An experimentalist's guide to the matrix element in angle resolved photoemission

Moser, Simon

doi:10.1016/j.elspec.2016.11.007

Cited by 164 publications

(142 citation statements)

References 210 publications

(255 reference statements)

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“…This is substantially different from the case of graphene where it mainly originates from the interference term, i.e. P graphene AB ∝ ∓(q x /q) [21,40] for the CB (+) and VB (−). For graphene this term originates from the two p z orbitals localized on the two carbon atoms in the primitive unit cell.…”

Section: Momentum-dependence Of the Matrix Elementsmentioning

confidence: 68%

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Layer and orbital interference effects in photoemission from transition metal dichalcogenides

et al. 2019

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In this work, we provide an effective model to evaluate the one-electron dipole matrix elements governing optical excitations and the photoemission process of single-layer (SL) and bilayer (BL) transition metal dichalcogenides. By utilizing a k · p Hamiltonian, we calculate the photoemission intensity as observed in angle-resolved photoemission from the valence bands around theK-valley of MoS2. In SL MoS2 we find a significant masking of intensity outside the first Brillouin zone, which originates from an in-plane interference effect between photoelectrons emitted from the Mo d orbitals. In BL MoS2 an additional inter-layer interference effect leads to a distinctive modulation of intensity with photon energy. Finally, we use the semiconductor Bloch equations to model the optical excitation in a time-and angle-resolved pump-probe photoemission experiment. We find that the momentum dependence of an optically excited population in the conduction band leads to an observable dichroism in both SL and BL MoS2. * Electronic address: habib.rostami@su.se † current address:

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Section: Momentum-dependence Of the Matrix Elementsmentioning

confidence: 68%

“…In this section we adapt the procedure in Ref. 40 in order to determine M n for the TMDCs. The initial state is written as a Bloch wave |ψ i = |ψ j (q, τ z , s z ) and the final state is approximated as a single plane wave |ψ f = |k f , leading to…”

Section: Matrix Elements For the Photoemission Processmentioning

confidence: 99%

Layer and orbital interference effects in photoemission from transition metal dichalcogenides

et al. 2019

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“…We note that elsewhere it is common to take advantage of the plane-wave final state to recast the matrix element as a polarization modulated Fourier transform of the initial state [19,30]. Specifically, M F T can be expanded as in Eq.…”

Section: Computation Of Matrix Elementsmentioning

confidence: 99%

Computational framework chinook for angle-resolved photoemission spectroscopy

et al. 2019

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We have developed the numerical software package chinook, designed for the simulation of photoemission matrix elements a . This quantity encodes a depth of information regarding the orbital structure of the underlying wavefunctions from which photoemission occurs. Extraction of this information is often nontrivial, owing to the influence of the experimental geometry and photoelectron interference, precluding straightforward solutions. The chinook code has been designed to simulate and predict the ARPES intensity measured for arbitrary experimental configuration, including photon-energy, polarization and spin-projection, as well as consideration of both surface-projected slab and bulk models. This framework then facilitates an efficient interpretation of the photoemission experiment, allowing for a deeper understanding of the electronic structure in addition to the design of new experiments which leverage the matrix element effects towards the objective of selective photoemission from states of particular interest. arXiv:1909.12081v2 [cond-mat.str-el]

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“…This assumption leads to the expression M n (q) ∝ê p · k f k f |ψ n (q) , whereê p is the polarization unit vector of the probe pulse (see Fig. 1(a)) and k f is the wavevector of the free electron [27,28]. The wave functions and dispersion are determined by diagonalizing a k · p Hamiltonian given bŷ…”

Section: Scattering Planementioning

confidence: 99%

Momentum-resolved linear dichroism in bilayerMoS2

et al. 2019

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Inversion-symmetric crystals are optically isotropic and thus naively not expected to show dichroism effects in optical absorption and photoemission processes. Here, we find a strong linear dichroism effect (up to 42.4%) in the conduction band of inversion-symmetric bilayer MoS2, when measuring energy-and momentum-resolved snapshots of excited electrons by time-and angle-resolved photoemission spectroscopy. We model the polarization-dependent photoemission intensity in the transiently-populated conduction band using the semiconductor Bloch equations and show that the observed dichroism emerges from intralayer single-particle effects within the isotropic part of the dispersion. This leads to optical excitations with an anisotropic momentum-dependence in an otherwise inversion symmetric material.Optical selection rules in absoprtion experiments are powerful tools that can be used to determine the symmetry of electronic states in solids [1]. Given the similarity of the processes underlying optical absorption and photoemission, selection rules have also been exploited in angle-resolved photoemission spectroscopy (ARPES) for decades [2]. More recently, optical dichroism has been used in ARPES to study orbital degrees of freedom [3][4][5], as well as the Berry curvature of the initial Bloch states [6, 7]. A particularly interesting opportunity for polarization-dependent excitations arises in single-layer (SL) transition metal dichalcogenides (TMDCs) such as MoS 2 , where the helicity of circularly polarized light strongly couples to the valley and spin degrees of freedom [8, 9], permitting the generation of a finite valley polarization [10, 11].Adding time-resolution (TR) to ARPES in a pumpprobe experiment leads to a process involving two optical excitations. This opens the possibility of exploiting not only the selection rules governing the photoemission process, but also those giving rise to the initial optical excitation into a transiently populated conduction band (CB) state [12][13][14][15][16][17][18]. Indeed, the creation of a finite valleypolarization in SL WS 2 has recently been followed in momentum space by TR-ARPES using circularly polarized pump pulses [19,20]. Here, we extend such an experiment to the case of bilayer (BL) MoS 2 in the 2H structure, which is inversion-symmetric and hence an optically isotropic material. Surprisingly, we observe a substantial linear dichroism effect. Our results can be reconciled with the momentum-dependent excited state population determined by solving the semiconductor Bloch equations within the framework of a low energy k · p model that ac-counts for intra-and interlayer interactions between the d orbitals forming the valence band maximum (VBM) and conduction band minimum (CBM) aroundK (K ). These findings underline the necessity of accounting for selection rules governing the optical excitation in addition to the photoemission matrix elements when interpreting the intensity in dichroic TR-ARPES.Our BL MoS 2 sample is grown on Ag(111) and has predominantly one domain orie...

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An experimentalist's guide to the matrix element in angle resolved photoemission

Cited by 164 publications

References 210 publications

Layer and orbital interference effects in photoemission from transition metal dichalcogenides

Layer and orbital interference effects in photoemission from transition metal dichalcogenides

Computational framework chinook for angle-resolved photoemission spectroscopy

Momentum-resolved linear dichroism in bilayerMoS2

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