Optical Activity of Semiconductor Gammadions Beyond the Planar

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Optical Activity of Semiconductor Gammadions Beyond the Planar Chirality Nikita V. Tepliakov, Ilia A. Vovk, Anvar S. Baimuratov, Mikhail Yu. Leonov, Alexander V. Baranov, Anatoly V. Fedorov, and Ivan D. Rukhlenko J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01334 • Publication Date (Web): 16 May 2018 Downloaded from http://pubs.acs.org on May 17, 2018

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The Journal of Physical Chemistry Letters

Optical Activity of Semiconductor Gammadions Beyond the Planar Chirality Nikita V. Tepliakov, Ilia A. Vovk, Anvar S. Baimuratov, Mikhail Yu. Leonov, Alexander V. Baranov, Anatoly V. Fedorov, and Ivan D. Rukhlenko∗ Information Optical Technologies Centre, ITMO University, Saint Petersburg 197101, Russia E-mail: [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We present a rigorous analysis of optical activity of chiral semiconductor gammadions whose chirality in three dimensions is caused by the nonuniformity of thickness in the transverse plane. It is shown that such gammadions not only distinguish between the two circular polarisations upon scattering and reflection of light, like all two-dimensional semiconductor nanostructures with planar chirality do, but also exhibit circular dichroism and circularly polarized luminescence. Chiral semiconductor gammadions whose charge carriers are mostly confined to the arms are found to feature both high dissymmetry of optical response and a constant-sign circular dichroism signal over a wide frequency range. It is also shown that the strength of the gammadion’s chiroptical response is determined solely by two geometric factors: the variation range of the gammadion’s thickness and the arms’ curvature. Our seminal theoretical study is intended to lay the foundation for future applications of semiconductor gammadions in chiral nanophotonics and nanotechnology.

Graphical TOC Entry Absorption CD hω

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Chirality is a property of an object or a system to be not superimposable with its mirror image through any rotations and translations. 1 Being inherent to a variety of three-dimensional bodies and materials, this property can be naturally occurring or artificially introduced. 2,3 For example, many organic molecules and semiconductor crystals are naturally chiral due to the arrangement of their atoms 4,5 whereas originally achiral inorganic nanoparticles can acquire chirality in the presence of defects 6–14 or chiral ligands on their surface. 15,16 Further to that, achiral nanoparticles can be self-assembled into chiral superstructures on large organic molecules such as DNA or β-helices. 17–19 The lack of mirror symmetry results in different interaction strengths of chiral objects with left- and right-circularly polarized light. The associated chiroptical effects — such as circular dichroism, optical rotation, and circularly polarized luminescence 20 — have a multitude of useful applications in different disciplines, including biophysics, engineering, and analytical chemistry. In particular, chiral nanoparticles can be used for spin-selective electron transfer in spintronic devices, 21–23 sensing handedness of organic molecules, 24 and separation of chiral molecular mixtures in specifically tailored optical fields. 25,26 Chiral nanostructures have also proven themselves useful as emitters of circularly polarized light 27 and catalysts in asymmetric chemical synthesis. 28 The general definition of chirality can be narrowed down to the concept of planar chirality, which refers to the absence of mirror symmetry in a particular plane. 29 One common example of nanostructures possessing this type of chirality is an array of planar gammadions which all have the same handedness with respect to the substrate. 30 Similar to three-dimensional chiral objects, nanostructures with planar chirality distinguish between left and right circular polarizations and can introduce ellipticity into the transmitted light. In metallic nanostructures these effects are due to light scattering by free electrons 31 whereas in dielectric nanostructures they are caused by light coupling to chiral photon modes. 32 Planar chiral semiconductor nanostructures can also modify the emission of their adjacent light sources by making it elliptically polarized. 33 It is significant that the optical activity resulting from planar chirality is somewhat

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different from the proper optical activity of three-dimensional chiral nanostructures. 34 This difference is evident from the fact that planar chiral semiconductor nanostructures show neither circular dichroism nor circularly polarized luminescence. Still, they demonstrate coherent effects that depend on the direction of light propagation — differential scattering and differential reflection of circularly polarized light. Despite the rich optics of planar metallic gammadions and the long history of their use in plasmonics, a rigorous theoretical framework of similar nanostructures made of semiconductors is still lacking. In this Letter we analyze optical activity of chiral semiconductor gammadions of variable thickness, showing that they exhibit the incoherent phenomena of circular dichroism (CD) and circularly polarized luminescence. We then consider gammadions of three different shapes to establish general guidelines for the optimisation of the gammadion’s geometry and the intensification of its CD signal. For the first time to the best of our knowledge semiconductor gammadions are inferred to be quasi-x-dimensional nanocrystals with 1 < x < 2. The revealed strong and tuneable chiroptical response of chiral semiconductor gammadions make them promising material base for chiral spintronics, sensorics, and nanophotonics. Consider a semiconductor gammadion that turns into a cross (see Fig. 1) upon the following transformation of Cartesian coordinates {X, Y, Z} to curvilinear coordinates {x, y, z}:

X = x − αy 3 ,

Y = y + αx3 ,

Z = z.

(1)

Much like other semiconductor nanostructures, this gammadion can exhibit optical activity upon both intraband and interband electronic transitions. 35 The optical activity of the first kind is inherent to gammadions of chiral shapes 7,36 whereas the second kind of optical activity comes from the chiral distortion of the gammadion’s crystal lattice. 37 In what follows, we focus on interband transitions and describe the lattice distortion in the XY plane using the recently developed coordinate transformation method. 35,37,38 The intraband transitions are ignored, because their energies are in the far infrared spectral range. The curvature of the

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(a)

Z

y Y x

X

z

(b) y x

Figure 1: (a) Semiconductor gammadion in Cartesian coordinates {X, Y, Z} turns into (b) a cross in curvilinear coordinates {x, y, z}. The gammadion represents an equilateral cross with arms slightly curved in the same rotary direction. gammadion arms of length L is assumed to be so small that α L−2 . The probability of an interband transition, induced by circularly polarized light (CPL) which creates an electron in state |ni and a hole in state |mi, is given by Fermi’s golden rule:

± Wnm (E) =

2π |hn, m|H± |0i|2 f (E − Enm ), ~

(2)

where the plus or minus sign refers to the left-CPL or right-CPL, E = ~ω, f (E − Enm ) is the lineshape function centered at the transition energy Enm = En + Em + Eg , Eg is the bandgap of bulk semiconductor, En and Em are the confinement energies of electron and hole respectively, H± = e/(m0 c)(A± p), A± is the vector potential, p is the electron momentum, −e and m0 are the charge and mass of a free electron, and c is the speed of light in vacuum. By assuming that the excitation wavelength significantly exceeds the characteristic gammadion size in the direction of light propagation, we use the approximation √ A± ≈ e± (1 + ikR) 4πcI/ω, where e± , k, and R are the unit vector of circular polarization, wave vector, and radius vector in Cartesian coordinates, and I is the CPL intensity. 5



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The circular dichroism (CD) of a semiconductor gammadion is the transition rates dif+ − (E). If the excitation light propagates in the −z (E) − Wnm ference ∆Wnm (E) = Wnm √ direction, then kR = −(ω/c)z and e± p = (∓pX + ipY )/ 2, where according to Eq. (1)

pX = px − 3αx2 py and pY = py + 3αy 2 px . In this case, Eq. (2) yields

∆Wnm (E) = 3α

4πe 2 I m0 c

E

hn, m|x2 py |0ihn, m|zpy |0i + hn, m|y 2 px |0ihn, m|zpx |0i

− hn, m|px |0ihn, m|zy 2 px |0i − hn, m|py |0ihn, m|zx2 py |0i f (E − Enm ). (3)

Planar semiconductor nanostructures are typically made of III–V isotropic semiconductors such as GaAs, 33 whose conduction and valence bands have minima in the Brillouin zone center. For simplicity, we ignore the spin-orbit coupling and use a simple two-band model of a semiconductor. 39 Then the states of charge carriers in the vicinity of the Γ point can be (e)

(h)

represented as the direct product of four states |n, mi = |ue i ⊗ |ψn i ⊗ |uh i ⊗ |ψm i, where (e)

(h)

|ue i and |uh i are the Bloch functions and |ψn i and |ψm i are the envelope functions. 40 Since the envelope functions are almost constant inside the unit cell, the matrix elements in Eq. (3) (e)

(h)

can be evaluated using the approximation hn, m|χ(r)pj |0i ≈ hψn |χ(r)|ψm iP, where χ(r) is a function of coordinates, pj is the jth component of momentum, and P = hue |pj |uh i is the Kane parameter. The CD signal is then simplified to the form

∆Wnm (E) = 3α (e)

(h)

(e)

(h)

4πeP 2 I m0 c (e)

E (h)

Vnm f (E − Enm ), (e)

(4)

(h)

where Vnm = hψn |z|ψm ihψn |r2 |ψm i − hψn |ψm ihψn |zr2 |ψm i and r2 = x2 + y 2 . Equation (4) shows that a semiconductor gammadion of constant thickness (i.e. possessing planar chirality) is optically inactive. In this case Vnm = 0, because operators x2 + y 2 and z belong to irreducible representations A1g and A2u of the gammadion’s point symmetry (e)

(h)

group D4h , in which functions |ψn i and |ψm i cannot be described by the sum of these representations, A1g ⊕ A2u . However, if the gammadion lacks the mirror symmetry in the

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z direction due to the nonuniform thickness in the xy plane, then its symmetry group is lowered to at least C4v and the above operators belong to the unitary representation A1 . In this case Vnm may be nonzero if the envelope functions of electron and hole have the same (e)

(h)

spatial symmetry and their direct product |ψn i ⊗ |ψm i transforms according to the unitary representation. It should be noted that matrix elements Vnm determine not only the probabilities of absorption transitions induced by CPL but the probabilities of the spontaneous radiative transitions as well. This implies that in addition to strong circular dichroism chiral semiconductor gammadions can exhibit pronounced circularly polarized luminescence. In particular, the dissymmetry of the gammadion’s luminescence upon the fundamental interband transition accompanied by the recombination of electron and hole in their ground states is characterized by function ∆W11 (E). Summarising the above results yields the following absorption and CD spectra of semiconductor gammadions of surface density N :

A(E) = N

2πeP 2 ~c X

CD(E) = 3αN

m0 c E n 4πeP 2 X m0 c

f (E − Enn ),

Vnm f (E − Enm ).

(5) (6)

n,m

One can see that the absorption spectrum consists of dipole-allowed transitions between the similar states of electrons and holes 41,42 whereas the CD spectrum comprises both dipoleallowed transitions (with n = m) and dipole-forbidden transitions (with n 6= m) between the states of the same symmetry, which become possible due to the distortion of the gammadion’s crystal lattice. Consider three types of chiral semiconductor gammadions shown in Fig. 2: a conical gammadion of thickness h = h0 (1 − 2r/L), an inverse conical gammadion with h = 2h0 r/L, and a sloped gammadion with h = h0 (1/2+x/L). Since the crystal lattice is mostly distorted in the gammadion’s arms, where most of the charge carriers of the inverse conical gammadion 7



(a)

(b)

(c)

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(d)

a L h0

Figure 2: (a) Conical, (b) inverse conical, and (c) sloped semiconductor gammadions (top) and their ground-state wave functions (bottom), which were calculated by assuming that the gammadion’s surface is impenetrable for the confined charge carriers. Panel (d) shows three gammadion dimensions: arm length L, arm width a, and maximal thickness h0 . reside, this gammadion can be anticipated to exhibit the strongest optical activity. Before we proceed with our analysis any further, it is important to note a key difference of semiconductor gammadions from nanocrystals of simple shapes such as quasi-1D nanorods (NRs) and quasi-2D nanoplatelets (NPLs). It turns out that the confinement energies of electrons and holes inside semiconductor gammadions have a square-root dependence on √ state number n, En ∝ n, and their density of states (DoS) is approximately linear, ρ(E) = dn/dE ∝ E. The former is evidenced by Figs. 3(a)–3(c), which show the energies of interband transitions for the three types of gammadions in Fig. 2. This observation, and the fact that the shape of gammadions is somewhat intermediate between the shapes of NRs and NPLs, allow one to consider them as nanocrystals of fractional quasi-dimensionality x between 1 and 2. This insight is further supported by the comparison of the transition energies in the three kinds of nanocrystals presented in Fig. 3(d). The linearity of the density of electronic states allows one to roughly approximate the sum in the interband absorption spectra [Eq. (5)] by the function ρ(E) = 2ζ

E − Eg , (E11 − Eg )2

(7)

where ζ is a shape factor determined by the gammadion geometry and E11 is the energy of 8


2.5 2.3 2.1

(a)

(b)

Light holes

Light holes

1.9 Heavy holes

1.7 2.5

Transition energy, E nn (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Transition energy, E nn (eV)

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2.3 2.1

Heavy holes

(d)

(c)

2

1D NR (Enn∝ Σn )

Light holes

xD G

1.9 Heavy holes

1.7 1.5 0

(Enn∝ n)

15

30 45 State number, n

60

15

2D NPL (Enn ∝ n)

30 45 State number, n

60

Figure 3: [(a)–(c)] Energies of dipole-allowed interband transitions from the subbands of heavy and light holes for three GaAs gammadions (Fig. 2); solid curves are the square-root function approximations to the exact values (open circles). It is assumed that L = 5a = 50 nm, h0 = 20 nm, Eg = 1.52 eV, 2P 2 /m0 = 25 eV, me = 0.06 m0 , mlh = 0.09 m0 , and mhh = 0.38 m0 . 43 Panel (d) show similar energies for transitions from the subband of heavy holes for 50 × 50 × 10-nm3 nanoplatelet (NPL), 10 × 10 × 50-nm3 nanorod (NR), and gammadion (G) of uniform thickness h0 = 10 nm and of lateral dimensions L = 5a = 50 nm. fundamental transition |0i → |1, 1i. The absorption and CD spectra of the three types of semiconductor gammadions are plotted in Fig. 4. The lower panels also show the ratios of the CD and absorption spectra, g(E) = CD(E)/A(E), which will be referred to as the g-factor spectra. The good correspondence between the exact absorption spectra (solid curves) and their approximations with the linear density of states (dashed lines) proves that semiconductor gammadions are quasi-xD nanocrystals with 1 < x < 2. The CD and g-factor spectra confirm our earlier conclusion that the strongest optical activity is exhibited by the inverse conical gammadions. In contrast to this, the conical

9



8×10–3

A(E)

6

Exact DoS

(a)

4 2

HH

Exact DoS LH

(b)

LH

HH

LH

Exact DoS

(c)

HH

0

CD(E)

10×10–7

Left-handed (α < 0)

Left-handed

Left-handed

Right-handed (α > 0)

Right-handed

Right-handed

Left-handed

Left-handed

Left-handed

Right-handed

Right-handed

Right-handed

5 0 -5 -10

6×10–4 4 2

g(E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0 -2 -4 -6 1.5

1.6

1.7

1.8

1.9

Photon energy, E (eV)

2.0

1.6

1.7

1.8

1.9


2.0

1.6

1.7

1.8

1.9


2.0

Figure 4: Room-temperature absorption, CD, and g-factor spectra of three types of GaAs gammadions. The linewidths of interband transitions are all alike and correspond to the thermal energy of 30 meV. Labels ‘HH’ and ‘LH’ indicate exciton peaks corresponding to the transitions from the subbands of heavy and light holes. The solid absorption spectra were calculated using Eq. (5) whereas the dashed lines were calculated using Eq. (7) with ζ = 1, 3, and 2 for the conical, inverse conical, and sloped gammadions respectively. It is assumed that αL2 = ±1/10 and N = 100 µm−2 ; the rest of parameters are the same as in Fig. 3. gammadions are seen to have the lowest CD signal near the absorption edge and the weakest fundamental absorption peaks due to the subbands of heavy and light holes. The latter is explained by the weak lattice distortion at the gammadion center (where most of the charge carriers in their ground states reside) and the resulting poor optical activity of the fundamental exciton transitions. On the other hand, the inverse conical gammadions can reach g-factors of ±5×10−4 and ellipticities of 0.03 mdeg for the surface density of 100 µm−2 , which is typical for other types of chiral semiconductor nanocrystals and small organic molecules. 36

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Table 1: Matrix element vnn for the first three dipole-allowed interband transitions inside three chiral gammadions shown in Fig. 2. Gammadion Type Conical Inverse conical Sloped

v11 0.2 × 10−3 1.5 × 10−3 2.7 × 10−3

v22 0.6 × 10−3 1.4 × 10−3 4.6 × 10−3

v33 0.6 × 10−3 1.5 × 10−3 0.1 × 10−3

The strong CD signal and its constant sign over a broad spectral range make inverse conical gammadions highly attractive for chiroptical applications. It is instructive to analyze how the chiroptical response of semiconductor gammadions depends on the characteristic gammadion dimensions. This can be done by evaluating the dissymmetry factor of dipole-allowed transitions |0i → |n, ni, which can be written in the form gnn = 12 αL2 kh0 vnn , where vnn = Vnn /(h0 L2 ) is almost independent of L, a, and h0 , provided that a L. By taking into account that the effects of quantum confinement are significant for kh0 . 1/10 and that the curvature of the gammadion arms is limited by the condition αL2 . 1/10, we get the estimate from above gnn . vnn /10. The first three values of vnn for the three shapes of gammadions are given in Table 1. Since matrix element vnn is dimensionless, the size dependence of the dissymmetry factor is determined by the product of factors αL2 and kh0 , and does not involve the gammadion arms width a, which determines the confinement energies and the positions of the CD peaks. Hence, the lateral gammadion profile and parameters L, h0 , and α control the absolute strength (amplitude) of the chiroptical response whereas parameter a controls the local strength (intensity) of the CD signal. This feature enables flexible engineering of chiroptical response of semiconductor gammadions. By varying the gammadion’s dimensions one at a time, one can achieve the desirable CD strength at each wavelength of interest. In summary, we have comprehensively analyzed optical activity upon interband transitions inside chiral semiconductor gammadions of variable thickness. The dissymmetry factors of optically active transitions were found to be comparable to those of small organic molecules and other types of chiral semiconductor nanocrystals. It was shown that the strongest optical

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activity and the constant-sign CD signal are exhibited by chiral gammadions whose thickness increases from the center to the periphery. The strength of the gammadion’s chiroptical response was found to be determined solely by the gammadion arms’ curvature and the modulation depth of the gammadion’s thickness. For the first time to the best of our knowledge we notice the fact that the shape of semiconductor gammadions is somewhat intermediate between the shapes of quasi-1D nanorods and quasi-2D nanoplatelets and, as a consequence, the density of electronic states in semiconductor gammadions is a linear function of energy. We believe that the unusual electronic and optical properties of chiral semiconductor gammadions will benefit the field of chiral nanotechnology, including the development of novel chiroptical sensors and spintronic devices.

Acknowledgement This work was funded by Grant MD-1294.2017.2 of the President of the Russian Federation for Young Scientists. The authors also thank the Ministry of Education and Science of the Russian Federation for its Project 16.8981.2017/8.9, Scholarships SP-2066.2016.1 and SP-1975.2016.1, and Grant 14.Y26.31.0028.

References (1) Bonner, W. A. Chirality and Life. Orig. Life Evol. Biospheres 1995, 25, 175–190. (2) Ma, W.; Xu, L.; de Moura, A. F.; Wu, X.; Kuang, H.; Xu, C.; Kotov, N. A. Chiral Inorganic Nanostructures. Chem. Rev. 2017, 117, 8041–8093. (3) Milton, F. P.; Govan, J.; Mukhina, M. V.; Gun’ko, Y. K. The Chiral Nano-World: Chiroptically Active Quantum Nanostructures. Nanoscale Horiz. 2016, 1, 14–26. (4) Compton, R. N.; Pagni, R. M. The Chirality of Biomolecules. Adv. At. Mol. Opt. Phys. 2002, 48, 219–261. 12


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Page 13 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(5) Green, B. S.; Lahav, M.; Rabinovich, D. Asymmetric Synthesis via Reactions in Chiral Crystals. Acc. Chem. Res. 1979, 12, 191–197. (6) Baimuratov, A. S.; Tepliakov, N. V.; Gun’Ko, Y. K.; Shalkovskiy, A. G.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Intraband Optical Activity of Semiconductor Nanocrystals. Chirality 2017, 29, 159–166. (7) Rukhlenko, I. D.; Baimuratov, A. S.; Tepliakov, N. V.; Baranov, A. V.; Fedorov, A. V. Shape-Induced Optical Activity of Chiral Nanocrystals. Opt. Lett. 2016, 41, 2438–2441. (8) Tepliakov, N. V.; Baimuratov, A. S.; Gun’ko, Y. K.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Engineering Optical Activity of Semiconductor Nanocrystals via Ion Doping. Nanophotonics 2016, 5, 573–578. (9) Baimuratov, A. S.; Tepliakov, N. V.; Gun’ko, Y. K.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Mixing of Quantum States: A New Route to Creating Optical Activity. Sci. Rep. 2016, 6, 5. (10) Baimuratov, A. S.; Rukhlenko, I. D.; Gun’ko, Y. K.; Baranov, A. V.; Fedorov, A. V. Dislocation-Induced Chirality of Semiconductor Nanocrystals. Nano Lett. 2015, 15, 1710–1715. (11) Mukhina, M. V.; Maslov, V. G.; Baranov, A. V.; Fedorov, A. V.; Orlova, A. O.; PurcellMilton, F.; Govan, J.; Gun’ko, Y. K. Intrinsic Chirality of CdSe/ZnS Quantum Dots and Quantum Rods. Nano Lett. 2015, 15, 2844–2851. (12) Valev, V. K.; Baumberg, J. J.; Sibilia, C.; Verbiest, T. Chirality and Chiroptical Effects in Plasmonic Nanostructures: Fundamentals, Recent Progress, and Outlook. Adv. Mater. 2013, 25, 2517–2534. (13) Guerrero-Martínez, A.; Alonso-Gómez, J. L.; Auguié, B.; Cid, M. M.; Liz-Marzán, L. M.

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From Individual to Collective Chirality in Metal Nanoparticles. Nano Today 2011, 6, 381–400. (14) Canfield, B. K.; Kujala, S.; Laiho, K.; Jefimovs, K.; Turunen, J.; Kauranen, M. Chirality Arising from Small Defects in Gold Nanoparticle Arrays. Opt. Express 2006, 14, 950– 955. (15) Kundelev, E. V.; Orlova, A. O.; Maslov, V. G.; Baranov, A. V.; Fedorov, A. V. Circular Dichroism of Surface Complexes Based on Quantum Dots and Azo Dye. Chirality 2018, 30, 261–267. (16) Elliott, S. D.; Moloney, M. P.; Gun’ko, Y. K. Chiral Shells and Achiral Cores in CdS Quantum Dots. Nano Lett. 2008, 8, 2452–2457. (17) Baimuratov, A. S.; Gun’ko, Y. K.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Chiral Quantum Supercrystals with Total Dissymmetry of Optical Response. Sci. Rep. 2016, 6, 23321. (18) Kuzyk, A.; Schreiber, R.; Fan, Z.; Pardatscher, G.; Roller, E.-M.; Högele, A.; Simmel, F. C.; Govorov, A. O.; Liedl, T. DNA-based Self-Assembly of Chiral Plasmonic Nanostructures with Tailored Optical Response. Nature 2012, 483, 311. (19) Zhang, S. Fabrication of Novel Biomaterials through Molecular Self-Assembly. Nature Biotechnol. 2003, 21, 1171. (20) Berova, N.; Polavarapu, P. L.; Nakanishi, K.; Woody, R. W. Comprehensive Chiroptical Spectroscopy: Instrumentation, Methodologies, and Theoretical Simulations; Wiley Online Library, 2012; Vol. 1. (21) Brandt, J. R.; Salerno, F.; Fuchter, M. J. The Added Value of Small-Molecule Chirality in Technological Applications. Nat. Rev. Chem. 2017, 1, 0045.

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(22) Naaman, R.; Waldeck, D. H. Spintronics and Chirality: Spin Selectivity in Electron Transport through Chiral Molecules. Ann. Rev. Phys. Chem. 2015, 66, 263–281. (23) Dor, O. B.; Yochelis, S.; Mathew, S. P.; Naaman, R.; Paltiel, Y. A Chiral-Based Magnetic Memory Device Without a Permanent Magnet. Nature Commun. 2013, 4, 2256. (24) Han, C.; Li, H. Chiral Recognition of Amino Acids Based on Cyclodextrin-Capped Quantum Dots. Small 2008, 4, 1344–1350. (25) Rukhlenko, I. D.; Tepliakov, N. V.; Baimuratov, A. S.; Andronaki, S. A.; Gun’ko, Y. K.; Baranov, A. V.; Fedorov, A. V. Completely Chiral Optical Force for Enantioseparation. Sci. Rep. 2016, 6, 36884. (26) Vovk, I. A.; Baimuratov, A. S.; Zhu, W.; Shalkovskiy, A. G.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Chiral Nanoparticles in Singular Light Fields. Sci. Rep. 2017, 7, 45925. (27) Moloney, M. P.; Gun’ko, Y. K.; Kelly, J. M. Chiral Highly Luminescent CdS Quantum Dots. Chem. Commun. 2007, 38, 3900–3902. (28) Choudary, B. M.; Ranganath, K. V.; Pal, U.; Kantam, M. L.; Sreedhar, B. Nanocrystalline MgO for Asymmetric Henry and Michael Reactions. J. Am. Chem. Soc. 2005, 127, 13167–13171. (29) Papakostas, A.; Potts, A.; Bagnall, D.; Prosvirnin, S.; Coles, H.; Zheludev, N. Optical Manifestations of Planar Chirality. Phys. Rev. Lett. 2003, 90, 107404. (30) Kwon, D.-H.; Werner, P. L.; Werner, D. H. Optical Planar Chiral Metamaterial Designs for Strong Circular Dichroism and Polarization Rotation. Opt. Express 2008, 16, 11802–11807. (31) Fedotov, V.; Schwanecke, A.; Zheludev, N.; Khardikov, V.; Prosvirnin, S. Asymmetric

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Transmission of Light and Enantiomerically Sensitive Plasmon Resonance in Planar Chiral Nanostructures. Nano Lett. 2007, 7, 1996–1999. (32) Konishi, K.; Bai, B.; Meng, X.; Karvinen, P.; Turunen, J.; Svirko, Y. P.; KuwataGonokami, M. Observation of Extraordinary Optical Activity in Planar Chiral Photonic Crystals. Opt. Express 2008, 16, 7189–7196. (33) Konishi, K.; Nomura, M.; Kumagai, N.; Iwamoto, S.; Arakawa, Y.; KuwataGonokami, M. Circularly Polarized Light Emission from Semiconductor Planar Chiral Nanostructures. Phys. Rev. Lett. 2011, 106, 057402. (34) Gao, W.; Tam, W. Y. Optical Activities in Complementary Double Layers of Six-Armed Metallic Gammadion Structures. J. Optics 2010, 13, 015101. (35) Baimuratov, A. S.; Pereziabova, T. P.; Zhu, W.; Leonov, M. Y.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Optical Anisotropy of Topologically Distorted Semiconductor Nanocrystals. Nano Lett. 2017, 17, 5514–5520. (36) Tepliakov, N. V.; Baimuratov, A. S.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Optical Activity of Chirally Distorted Nanocrystals. J. Appl. Phys. 2016, 119, 194302. (37) Tepliakov, N. V.; Baimuratov, A. S.; Vovk, I. A.; Leonov, M. Y.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Chiral Optical Properties of Tapered Semiconductor Nanoscrolls. ACS Nano 2017, 11, 7508–7515. (38) Purcell-Milton, F.; McKenna, R.; Brennan, L.; Cullen, C. P.; Guillemeney, L.; Tepliakov, N. V.; Baimuratov, A. S.; Rukhlenko, I. D.; Perova, T. S.; Duesberg, G. S. et al. Induction of Chirality in Two-Dimensional Nanomaterials: Chiral 2D MoS2 Nanostructures. ACS Nano 2018, 12, 954–964. (39) Lassnig, R. k · p Theory, Effective-Mass Approach, and Spin Splitting for TwoDimensional Electrons in GaAs-GaAlAs Heterostructures. Phys. Rev. B 1985, 31, 8076. 16


Page 16 of 17

Page 17 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(40) Haug, H.; Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors; World Scientific, 1990. (41) Tepliakov, N. V.; Ponomareva, I. O.; Leonov, M. Y.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Field-Induced Broadening of Electroabsorption Spectra of Semiconductor Nanorods and Nanoplatelets. J. Phys. Chem. C 2016, 120, 2379–2385. (42) Tepliakov, N. V.; Leonov, M. Y.; Baranov, A. V.; Fedorov, A. V.; Rukhlenko, I. D. Quantum Theory of Electroabsorption in Semiconductor Nanocrystals. Opt. Express 2016, 24, A52–A57. (43) Vurgaftman, I.; Meyer, J.; Ram-Mohan, L. Band Parameters for III–V Compound Semiconductors and Their Alloys. J. Appl. Phys. 2001, 89, 5815–5875.

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Optical Activity of Semiconductor Gammadions Beyond the Planar

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