on the nature of the electronic and optical excitations of

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On the Nature of the Electronic and Optical Excitations of

Ruddlesden--Popper Hybrid Organic--Inorganic Perovskites: the Role of Many-Body Interactions

Journal: The Journal of Physical Chemistry Letters

Manuscript ID jz-2018-02653b.R1

Manuscript Type: Letter

Date Submitted by the Author: n/a

Complete List of Authors: Giorgi, Giacomo; Universita degli Studi di Perugia, Department of Civil & Environmental Engineering Yamashita, Koichi; The University of Tokyo, Chemical System Engineering Palummo, Maurizia; Università di Roma "Tor Vergata", Diaprtimento di Fisica

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters

On the Nature of the Electronic and Optical

Excitations of Ruddlesden–Popper Hybrid

Organic–Inorganic Perovskites: the Role of the

Many-Body Interactions

Giacomo Giorgi,† Koichi Yamashita,‡ and Maurizia Palummo∗,Π

†Dipartimento di Ingegneria Civile e Ambientale, Universita di Perugia (DICA),

Via G. Duranti, 93 - 06125 - Perugia, Italy

‡Department of Chemical System Engineering, School of Engineering, The University of

Tokyo, Tokyo, Japan & CREST-JST, Tokyo, Japan

ΠDipartimento di Fisica and INFN, Universita di Roma ”Tor Vergata”

Via della Ricerca Scientifica 1, Roma, Italy

E-mail: [email protected],[email protected]

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Abstract

The knowledge of the exact nature of the electronic and optical excitations of

Ruddlesden–Popper organic–inorganic halide perovskites (RPPs) is particularly rel-

evant in view of their usage in optoelectronic devices. By means of parameter-free

quantum-mechanical simulations we unambiguously demonstrate the dominant role of

many-body Coulomb interaction, as recently proposed by Blancon et al.. Indeed, fo-

cusing on the first two terms (n=1,2) of the Pb–based buthylammonium series, both in

the form of isolated nanosheet and repeated bulk–like quantum–well, we observe large

band-gap renormalization and strongly bound excitons with binding energies up to

about 1 eV in the thinnest isolated nanosheet. Notably, taking into account electronic

correlation beyond DFT, we obtain exciton reduced masses similar to the correspond-

ing 3D bulk counterpart and large Rashba splitting of the same order of the value

reported by Zhai et al. in a recent experimental work.

Graphical TOC Entry

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In the last decade the scientific community has faced the raise of Hybrid Organic-

Inorganic halide Perovskites (OIHPs) as leading materials in the realm of low–cost pho-

tovoltaics (PV).1 The relevance of these materials, whose archetypal compound is repre-

sented by MAPbI3 (hereafter also MAPI, where MA=CH3NH3+, methylammonium), stems

from a long list of striking properties in the photoconversion process.2–9 There remain any-

way some detrimental shortages that make OIHP devices yet unsuitable for solar device

mass production. The major is the instability over heat, light, and moisture: the pres-

ence of the organic moiety highly reduces the durability of 3D OIHPs solar cells.10 To

overcome this issue the scientific community has focused its attention on more efficient alter-

natives, finding as ideal candidates the so–called Ruddlesden–Popper perovskites (hereafter

also RPPs),11 a mixed 2D/3D class of materials which has been recently successfully applied

both in PV12–14 and, due to their intense photoluminescence that persists also at RT, also in

light emitting diodes (LED) applications.14,15 In these layered structures of general stoichio-

metric relation (RNH3)2An−1MnI3n+1 (n = 1, 2, 3,...), layers of [MX6]4− (M=Pb2+, Sn2+;

X=halide) semiconductors form quantum wells (QWs) of different thickness (n). Their cav-

ities are filled with a small organic cation (usually MA) and are separated by a long chain

organic cation. The presence of the latter ones in the structure highly increases the hy-

drophobicity of the RPPs and also minimizes the environmental risk due to the presence

of Pb. The case n=1 corresponds to the more general case of pure 2D OIHPs, materials

already investigated at the end of the nineties for their possible optoelectronic applica-

tions.16 n–butylammonium (BA=CH3(CH2)3NH3+) is the aliphatic most studied organic

spacer,12,14 while 2–phenylethylammonium (PEA=C6H5(CH2)2NH3+) is the aromatic most

studied one.17–21 Although works focusing on the electronic and optical properties of such

materials have been recently published,22–28 to the best of our knowledge an unbiased theo-

retical analysis based on parameter-free excited state methods is yet unavailable. Moreover,

recent experimental works29 demonstrated that by means of a solution–based process it is

possible to grow and characterize not only QWs but also isolated nanosheets (NS-RPPs),

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which offer extreme mechanical flexibility and strong optical tunability that varies as func-

tion of the halide anions. It is then important to compute the excited-state properties

of isolated NS and periodic QW-RPPs including many-body effects beyond the mean-field

Density Functional Theory (DFT). Ideally continuing our research on layered materials with

optoelectronic applicability,30–35 we here investigate (BA)2(MA)n−1PbnI3n+1 n=1, 2 RPPs,

i.e. those which show intense room–temperature photoluminescence, and accordingly bet-

ter suitable for LED applications.12,20 Starting from few available experimental data14,29 we

obtain fully optimized atomic structures both in the form of isolated nanosheet (NS) and

bulk quantum-well (QW) structures. All the computational details and a detailed analysis

of the structural data are reported in the S.I. section (see text and Table S1). The NS and

QW structures for n = 1 are reported in Fig. S1 in S.I., while those for n = 2 are reported

in Fig. 1. Larger geometrical distortions in the latter ones (see S.I. section) are associated

with a larger Rashba–Dresselhaus splitting, as discussed in the following.

We initially focus on the electronic properties, showing in Fig. 2 the DFT-KS (dashed

black curve) and the GW (red solid curve) bandstructure of n=1 (top panels), n=2 (bottom

panels) NS (left) and QW-RPPs (right). Notably, the inclusion of the quasi-particle self-

energy largely renormalizes the DFT-KS electronic gap, increasing the band dispersion and

thus reducing the effective masses. For the NS (QW)-RPP the KS gap increases of ∼ 2.1

(1.5 eV) in n=1 and of ∼ 1.8 eV (1.3 eV) in n=2 RPPs.36 It is worth noting that for

n=1 NS, the QP gap is larger than that recently obtained by Ma et al.37 by means of a

hybrid exchange-correlation functional. Concerning the hole (electron) effective mass along

the X→Γ direction we obtain mdfth = 0.37 (mdft

e = 0.26) at the DFT-KS level and mgwh =

0.34 (mgwe = 0.19 ) at the GW level, which result lighter than the effective masses reported

in the same reference.37 Interestingly, the GW calculated exciton reduced masses, both for

the QW (0.12) and the NS (0.11), are of the same order of magnitude of that predicted in

bulk tetragonal MAPI,38 at the same level of theoretical approximation, and also very close

to the value reported by Kanatzidis et al.14 for bulk QW (BA)2(MA)n−1PbnI3n+1 RPPs.

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Figure 1: (a) lateral view and (b) top view of the n=2 sheet (NS-RPP) optimized structure.Same (c, d) for the bulk QW (QW-RPP). [Grey: Pb; Purple: I; Brown: C; Light blue: N;White: H atoms]

The large influence of spin-orbit coupling in 3D-OIHPs bandstructure is well documented

in the literature,8,39 nevertheless the importance of local or extended inversion symmetry

breaking, leading to Rashba-Dresselhaus (RD) effect, is still under debate.40,41 Due to the

layered structure, RPP OIHPs are more prone to a break of symmetry and then manifest

this exotic effect. Indeed, a recent experimental work, supported by DFT calculations,

reported the presence of a giant Rashba splitting in a RPP using PEA as spacer.42 Notably,

all the atomic structures calculated here, except the n=1 NS-RPP, show the presence of RD

splitting in their bandstructure. In particular, for n=2 NS-RPP, quite large RD parameters,

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comparable to values reported in ref. [39], are obtained at the GW level of approximation,

being about αc,v ' 1 eV A, along the Γ →S direction. Indeed, in Fig.3 the expectation

value (red (blue) color indicate negative(positive) numbers) of the three spin-components

(Sx, Sy, Sz from left to right) along the −0.25S → Γ → 0.25S directions is reported.

To gain better understanding of the origin of the valence and conduction band, the

projected density of states (PDOS) have been calculated for the n=1 case (see Fig.S2 in

the S.I. section). The corresponding data for n=2 are qualitatively similar and are not

reported. We found, consistently with what observed in bulk MAPI,8,39 that near the gap

the conduction states are mainly due to p orbital of Pb-atoms, while valence band stems

from the anti–bonding overlap between p (s) orbitals of I (Pb) atoms. The states associated

to the RPP organic components are far from the gap region and are not reported for clarity.

Similarly, the PDOS for the bulk n=1 QW structure confirms the presence of an isolated

and localized CB peak, feature previously observed at the pure DFT level of theory14 and

that is mainly formed by Pb p 3/2 orbitals.43 Once determined the QP bandstructures, we

solved in a fully ab-initio way the Bethe-Salpeter Equation to look at the role played by

excitons in the optical response of both isolated NS and QW structures.

In Fig. 4 we report the optical spectra of NS (left) and QW (right) for n=1 (top pan-

els) and n=2 RPP (bottom panels). The blue arrows indicate the position of the minimum

direct electronic gap as obtained by means of GW calculations. For the QW-RPPs, the

experimental curves obtained from ref. [22,23] are also reported. The good agreement be-

tween experimental and unbiased theoretical BSE curves, definitively confirms that the first

optical peaks are due to strongly bound excitons, as reported by Blancon et al.22,23 using

optical spectroscopy joined to a simplified exciton model. Due to a lower dielectric screening

the exciton binding energy of the isolated NS is more than three times larger than that of

the corresponding QW. Nevertheless, as observed in several other two-dimensional materi-

als,31,32,34,44 a large compensation of the electronic self-energy blue-shift and e-h interaction

red-shift, makes the energetic position of the first optical peak quite similar in the NS and

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Figure 2: DFT-KS (dashed) and GW (red, solid) Bandstructure of the Pb-based single sheet(left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels)

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Figure 3: Expectation values of Sx, Sy,Sz (left,center,right) for the n=2 NS–RPP. (Bandsare plotted here at the DFT-PBE level of approximation )

QW (for NS we observe a slight blue-shift in agreement with experimental data of Dou et

al.29). For n=1 (n=2) NS and QW, the estimated exciton binding energies are about 950

(650) and 300 (260) meV, respectively. It is worth to point out that while the exciton binding

energy obtained for the n=2 QW-RPP is in quite good agreement with data of ref.,23 the

corresponding value for n=1 QW is smaller than that reported in the same reference.

The role played by the electron-phonon interaction and polarons on the opto-electronic

properties of hybrid halide perovskites is an highly debated topic in the literature,45–48 then

it is important to underline that our present theoretical analysis does not take into account

this aspect but we plan to include it a near future. Nevertheless, the good agreement between

our unbiased BSE optical spectra and the experimental curves, seems to suggest that the

role of polarons in these specific layered hybrid halide perovskites with short organic spacers,

could be negligible, as also suggested by the very small Stock-shifts observed at experimental

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level.23 Longer organic spacers49 or different sample dimensionality50 certainly change the

scenario as demonstrated by several recent works.

Very delocalized excitons (∼ 20-50 A)51–53 along with their very small binding energies

(reported values from 6 to 50 meV),51–53 characterize the optical properties of the 3D coun-

terpart. Such values stress the intriguing and still debated dual free-carrier54–56vs. exciton

bound behavior of bulk MAPbI3, regimes that co–exist at room temperature (kBT ∼ 25

meV, where kB is the Boltzmann constant).3,57,58 As illustrated before, the reduced dielec-

tric screening and spatial quantum-confinement of RPPs induce the formation of strongly

bound excitons whose spatial localization is completely different from what expected in the

3D bulk counterpart. Fig. 5 shows the side view of the spatial distribution of the first bright

exciton for n=1 (left) and n=2 (right) NS. Notably, in both cases, the exciton is localized

only in the inorganic parts of the RPP, but for n=2 NS it has a more delocalized lateral

spatial distribution compared to n=1 . Indeed, a non–zero probability to find the electron

quite far from the fixed hole position (red cross in the plots) and in both adjacent inor-

ganic layers, is observed. The exciton spatial localization in the QW–RPPs does not change

substantially and for this reason it is not reported: when fixing the hole position in one of

the two PbI4 planes the exciton is spread in the same plane for n=1, while for n=2 there

is the non–zero probability to find the electron also in the other PbI6 layer for n=2. This

suggests that the large spatial delocalization characteristic of the first optical excitation in

the corresponding perovskite bulk should be rapidly recovered, favoring the e–h separation

and supporting the experimental observation of an increase of photo-conversion efficiency

for n > 2.22 On the other hand the larger e-h overlap in n = 1 RPPs clearly explains why

the experimental photoluminescence efficiency increases reducing the index n23 and is very

high in isolated nanosheets with n = 1.29

To summarize, starting from the few available structural experimental data we have in-

vestigated the role of many-body effects, such as e–e and e–h interactions, on the electronic

and optical properties of the first two terms (n=1, 2) of (BA)2MAn−1PbnI3n+1 Ruddlesden–

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Figure 4: Optical spectra of Pb-based single sheet (left) and QW (right) with n=1 (toppanels) and n= 2 (bottom panels)

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Figure 5: Side view of the first bright exciton for the isolated Pb-Based RPP sheet n=1(left) and n=2 (right). Hole position is represented by the red cross

Popper hybrid organic–inorganic halide perovskites. The confined geometries in the form

of isolated nanosheets clearly show the presence of strongly bound excitons, which remain

present even in the repeated quantum–well structures, a feature ascribed to the low dielec-

tric screening of the organic parts of the RPPs. For the n=1 NS, the electron-hole spatial

distribution tends to be extremely localized, i.e. both the hole and electron forming the

first bright exciton resides in the same semiconductor PbI6 octahedral layers. This tendency

which could be expected in the isolated sheet holds in a similar way also for the corresponding

bulk quantum–well structure. Notably, in the n=2 structures the excitonic spatial distribu-

tion is more spread laterally and is non zero in both the two adjacent PbI6 semiconductor

layers, even if the hole position is fixed in one of the two layers. This observation clearly

suggests that in these layered materials the delocalized nature of the exciton observed in 3D

hybrid perovskites should be rapidly recovered increasing n. Interestingly an evident Ras-

bha splitting is found in the n = 2 nanosheet confirming the interest of these novel layered

materials for spintronics applications.

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Acknowledgments

M.P. and G.G. acknowledge MIUR for FFABR funds. M.P. acknowledges INFN for financial

support through the National project Nemesys and for allocated computational resources

at Cineca with the project INF16-nemesys and the EC for the RISE Project No. CoExAN

GA644076. G.G acknowledges PRACE for awarding us access to resource Marconi based

in Italy at CINECA (Grant No. Pra14 3664). G.G. is similarly grateful to CARIT project

”Progetto per l’ applicazione delle attivita di ricerca pubblica nell’ area di crisi complessa

ternana. Valutazione della possibilita di utilizzo di materiali metallici innovativi per appli-

cazioni antisismiche, automobilistiche ed energetiche” (ref. FCARITR17FR) for supporting

this research. K.Y. thanks the supported by MEXT as ”Priority Issue on Post-K com-

puter”(Development of new fundamental technologies for high-efficiency energy creation,

conversion/storage and use).

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(a) lateral view and (b) top view of the n=2 sheet (NS-RPP) optimized structure. Same (c, d) for the bulk QW (QW-RPP). [Grey: Pb; Purple: I; Brown: C; Light blue: N;

White: H atoms]

280x323mm (120 x 120 DPI)

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DFT-KS (dashed) and GW (red, solid) Bandstructure of the Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels).

161x205mm (120 x 120 DPI)

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Expectation values of Sx, Sy,Sz (left,center,right) for the n=2 NS{RPP. (Bands are plotted here at the DFT-PBE level of approximation ).

219x138mm (120 x 120 DPI)

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Optical spectra of Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels).

164x218mm (120 x 120 DPI)

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Side view of the first bright exciton for the isolated Pb-Based RPP sheet n=1 (left) and n=2 (right). Hole position is represented by the red cross.

241x89mm (120 x 120 DPI)

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on the nature of the electronic and optical excitations of

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