Recovery of high-energy photoelectron circular dichroism through Fano interference
G. Hartmann, M. Ilchen, Ph. Schmidt, C. Küstner-Wetekam, C. Ozga, F. Scholz, J. Buck, F. Trinter, J. Viefhaus, A. Ehresmann, M. S. Schöffler, A. Knie, Ph. V. Demekhin
aa r X i v : . [ phy s i c s . a t m - c l u s ] J un Recovery of high-energy photoelectron circular dichroism through Fano interference
G. Hartmann, M. Ilchen,
1, 2
Ph. Schmidt, C. K¨ustner-Wetekam, C. Ozga, F. Scholz, J. Buck,
3, 4
F. Trinter,
3, 5
J. Viefhaus,
3, 6
A. Ehresmann, M. S. Sch¨offler, A. Knie, and Ph. V. Demekhin ∗ Institut f¨ur Physik und CINSaT, Universit¨at Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, 22607 Hamburg, Germany Institut f¨ur Experimentelle und Angewandte Physik,Universit¨at Kiel, Leibnizstr. 19, 24118 Kiel, Germany Molecular Physics, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4, 14195 Berlin, Germany Helmholtz-Zentrum Berlin (HZB), Albert-Einstein-Str. 15, 12489 Berlin, Germany Institut f¨ur Kernphysik, J.W. Goethe-Universit¨at,Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
It is commonly accepted that the magnitude of a photoelectron circular dichroism (PECD) isgoverned by the ability of an outgoing photoelectron wave packet to probe the chiral asymmetryof a molecule. To be able to accumulate this characteristic asymmetry while escaping the chiralion, photoelectrons need to have relatively small kinetic energies of up to a few tens of electronvolts. Here, we demonstrate a substantial PECD for very fast photoelectrons above 500 eV kineticenergy released from methyloxirane by a participator resonant Auger decay of its lowermost O1 s -excitation. This effect emerges as a result of the Fano interference between the direct andresonant photoionization pathways, notwithstanding that their individual effects are negligibly small.The resulting dichroic parameter has an anomalous dispersion, i.e. it changes its sign across theresonance, which can be considered as an analogue of the Cotton effect in the X-ray regime. PACS numbers: 33.80.-b, 32.80.Hd, 33.55.+b, 81.05.Xj
Photoelectron circular dichroism (PECD) is a fun-damental chiroptical effect causing a forward-backwardasymmetry in the laboratory-frame angular distributionof photoelectrons emitted from chiral molecules in thegas phase. PECD was first predicted theoretically forone-photon ionization [1–3] and then verified in pioneer-ing experiments with circularly polarized synchrotron ra-diation [4, 5]. The effect persists also in the multiphotonionization regime using intense laser pulses [6, 7]. Be-cause PECD is a pure electric-dipole effect, it is muchstronger than the traditional CD in the photoabsorptionspectra of chiral molecules [8]. This fact, together withits enantioselectivity, has established PECD as a power-ful tool for chiral recognition in the gas phase [8–11].Ritchie [1–3] has proven analytically that PECD arisesdue to an incomplete compensation of the contributionsfrom emitted partial electron waves with different projec-tions ± m of the carried angular momentum ℓ . Such aninequivalence occurs only for chiral molecules and has atwofold origin: It is induced by the chiral asymmetries ofboth, the initial bound and the final continuum electronicstates entering the dipole-transition amplitudes. For slowphotoelectrons with kinetic energies of a few electronvolts, initial and final state contributions to PECD canbe comparable [12]. As the electron kinetic energy grows,the photoelectron wave packet escapes the molecular ionquickly and does not have enough time to adopt its chi-ral asymmetry. In other words, both, the chiral initialstate and the chiral potential of the ion can be consid-ered almost symmetric for very fast photoelectrons. As aconsequence, at high kinetic energies, typically at a few tens of electron volts [12, 13] and in extreme cases atabout 70 eV [14], PECD vanishes.In the present work, we demonstrate a very generalmechanism of PECD recovery for electrons with kineticenergies of as high as a few hundreds of electron volts.This scenario involves an intermediate electronic reso-nance, which enables an excited metastable wave packetto accumulate chiral asymmetry during its natural decaylifetime, and it does not imply an explicit upper boundfor the kinetic energy of a photoelectron. In the vicinityof a resonant excitation, the total transition amplitudefor the population of a selected ionic state via the emis-sion of the partial photoelectron continuum wave εℓm is given by the well-known Kramers-Heisenberg formula(atomic units are used throughout): D ℓmk ( δ ) = d εℓmk + V εℓm D k δ + iγ . (1)Here, δ = ω − E r is the detuning of the exciting-photonenergy ω from the resonance energy E r and γ = Γ r / r . The photoelectronkinetic energy ε is related to the ionization potential ( IP )of the final ionic state via ε = ω − IP .Equation (1) describes the Fano interference [15] be-tween the amplitude d εℓmk for the direct ionization of aselected ionic state (here k = 0 , ± D k ) and subsequent electronic decay into the same finalstate of the ‘ion + photoelectron’ (represented by theCoulomb matrix element V εℓm ). The Fano interference isresponsible for the shape of a resonant profile in the totalphotoionization cross section across an intermediate ex-cited state [15]. For a high-energy inner-shell excitationand subsequent resonant Auger decay, the contribution ofthe direct ionization channel is usually small compared tothe resonant pathway. As a consequence, the Fano inter-ference is rather weak, and the respective profile in theangle-averaged cross section has the form of an almostsymmetric peak on a small constant background.The angle-resolved one-photon ionization spectrum ofrandomly-oriented molecules induced by circularly polar-ized light is given by the following standard formula forthe differential cross section [16]d σ ± dΩ = σ π (cid:20) ± β P (cos θ ) − β P (cos θ ) (cid:21) . (2)Here, σ is the total photoionization cross section, β isthe dichroic parameter which describes PECD in chiralmolecules, β is the anisotropy parameter, ‘ ± ’ stands forthe positive and negative helicity of the circularly polar-ized radiation, P L (cos θ ) are the Legendre polynomials,and θ is the angle between the direction of the propa-gation of the ionizing radiation and the direction of theemission of photoelectrons.In general, the dichroic β and anisotropy β parame-ters are given by coherent superpositions [16, 17] of thetransition amplitudes D ℓmk ( δ ) = D j β L = P pj b Lpj D ∗ p D j , (3)where b Lpj are known kinematic coefficients. The im-pact of Fano interferences on anisotropy parameters β of high-energy photoelectrons in molecules is well docu-mented [18–25]. In the off-resonance excitation regime,anisotropy in the photoemission is governed by the directionization channel, while in the on-resonance regime, it isdetermined by the resonant channel (the first and secondterms in the amplitude (1), respectively). This inducesa rather broad dispersion of the β parameter across theresonance [18–25]. The Fano interference, i.e. the impactof the cross terms of the direct and resonant contribu-tions, causes moderate changes of the dispersion createdby incoherent effects of those two contributions [25].The situation changes completely if one considers thedichroic parameter β . In the high kinetic energy regime,the chiral asymmetry parameter provided by the directphotoionization channel is negligibly small: β Dir ≈ β Res = 0, asin the case of the traditional CD in the photoabsorptionspectra of chiral molecules. This is because the angu-lar momentum indices ℓm in the decay transition matrixelement in the second term of the amplitude (1) are de-coupled from the polarization index k in the excitationmatrix element, and the respective summations in Eq. (3) can be performed independently. This validates the so-called two-step model [26], in which an electronic decayof an excited state can be described independently of theinitial excitation step.The contribution of the Fano interference betweenthe direct and resonant photoionization pathways to thedichroic parameter is given by: β F ano ( δ ) = P pj b pj (cid:26) d ∗ p ( V D ) j δ + iγ + d j ( V D ) ∗ p δ − iγ (cid:27) . (4)In this equation, the angular momentum indices of thephotoelectron are still coupled to the polarization of theexciting photon through the direct transition amplitudein each term. Moreover, equation (4) can straightfor-wardly be simplified to the following analytic form: β F ano ( δ ) = κδ + µδ + γ , (5)with the real coefficients κ and µ . Equation (5) describesan anomalous dispersion of β F ano across the resonance:This dichroic parameter changes its sign in a very closeproximity of the resonance energy E r at δ = − µ/κ . Thissituation is very similar to the anomalous optical rota-tory dispersion, also known in the literature as Cottoneffect [27–29]. The Fano interference between the over-lapping bright and dark plasmonic modes is known tobe responsible for an enhancement of the traditional CDin the photoabsorption of chiral nanostructures in thevisible and infrared spectral ranges [30, 31]. A sizableinfluence of electron correlation processes on the dichroicparameter in the vicinity of an autoionizing resonance hasalso been observed for chiral metal-organic complexes atmoderate photoelectron kinetic energies of about 55 eV[32]. The present theoretical analysis suggests a novelmechanism of recovery of PECD in the vicinity of high-energy resonant excitation through the Fano interference,where this chiroptical effect due to the direct ionizationof valence electrons is expected to be negligibly small.In order to make an estimate of the magnitude of theproposed effect, we considered the participator resonantAuger decay of the lowermost O 1 s -excitation in the pro-totypical methyloxirane molecule, for which one-photonPECD has been studied extensively [12, 33–38]. Thesuggested resonant excitation appears in the ionizationyield as a broad peak with the maximum at the photonenergy of ω = 535 .
11 eV [35]. We consider the partici-pator resonant Auger decay in the ground and first ex-cited electronic states of the molecular ion. The photo-electron signals associated with the ionization of HOMOand HOMO-1 of methyloxirane emerge in the spectrumas slightly overlapping vibronic bands centered at thebinding energies of about 10.4 and 11.4 eV, respectively,and they are separated well from the rest of the spectrum[34]. We, thus, investigate PECD for electrons with ki-netic energies of around ε ≈
524 eV.The participator resonant Auger decay of methyloxi-rane was described by an ab initio theoretical approachdeveloped in our previous angle-resolved studies of core-excited/ionized diatomic [18–21], polyatomic [22–25],and chiral [17, 38] molecules. The electronic transi-tion amplitudes were computed by the stationary Sin-gle Center (SC) method [39–41], which enables an accu-rate description of partial electron continuum waves inmolecules. Calculations were performed in the relaxed-core Hartee-Fock approximation at the equilibrium inter-nuclear geometry of the electronic ground state of R(+)methyloxirane [42], as described in details in Refs. [18–25]. The SC expansions of all occupied/excited molecularorbitals and of the photoelectron continuum waves wererestricted by harmonics with ℓ, | m | ≤
50 and 35, respec-tively. The angle-resolved participator Auger decay spec-tra were computed for the whole vibrational band of eachfinal ionic state. In order to obtain such vibrationallyunresolved decay spectra, we applied an analytical pro-cedure described in the appendix of Ref. [22]. It requiresonly the shape of the excitation spectrum of the reso-nance and keeps the Fano interference unchanged. Therespective excitation spectrum was approximated by theGaussian function with a FWHM = 2 eV [35].Results of the present calculations are summarized inFig. 1. As one can see from the upper panel of this figure,the direct ionizations of HOMO and HOMO-1 electronsat the considered exciting-photon energies are rather sub-stantial (note a constant background in each photoion-ization cross section). Nevertheless, the influence of theFano interference on σ ( ω ) is moderate: The resultingprofiles have a form of slightly asymmetric peaks. Forthe HOMO ionized final state, for instance, the presentlycomputed on- and off-resonance anisotropy parametersare equal to: β Dir = 0 .
90 and β Res = 0 .
04. Their in-coherent incorporation (no interference) induces a verybroad dispersion of the computed anisotropy parameteracross the considered core excitation (green dotted curvein the lowermost panel of Fig. 1). The Fano interferenceitself slightly changes the computed β ( ω ) dispersion (cf.,red dashed and green dotted curves in the lowermostpanel of the figure). Similar conclusions apply for thecomputed anisotropy parameter of the HOMO-1 ionizedfinal state (blue dash-dotted curve in the panel).We now turn to the discussion of the respective dichroicparameters depicted in the middle panel of Fig. 1.The off-resonance dichroic parameter, computed in thepresent work for the HOMO ionized state, is equal to β Dir = − . C r o ss s e c t i on ( a r b . un i t s ) HOMO (no interference) [x100] D i c h r o i c pa r a m e t e r HOMO (no interference) A n i s o t r op y pa r a m e t e r Exciting-photon energy (eV)
FIG. 1: Relative cross sections (upper panel) for the popula-tion of the HOMO and HOMO-1 ionized final states (see leg-end) together with the respective dichroic (middle panel) andanisotropy (lower panel) parameters computed in the presentwork as functions of the exciting-photon energy in the vicin-ity of the lowermost O 1 s -excitation of R(+) methyloxirane.The energy position of the resonance E r = 535 .
11 eV [35] isindicated by the vertical solid line. Dichroic parameters aregiven in percent of the respective total cross sections, whichare normalized to unity at their maxima. The dichroic andanisotropy parameters, computed for the HOMO ionized finalstate without including the Fano interference, are depicted bythe green dotted curves. Note that this dichroic parameter isshown on an enhanced scale, as indicated by the factor [ × − ) methyloxirane (dichroicparameter is shown with the opposite sign) measured for thetwo unresolved HOMO and HOMO-1 electron bands (see alsotext). Solid curves represent average theoretical results ob-tained with a 30% of HOMO to 70% of HOMO-1 ratio. ognize that the Fano interference enhances the computedchiral asymmetry by about two orders of magnitude andinduces an anomalous dispersion of the β ( ω ) parameteracross the resonance. A similar effect can be observedfor the HOMO-1 ionized final state, but the computedanomalous dispersion of β ( ω ) has an opposite sign (bluedash-dotted curve in the middle panel of Fig. 1).The present theoretical predictions were verified by anexperiment at the variable polarization XUV beamlineP04 [43] in the few-bunch mode of the synchrotron radia-tion facility PETRA III at DESY in Hamburg, Germany.This beamline uses an APPLE-II-type undulator to cover
532 534 536 538 540 5420.20.40.60.81.0 520 522 524 5260.00.20.40.60.81.0 Photon energy (eV) T o t a l ab s o rr p t i on ( a r b . un i t s ) Electron energy (eV) E l e c t r on s pe c t r u m ( a r b . un i t s ) = eV FIG. 2: Left panel: The presently measured total absorp-tion spectrum of methyloxirane. Exciting-photon energies ω used to record the angle-resolved photoelectron spectra aremarked by crosses. Right panel: A typical spectrum of elec-trons recorded at the photon energy of 534.77 eV (dark solidcurve) and the present fit of this spectrum around HOMOand HOMO-1 bands (light solid curve). The energy posi-tions of the HOMO- n electron bands, obtained using bindingenergies from Ref. [34], are indicated by the vertical dottedlines. Breakup of the spectrum into the individual contribu-tions from the HOMO – HOMO-3 electron bands, obtainedby the present fitting, is also shown by the dashed Gaussiancurves. The filled area, used in the present analysis of theelectron angular emission distributions, represents unresolvedcontributions from the HOMO and HOMO-1 electron bands. a large photon energy range from 250 eV to 3 keV witha resolving power higher than 10 and a flux higher than10 photons per second. A polarization analysis of thisbeamline, performed for the present experimental con-ditions, led to an estimated degree of circular polariza-tion of 97 ± − ) methyloxirane (99%,Sigma Aldrich) as well as gaseous neon, were introducedinto the interaction chamber effusively via a gas needle.At first, an absorption scan was performed in small stepsin the vicinity of the lowermost O 1 s -excitation of methy-loxirane, and the exciting-photon energy was calibratedto the data of Ref. [35]. The presently measured photoab-sorption spectrum of methyloxirane is depicted in the leftpanel of Fig. 2 by the solid curve.Thereafter, the angle-resolved electron spectra wererecorded for left- and right-handed circularly polarizedsynchrotron radiation at a few exciting-photon energiesacross the resonance (marked by crosses on top of the ab-sorption spectrum in Fig. 2). The electrons created in theinteraction region were detected with 16 independently-operating time-of-flight spectrometers oriented in a planerotated by 51.8 ◦ with respect to the light propagation di-rection. This allowed for the determination of electronangular emission distributions with dipole and non-dipolecontributions. This setup is described in more detail inRef. [44]. In order to achieve a better spectral energyresolution, a nominal retardation voltage of 510 V wasapplied to the flight tubes to decelerate fast Auger elec-trons. The magnetic field in the interaction region wasminimized by a set of three pairs of Helmholtz coils. The detector calibration, i.e. the time-of-flight to ki-netic energy conversion and the transmission functionas a function of kinetic energy, was performed by mea-suring a series of neon 2p-photoelectron spectra for dif-ferent photon energies. For these spectra, the respec-tive kinetic energies and anisotropy parameters β ( ω )are known [45, 46]. Importantly, at the employed highphoton energies, non-dipole effects cause a noticeableforward-backward asymmetry in the photoelectron emis-sion [45]. Since this non-dipole asymmetry of the neon2p-photoelectrons is constant within the narrow energyrange across the considered core excitation of methyloxi-rane [45], the forward-backward sensitivity of the detec-tors was calibrated using the known [45] constant valueof the asymmetry of 3.3%. In contrast to the presentlydiscussed contribution from PECD, the non-dipole con-tribution to the forward-backward asymmetry of methy-loxirane is helicity-independent. As a consequence, thisunknown constant contribution cancels out when sub-tracting two spectra measured for the left- and right-handed circular polarizations (see below).Unfortunately, we were not able to resolve resonantAuger electrons for the HOMO and HOMO-1 ioniza-tion bands of methyloxirane from each other, yet wecould resolve those two bands from the rest of the spec-trum. For this purpose, the calibrated, transmission- andpolarization-corrected electron spectra were fitted withGaussian curves, which were positioned at the kineticenergies given through the respective photon energy andthe binding energies of Ref. [34]. The present fitting pro-cedure is illustrated in the right panel of Fig. 2 on the ex-ample of a typical electron spectrum. As one can see, theunresolved contribution from the HOMO and HOMO-1 electron bands (high kinetic energy part of the spec-trum highlighted by the filled area) can unambiguouslybe separated from the contributions of the other elec-tron bands. Such unresolved contributions, determinedat the chosen photon energies for left- and right-handedcircularly polarized light and different emission angles θ ,were used to extract the respective quantities via the pa-rameterizations σ + ( θ ) + σ − ( θ ) = 2 σ − σβ P (cos θ ) and σ + ( θ ) − σ − ( θ ) = 2 σβ P (cos θ ).Results of the present measurement are depicted inFig. 1 by open circles. Its upper panel demonstrates avery good agreement between the normalized computedand measured cross sections σ ( ω ) (note that the last high-energy point contains a contribution from the next core-excited resonance, which was not included in the calcu-lations). The lowermost panel of Fig. 1 demonstratesa very good agreement between the measured averageanisotropy parameter β ( ω ) and that computed for theHOMO-1 band. The experimental uncertainties, indi-cated by error-bars have three sources: the Poisson sta-tistical counting, fitting errors, and calibration uncertain-ties. For β ( ω ), detector calibration using the neon 2p-line gave the major contribution (the available data varyfrom β = 1 .
14 [45] to β = 1 . ± .
11 [46]). For β ( ω ),all three sources provide comparable contributions to theexperimental uncertainties (note that, since β ( ω ) and β ( ω ) were determined via different parameterizations,calibration uncertainties for the former do not contributeto those for the latter). Similarly to β ( ω ), the mea-sured average dichroic parameter β ( ω ) follows the trendimposed by the parameter computed for the HOMO-1band (cf. open circles and blue dash-dotted curve in themiddle panel of Fig. 1). To guide the eye, the averagetheoretical results obtained with 30% contribution fromthe normalized cross section of HOMO and 70% fromthat of HOMO-1 bands are shown in Fig. 1 by blacksolid curves. The applied ratio is in reasonable agree-ment with previous measurements of Ref. [35]. Impor-tantly, the present experiment confirms the anomalousdispersion of the dichroic parameter β ( ω ), as predictedtheoretically. Even the size of the observed effect is insemi-quantitative agreement with theory.In conclusion, we demonstrate a dramatic effect of theFano interference between the direct and resonant ioniza-tion pathways on the PECD of high-energy photoelec-trons in the vicinity of the lowermost O 1 s -excitationof methyloxirane. The intermediate resonance causes ananomalous dispersion of PECD and enhances the chiralasymmetry by about two orders of magnitude. We justifyanalytically that this effect of a metastable core-excitedstate on PECD is general. The present angle-resolvedphotoionization experiment, performed with circularlypolarized synchrotron radiation, unambiguously confirmsthat the predicted recovery of PECD can be observedeven for two unresolved photoelectron bands. Takinginto account the element- and site-selectivity [17] of thepresently studied effect, PECD after energetically well-separated core excitation and subsequent resonant Augerdecay may become a powerful complementary tool forchiral recognition in the X-ray domain. The presentedresults reveal a significantly broadened applicability ofPECD for chiral recognition in the gas phase and sug-gest universality of this tool with respect to the exciting-photon spectral range and photoelectron kinetic energies.This work was funded by the Deutsche Forschungs-gemeinschaft (DFG) – Projektnummer 328961117 – SFB1319 ELCH (Extreme light for sensing and driving molec-ular chirality). M.I. acknowledges funding from theVolkswagen Foundation within a Peter Paul Ewald-Fellowship. We acknowledge DESY (Hamburg, Ger-many), a member of the Helmholtz Association HGF,for the allocation of synchrotron radiation beamline P04at PETRA III under proposal I-20170344. 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