shabaev and Al. L. Efros, unpublished

View on Pith
[22]

A. Shabaev et al. , Phys. Rev. B 68, 201305(R) (2003). 5

View on Pith 2003
[23]

G. Morigi, E. Solano, B.-G. Englert, and H. Walther, Phys. Rev. A 65, 040102(R) (2002)

View on Pith 2002
[24]

A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. 88, 186802 (2002)

View on Pith 2002
[25]

D. V. Bulaev and D. Loss, Phys. Rev. Lett. 95, 076805 (2005)

View on Pith 2005
[26]

S. E. Economou et al. , Phys. Rev. B 71, 195327 (2005)

View on Pith 2005

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [17]

A. V. Koudinov et al. , Phys. Rev. B 70, 241305(R) (2004)

View on Pith 2004

[2] [1]

The oscillation frequency increases with magnetic ﬁeld as expected from the spin-splitting of electron states: ℏΩ e =geµ BB , where ge is the electron g -factor and µ B is the Bohr magneton. We have analyzed the FR dynam- ics in Fig. 1(a) by an oscillatory function with exponen- tially damped amplitude, ∝ exp (−t/T ⋆ 2 ) cos (Ω et) . The resulting B -ﬁeld...

View on Pith 2000

[3] [2]

The spin beats become increasingly damped with increasing magnetic ﬁeld, corresponding to a reduction of the ensemble spin dephasing time T ⋆ 2 , plotted in Fig. 1(c). The damping of the spin precession arises from vari- ations of the electron g -factor within the QD ensemble, causing an enhanced spread of Ω e with increasing B , whose impact on the depha...

View on Pith

[4] [3]

The additional modulation of the FR traces at high ﬁelds is observable only during the trion lifetime and therefore can be naturally assigned to the photoexcited holes with a spin-splitting ℏΩ h = ghµ BB , where gh is the hole g -factor. The analysis gives | gh | =0.66 at B =5 T. The decay time of this mode is 170 ps which is signiﬁcantly shorter than the...

View on Pith

[5] [4]

J. M. Kikkawa and D. D. Awschalom, Science 287, 473 (2000)

View on Pith 2000

[6] [5]

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998)

View on Pith 1998

[7] [6]

A. Imamoglu et al. , Phys. Rev. Lett. 83, 4204 (1999)

View on Pith 1999

[8] [7]

Semiconductor Spintronics and Quantum Computation , ed. by D. D. Awschalom, D. Loss, and N. Samarth (Springer-Verlag, Heidelberg 2002)

View on Pith 2002

[9] [8]

In a ﬁrst step, however, electron spin coherence must be established, which recently was addressed in charged GaAs/AlGaAs interface QDs. [9] However, only rather low excitation powers were used in those experiments, so that coherent control of electron spin polarization in form of Rabi oscillations did not occur. In this Letter we demonstrate by pump-prob...

View on Pith

[10] [9]

J. M. Elzerman et al. , Nature 430, 431 (2004]; M. Krout- var et al. , Nature 432, 81 (2004)

View on Pith 2004

[11] [10]

W. A. Coish and D. Loss, Phys. Rev. B 70, 195340 (2004)

View on Pith 2004

[12] [11]

J. R. Petta et al. , Science 309, 2180 (2005)

View on Pith 2005

[13] [12]

P. Chen et al. , Phys. Rev. B 69, 075320 (2003)

View on Pith 2003

[14] [13]

M. V. Gurudev Dutt et al. , Phys. Rev. Lett. 94, 227403 (2005)

View on Pith 2005

[15] [14]

M. O. Scully and M. S. Zubairy, Quantum Optics. , Cam- bridge University Press (1997)

View on Pith 1997

[16] [15]

A. Greilich et al. , cond-mat/0505446 and /0601107

View on Pith Pith review arXiv

[17] [16]

I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B 65, 205309 (2002)

View on Pith 2002

[18] [18]

see, for example, T. H. Stievater et al. , Phys. Rev. Lett. 87, 133603 (2001); A. Zrenner et al. , Nature 418, 612 (2002) and references therein

View on Pith 2001

[19] [19]

P. Borri et al. , Phys. Rev. B 66, 081306(R) (2002)

View on Pith 2002

[20] [20]

J. G. Tischler et al. , Phys. Rev. B 66, 081310(R) (2002)

View on Pith 2002

[21] [21]

A. Shabaev and Al. L. Efros, unpublished

View on Pith

[22] [22]

A. Shabaev et al. , Phys. Rev. B 68, 201305(R) (2003). 5

View on Pith 2003

[23] [23]

G. Morigi, E. Solano, B.-G. Englert, and H. Walther, Phys. Rev. A 65, 040102(R) (2002)

View on Pith 2002

[24] [24]

A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. 88, 186802 (2002)

View on Pith 2002

[25] [25]

D. V. Bulaev and D. Loss, Phys. Rev. Lett. 95, 076805 (2005)

View on Pith 2005

[26] [26]

S. E. Economou et al. , Phys. Rev. B 71, 195327 (2005)

View on Pith 2005