Rashba and Dresselhaus effects in doped methylammonium lead halide perovskite MAPbI 3

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Rashba and Dresselhaus effects in doped

methylammonium lead halide perovskite

MAPbI3

Megha Arya,∗Preeti Bhumla, Sajjan Sheoran, Suraj, and S.

Bhattacharya∗

Department of Physics, Indian Institute of Technology Delhi, New Delhi, India

E-mail: meghaphy2@gmail.com[MA]; saswata@physics.iitd.ac.in[SB]

Phone: +91-11-2659 1359

arXiv:2210.06152v3 [cond-mat.mtrl-sci] 6 Dec 2022

Abstract

Inorganic-organic lead halide perovskites, particularly methylammonium lead halide

(MAPbI3) perovskite, is perceived to be a promising material for optoelectronics and spin-

tronics. However, lead toxicity and instability under air and moisture restrict its practical uses.

Hence, it is essential to reduce lead extent by substituting appropriate alternatives. Here, we

substitute Sn and Ge in cubic MAPbI3and compare various properties of hybrid perovskites by

employing state-of-the-art ﬁrst-principles-based methodologies, viz., density functional theory

(DFT) with semilocal and hybrid functional (HSE06) and generalized gradient approximation

(PBE) combined with spin-orbit coupling (SOC). We mainly study the Rashba-Dresselhaus

(RD) effect, which occurs here due to two major mechanisms breaking inversion symme-

try, i.e., static and dynamic, and the presence of heavy elements contributing to signiﬁcant

SOC. We ﬁnd non-negligible spin-splitting effects in the conduction band minimum (CBm)

and valence band maximum (VBM) for hybrid perovskites. For a deeper understanding of

the observed spin-splitting, the spin textures are analyzed and Rashba coefﬁcients are calcu-

lated. We ﬁnd that Dresselhaus effect comes into play in substituted hybrids in addition to

the usual Rashba effect observed in pristine compound. We also observe that the strength of

Rashba spin-splitting can be substantially tuned on application of uniaxial strain (±5%). Also,

we notice that some of the hybrids are mechanically stable and ductile. Hence these hybrid

perovskites can prove to be potent for perovskite-based spintronic applications.

Graphical TOC Entry

Keywords

DFT, Rashba, Dresselhaus, symmetry, spin-orbit coupling, spin texture, hybrid perovskites

In recent years, inorganic-organic lead halide perovskite compounds, particularly methylam-

monium lead halide perovskite (MAPbI3), have attracted a great attention from the scientiﬁc com-

munity. They have the potential of revolutionizing the ﬁeld of optoelectronics and spintronics

owing to their exotic properties like long diffusion length, appropriate band gaps, high carrier

mobility, high absorption coefﬁcient and cheap cost of manufacturing.1–12 In comparison to the

ﬁrst experimental work, where the power conversion efﬁciency (PCE) of perovskite solar cells

was only 3.8%4, intense efforts in past years have led to an impressive increase of PCE to over

25%.13,14 In addition to this, because of the presence of heavy element Pb, there is a large spin-

orbit coupling (SOC) which inﬂuences the band structure of these lead halide perovskites.15,16

Fascinatingly, SOC in association with inversion asymmetry, induces various exotic phenomena

like topological surface states17, persistent spin textures18,19 and Rashba-Dresselhaus (RD) ef-

fects.20–24 In case of crystals where center of inversion is not present, there is a ﬁnite gradient of

potential and hence a Lorentz transformed magnetic ﬁeld acts on relativistically moving electrons.

So, at non-time-reversal-invariant k-points, the degenerate bands split into states of opposite spins,

lifting Kramer’s degeneracy. The orientation of spin is decided by spin-orbit ﬁeld, which depends

on momentum. Dresselhaus25 studied that for crystals without a centre of inversion i.e. bulk in-

version asymmetry (BIA), SOC lifts spin degeneracy of the electronic bulk states and the effect

was originally reported in zinc-blende. Rashba26 studied spin-orbit effects in two-dimensional

crystals in an asymmetric potential referred to as structural inversion asymmetry (SIA) and the

effect was initially reported in wurtzite. The differentiator between these effects is the origin of

the non-centrosymmetry. RD effect has great applications in spintronics,27,28 and thus, lead halide

perovskites are seen as promising materials for applications in the ﬁeld.29–33

In the bulk of MAPbI3, the inversion symmetry is broken by two major mechanisms: static

and dynamic. In the static one, the octahedron PbI framework gets distorted due to small and long

bond lengths.34 The dynamic one is where the PbI framework is ﬁxed but inversion asymmetry

comes into the picture due to the rotation of MA ions.35 Dynamic structural ﬂuctuations can even

take place because of phonon modes or interaction of MA ions with the PbI framework.36–38 Also,

the system has strong SOC due to the presence of heavy element iodine in addition to lead.35

However, Pb has toxic nature that hampers MAPbI3from its practical uses. Additionally, under

air and moisture exposure, Pb is intrinsically unstable and ultimately oxidizes from Pb2+to Pb4+,

reducing the performance of devices based on MAPbI3.39,40 Thus, it is essential to reduce the Pb

extent in the compound by substituting appropriate alternatives and making a hybrid perovskite.

Pb extent can also be reduced by creating Pb-vacancies in the compound, however, they are not

stable at all.41

MAPbI3crystals exhibit multiple phases: cubic with a space group Pm¯

3m above 327 K42,

tetragonal with two debatable space groups, i.e, centrosymmetric I4/mcm (point group 4/mmm)

and non-centrosymmetric I4cm (point group 4mm) between 162 and 327 K34,42–44, and orthorhom-

bic with a space group Pnma below 162 K43. However, in case of solar cell applications, just the

tetragonal room temperature phase and the cubic high-temperature phase are of relevance. In our

present work, we studied the cubic phase of MAPbI3using state-of-the-art density functional the-

ory (DFT)45,46 and we intend to reduce Pb extent by substituting Sn and Ge in the perovskite and

parallelly maintain spin-splitting effects.

Vienna ab initio Simulation Package (VASP)47,48 is used to perform DFT calculations. The

projector augmented wave (PAW) pseudopotential method,49,50 as implemented in VASP, is used

to describe all ion-electron interactions in elemental constituents. The exchange-correlation (εxc)

functionals used for DFT calculations are Perdew-Burke-Ernzerhof (PBE)51 and the non-local

Heyd–Scuseria–Ernzerhof (HSE06)52 εxc functionals with SOC. We have increased the size of the

supercell till the state of single defect is completely localized with periodic boundary conditions.

The converged supercell (2×2×2) contains 96 atoms, i.e., MA8Pb8I24. Since in this supercell,

there are 8 Pb atoms, so all calculations are done until all the 8 Pb atoms are replaced one by one

by Sn/Ge. During optimization of the structures, the total energy difference between two ionic

relaxation steps is kept lesser than 0.0001 eV and the tolerance on forces between two steps is kept

0.01 eV/ Å. A 4×4×4 Monkhorst k-mesh size is used for optimization. For energy calculations, the

k-mesh is converged at 4×4×4. The plane wave energy cutoff is kept 520 eV for all the calculations.

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摘要：

RashbaandDresselhauseffectsindopedmethylammoniumleadhalideperovskiteMAPbI3MeghaArya,PreetiBhumla,SajjanSheoran,Suraj,andS.BhattacharyaDepartmentofPhysics,IndianInstituteofTechnologyDelhi,NewDelhi,IndiaE-mail:meghaphy2@gmail.com[MA];saswata@physics.iitd.ac.in[SB]Phone:+91-11-265913591arXiv:2210.061...

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Rashba and Dresselhaus effects in doped methylammonium lead halide perovskite MAPbI 3

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