Synthesis of achiral and chiral quasi-2D perovskite superlatticesChemicals<\/p>\n
Hydroiodic acid (Sigma Aldrich, 57% w\/w in H2O, 99.9%), hypophosphorous acid (Avra, 50% w\/w H2O), R-(+)-\u03b1-methyl benzylamine (RMBA, Sigma Aldrich, 99%) and S-(\u2212)-\u03b1-methylbenzylamine (SMBA, Sigma Aldrich, 99%) were used.<\/p>\n
Synthesis of MAPbBr3 single-crystal substrate<\/p>\n
A stoichiometric mixture of MABr (1\u2009mmol) and PbBr2 (1\u2009mmol) was dissolved in dimethylformamide (DMF) at room temperature. The solution was filtered through a 0.1-\u03bcm polytetrafluoroethylene (PTFE) membrane filter. High-quality MAPbBr3 single crystals were grown using inverse temperature crystallization by maintaining the filtered solution at 60\u2009\u00b0C in an oven.<\/p>\n
Synthesis of chiral (S\/R)MBA ligands<\/p>\n
In a 100-ml three-necked round-bottom flask cooled in an ice bath, (S\/R)MBA (39\u2009mmol, 5\u2009ml) were mixed with anhydrous ethanol (15\u2009ml). Hydrochloric acid (6.6\u2009ml, 58\u2009mmol) was added dropwise under vigorous stirring, and the reaction mixture was stirred overnight. The solution was then heated to 80\u2009\u00b0C for 30\u2009min to evaporate the solvent completely. The resulting yellowish residue was dissolved in hot ethanol (5\u2009ml) and refrigerated for 24\u2009h to induce recrystallization. The obtained crystals were washed repeatedly with diethyl ether until colourless, then vacuum-dried overnight to yield white (S\/R)MBA crystals.<\/p>\n
Synthesis of quasi-2D (PEA)2(MA)2Pb3I10 single crystals<\/p>\n
A precursor solution was prepared by dissolving MAI (5\u2009mmol), PEA (7\u2009mmol) and PbO powder (10\u2009mmol) in a mixture of 57% w\/w aqueous HI solution (10.0\u2009ml, 76\u2009mmol) and 50% aqueous H3PO2 (1.7\u2009ml, 15.5\u2009mmol) with heating until complete dissolution. The solution was cooled to room temperature for crystallization. The resulting crystals were washed with diethyl ether and vacuum-dried overnight.<\/p>\n
Synthesis of quasi-2D (PEA)1.2((S\/R)MBA)0.8(MA)2Pb3I10 single crystals<\/p>\n
PbO powder (10\u2009mmol), MAI (5\u2009mmol), (S\/R)MBA (2.8\u2009mmol) and PEA (4.2\u2009mmol) were dissolved in the same acid mixture as in the previous section (10.0\u2009ml HI\u2009+\u20091.7\u2009ml H3PO2) with heating. After cooling to room temperature, the precipitated crystals were washed with diethyl ether and vacuum-dried overnight. It should be noted that the inclusion of achiral PEA ligands is essential for stabilizing the quasi-2D phase39<\/a>.<\/p>\n Epitaxial growth of PEA, (S\/R)MBA perovskite superlattices<\/p>\n The epitaxial growth precursor solution was prepared by dissolving quasi-2D perovskite single crystals (achiral PEA only or PEA mixed with (S\/R)MBA, as described in the previous sections) in \u03b3-butyrolactone (GBL) to obtain a concentration of 1\u2009M. This non-volatile solvent was selected to enable controlled crystallization during subsequent processing. Each solution was subjected to spin-coating onto pristine MAPbBr3 single-crystal substrates at 2,000\u2009rpm for 30\u2009s, followed by annealing at 180\u2009\u00b0C to form PEA, SMBA and RMBA superlattices, respectively.<\/p>\n Structure and morphological characterizations<\/p>\n STEM specimens were prepared using a dual-beam focused ion beam system (Helios 600i, Thermo Fisher Scientific). High-angle annular dark-field STEM imaging was performed using an aberration-corrected STEM microscope (Spectra 300 (S)TEM).<\/p>\n Two-dimensional grazing-incidence wide-angle X-ray scattering (GIWAXS) measurements were performed using an XEUSS 3.0 UHR SAXS\/WAXS system (Xenocs) equipped with an Eiger2 R 1M 2D detector (75\u2009\u03bcm\u2009\u00d7\u200975\u2009\u03bcm pixel size) operating in integration mode. The sample-to-detector distance was set at 100\u2009mm and precisely calibrated using a silver behenate standard. Measurements used Cu K\u03b1 radiation (8\u2009keV) with a 0.5\u2009mm\u2009\u00d7\u20090.5\u2009mm beam spot, providing sufficient q-space coverage. GIWAXS patterns were corrected for missing wedge effects to obtain the qr and qz coordinates. The optimal incident angle of 0.7\u00b0 was determined by maximizing sample scattering intensity while minimizing substrate contributions, ensuring the X-rays propagated as an evanescent wave along the sample surface.<\/p>\n PL and time-resolved PL spectroscopy<\/p>\n The sample was excited by a femtosecond laser system consisting of a Ti:sapphire oscillator (Coherent Vitesse, 80\u2009MHz) seeding a regenerative amplifier (Coherent Libra, 800\u2009nm central wavelength, 50\u2009fs pulse duration, 1\u2009kHz repetition rate). The vertically polarized pump beam was frequency-tuned using an optical parametric amplifier (OperASolo) and focused to a 1-mm spot on the sample (point excitation configuration).<\/p>\n Time-integrated PL spectra were collected from the sample in a backscattering geometry using a pair of lenses, then directed to a monochromator (Acton Spectra Pro 2500i) coupled to an EMCCD detector (Princeton Instruments Pixis). For magneto-PL measurements, the magnetic field was applied parallel to the substrate of the crisscross superlattices (that is, perpendicular to the SF direction), as shown in Fig. 4a<\/a>.<\/p>\n Time-resolved PL was characterized using a streak camera (Optronis, OptoScope SC unit, temporal resolution of around 10\u2009ps under the fast sweep unit SSU11-10) coupled with a monochromator triggered with pump fs laser, and each time-resolved PL image datum was obtained by adding 150 frames of streak camera images. Unless otherwise specified (for example, the stability test in vacuum), all measurements were performed at room temperature in ambient air (relative humidity of about 50%).<\/p>\n Transient absorption spectroscopy<\/p>\n TA spectroscopy was performed on perovskite superlattice transferred from a single-crystal MAPbBr3 substrate to the quartz substrate (Supplementary Fig. 16<\/a>). The vertically polarized pump beam was generated by an optical parametric amplifier (OperASolo) pumped with the aforementioned Ti:sapphire femtosecond laser and modulated using a mechanical chopper. The horizontally polarized probe beam (spot diameter 0.5\u2009mm on the sample) passed through the pump-excited region (pump spot diameter 1\u2009mm on the sample) and was collected by a CMOS (complementary metal-oxide-semiconductor) sensor in a Helios spectrometer (Ultrafast Systems). The TA signal was recorded as a function of probe delay, controlled by a retroreflector mounted on a motorized linear stage with a minimum step size of 2.8\u2009fs, to resolve carrier dynamics. All measurements were conducted at room temperature in ambient air.<\/p>\n Theoretical modelling of chiral superfluorescence<\/p>\n Conjugation of the chiral quantum-well spacers to the perovskite superlattices results in a net crystallographic helicity according to the chirality of ligand25<\/a> (see Supplementary Note\u00a02<\/a> and circular dichroism spectra in Supplementary Fig. 20<\/a>). As a result, the crystal structure of each vertically oriented superlattice exhibits a screw axis parallel to the direction of SF emission. A minimal model of chiral SF must extend the canonical two-level SF model to include the influence of mirror symmetry breaking on the polarization of the emitted light. We first write down the combined dipole\u2013field Hamiltonian<\/p>\n $$H={\\omega }_{0}\\mathop{\\sum }\\limits_{j=1}^{N}{\\sigma }_{j}^{\\mathrm{ee}}+c{k}_{0}{\\sum }_{\\lambda }{a}_{\\lambda }^{\\dagger }{a}_{\\lambda }-\\mathop{\\sum }\\limits_{j=1}^{N}{{\\bf{p}}}_{j}\\cdot {\\bf{E}}({{\\bf{r}}}_{j})$$<\/p>\n \n (4)\n <\/p>\n where \\({\\sigma }_{j}^{{\\rm{ee}}}=|{e}_{j}\\rangle \\langle {e}_{j}|\\) is the population operator for the excited state |ej\u27e9 of emitter j, \u03c90 is the frequency of the dipole transition, \\({a}_{\\lambda }^{\\dagger }\\) and \\({a}_{\\lambda }\\) are bosonic creation and annihilation operators for polarization \u03bb with \\([{a}_{\\lambda },\\,{a}_{{\\lambda }^{{\\prime} }}^{\\dagger }]={\\delta }_{\\lambda {\\lambda }^{{\\prime} }}\\), c is the speed of light, and k0\u2009=\u2009\u03c90\/c is the photonic wavevector (assumed to be on resonance with the dipole transition). Notice that, in contrast to the usual single-mode SF model, we explicitly retain both field polarizations. The dipole operator for each two-level emitter is given in the main text as \\({{\\bf{p}}}_{j}={\\wp }_{j}({\\sigma }_{j}^{\\mathrm{ge}}+{\\sigma }_{j}^{\\mathrm{eg}})\\), and the transition dipole moments for a 1D lattice that reflect the screw axis symmetry of the chiral superlattices are given by equation (1<\/a>). Applying the definition of the field operator in equation (2<\/a>) and neglecting the energy non-conserving terms \\(\\propto {\\sigma }_{j}^{\\mathrm{ge}}{a}_{\\lambda }\\) and \\(\\propto {\\sigma }_{j}^{\\mathrm{eg}}{a}_{\\lambda }^{\\dagger }\\) in the interaction Hamiltonian yields equation (3<\/a>).<\/p>\n Because the cavity mode is assumed to be on resonance with the dipole transition, Hint remains time-independent in the interaction picture representation, and we can neglect the free evolution of the dipole and field Hamiltonians (first two terms in equation (4<\/a>)). Following ref.\u200937<\/a>, we trace over the field mode in the bad cavity limit to arrive at a Markovian master equation for the dipole reduced density matrix<\/p>\n $$\\frac{{\\rm{d}}\\rho }{{\\rm{d}}t}=\\frac{\\varGamma }{2}\\sum _{q={k}_{0}\\pm p}(2{S}_{q}^{-}\\rho {S}_{q}^{+}-\\{{S}_{q}^{+}{S}_{q}^{-},\\rho \\})$$<\/p>\n \n (5)\n <\/p>\n where \u0393 is the cavity-mediated decay rate (assumed to be 1\/1,500\u2009ps\u22121 based on our measurements). Equation (5<\/a>) consists of two copies of the usual SF master equation\u2014one for each quasimomentum and photon polarization. For simplicity, we make the approximation \\({[S}_{q}^{+},{S}_{{q}^{{\\prime} }}^{-}]=2{S}^{z}{\\delta }_{{{qq}}^{{\\prime} }}\\), where \\({S}^{z}={\\sum }_{j}{\\sigma }_{j}^{z}\/2={\\sum }_{j}({\\sigma }_{j}^{\\mathrm{ee}}-{\\sigma }_{j}^{\\mathrm{gg}})\/2\\). In other words, we assume collective modes with opposite circular polarization are uncoupled, except through their mutual contribution to the total dipole inversion.<\/p>\n To account for the influence of room-temperature lattice vibrations on each dipole, we add to equation (5<\/a>) the pure dephasing Lindbladian<\/p>\n $${{\\mathcal{L}}}_{\\phi }[\\rho ]=\\frac{{\\gamma }_{\\phi }}{2}\\mathop{\\sum }\\limits_{j=1}^{N}({\\sigma }_{j}^{z}\\rho {\\sigma }_{j}^{z}-\\rho ).$$<\/p>\n \n (6)\n <\/p>\n Applying the standard quasi-classical approximation \\({\\langle {(S}^{z})}^{2}\\rangle \\approx {\\langle {S}^{z}\\rangle }^{2}\\), equations (5<\/a>) and (6<\/a>) yield the following coupled differential equations for the average dipole inversion and the radiation intensity \\({I}_{q}(t)=\\varGamma \\langle {S}_{q}^{+}{S}_{q}^{-}\\rangle \\) of each mode<\/p>\n $$\\frac{{\\rm{d}}}{{\\rm{d}}t}\\langle {S}^{z}\\rangle =-I(t)$$<\/p>\n \n (7)\n <\/p>\n $$\\frac{{\\rm{d}}}{{\\rm{d}}t}{I}_{q}(t)=2\\varGamma {I}_{q}(t)\\left[\\langle {S}^{z}\\rangle -\\left(\\frac{1}{2}+\\frac{{\\gamma }_{\\phi }}{\\varGamma }\\right)\\right]+\\varGamma {\\gamma }_{\\phi }(2\\langle {S}^{z}\\rangle +N).$$<\/p>\n \n (8)\n <\/p>\n These equations can be solved numerically, together with the total-intensity constraint \\(I(t)={\\sum }_{q}{I}_{q}(t)\\) and the initial SF conditions \\(\\langle {S}^{z}(0)\\rangle =N\/2\\) and I(0)\u2009=\u2009\u0393N. Because of the spin\u2013orbit coupling present in equation (3<\/a>), the solutions for the two different collective modes q correspond to ILCP(t) and IRCP(t), respectively. In the pure SF regime, where \u0393N\u2009\u226b\u2009\u03b3\u03d5, these equations admit the analytical result<\/p>\n $${I}_{q}(t)=\\frac{{I}_{q}(0)}{I(0)}{\\left(\\frac{N+1}{2}\\right)}^{2}\\varGamma {\\sec {\\rm{h}}}^{2}\\left(\\frac{t-{\\tau }_{{\\rm{D}}}}{{\\tau }_{{\\rm{P}}}}\\right)$$<\/p>\n \n (9)\n <\/p>\n where \u03c4D\u2009=\u2009(1\/\u0393)ln(N)\/(N\u2009+\u20091) is the delay time and \u03c4P\u2009=2\u03c4D\/ln(N) is the SF pulse width. Equation (9<\/a>) is identical to the canonical, unpolarized SF intensity37<\/a>, except for the initial mode-weighting factor Iq(0)\/I(0). This limit corresponds to the high pump fluence regime, in which the photo excited dipole density is large and the system behaves as a coherent and collectively enhanced circularly polarized dipole. Conversely, the low pump fluence regime is described by the opposite limit \u0393N\u2009\u226a\u2009\u03b3\u03d5 in which dynamical dephasing by equation (6<\/a>) is the dominant process. In this regime, phase coherence is rapidly lost, giving rise to unpolarized spontaneous emission from independent emitters.<\/p>\n To facilitate a quantitative comparison to our experimental measurements, we first determined the relationship between the number of excited dipoles N and the pump fluence P in \u00b5J\u2009cm\u22122. Using the known linear dependence of the photoluminescence intensity on the dipole density in the spontaneous emission regime, we fit the relationship ISE\u2009=\u2009\u03b2P\u03b1 based on the data in Fig. 2c<\/a> for the SMBA sample and Extended Data Fig. 7<\/a> for the RMBA sample. This yields the relationship N\u2009=\u2009bP\u03b1 for unknown parameter \\(b\\). The parameter \\(b\\) was determined by fitting the delay time data (Fig. 2c<\/a> for SMBA, Supplementary Fig. 17e<\/a> for RMBA) with the relationship \u03c4D\u2009=\u2009(1\/\u0393)ln(bP\u03b1)\/(bP\u03b1\u2009+\u20091). In this way, the parameters \u03b1 and b for each sample are fixed by the experimental data. This allows for a numerical solution of ILCP(t) and IRCP(t) with only two free parameters: the initial mode imbalance at t\u2009=\u20090 and the dephasing rate \u03b3\u03d5.<\/p>\n DFT calculations<\/p>\n All calculations were performed using the projector augmented wave pseudopotentials with the exchange and correlation in the Perdew\u2013Burke\u2013Ernzerhof formalism of DFT as implemented in the Vienna ab initio simulation package. The crystal structure was obtained by Pyrovskite code based on experimental XRD parameters. Geometry optimizations were performed before single-point energy calculations, and the self-consistent convergence accuracy was set at 1\u2009\u00d7\u200910\u20135\u2009eV per atom. The convergence criterion for the maximal force on atoms was set to 0.02\u2009eV\u2009\u00c5\u20131. The cutoff energy of the plane-wave basis was set at 500\u2009eV. For the 2D bulk system, a 4\u2009\u00d7\u20094\u00d7\u2009\u20091 Monkhorst\u2013Pack k-point mesh was used. For the edge structure, which was extended along the Cartesian x-axis, a 1\u2009\u00d7\u20094\u2009\u00d7\u20091 mesh was adopted for Brillouin zones sampling. Dipole correction was included for the edge structure. Spin\u2212orbit coupling was included for electronic structure calculations but not for structural relaxation and total energy calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"Synthesis of achiral and chiral quasi-2D perovskite superlatticesChemicals Hydroiodic acid (Sigma Aldrich, 57% w\/w in H2O, 99.9%), hypophosphorous…\n","protected":false},"author":2,"featured_media":517399,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[271],"tags":[18,1099,19,17,1100,452,2571,133],"class_list":["post-517398","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-eire","tag-humanities-and-social-sciences","tag-ie","tag-ireland","tag-multidisciplinary","tag-physics","tag-quantum-optics","tag-science"],"share_on_mastodon":{"url":"","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/517398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/comments?post=517398"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/517398\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media\/517399"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media?parent=517398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/categories?post=517398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/tags?post=517398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}