MORTY Momentum resolved electron band structures from electron energy loss spectroscopy

• Leon, Dario A.; Cardoso, Claudia & Berland, Kristian (2026). Bulk plasmons in elemental metals. Physical review B (PRB). ISSN 2469-9950. 113(12). doi: 10.1103/w51n-p91p. Full text in Research Archive
• Leon, Dario A & Berland, Kristian (2026). Momentum- and frequency-resolved collective electronic excitations in solids: insights from spectroscopy and first-principles calculations. Journal of Physics: Condensed Matter. ISSN 0953-8984. 38(18), p. 183001–183001. doi: 10.1088/1361-648x/ae62e7. Full text in Research Archive Show summary

  Abstract Collective electronic excitations, including plasmons, excitons, and intra- and interband transitions, play a central role in determining the dynamic screening, optical response, and energy transport properties of materials. Recent advances in momentum- and frequency-resolved spectroscopies, such as electron energy-loss spectroscopy and inelastic x-ray scattering, together with progress in first-principles many-body perturbation theory calculations, now allow collective excitations to be mapped with considerable precision across the Brillouin zone. This topical review surveys current developments in the representation and interpretation of both experimental and theoretical dielectric-response spectra. Particular emphasis is placed on recent ways of representing spectral band structures of the direct and inverse dielectric functions, such as analytical approaches based on multipole-Padé approximants in momentum and frequency (MPA( q )), which provide a combined band-like description of the dispersion of the main collective excitations. We discuss how features observed in metals, semiconductors, and low dimensional systems reflect the interplay between electronic structure, screening strength, and local-field effects, and how post-processing procedures can improve the quantitative comparison between experiment and theory. Finally, we provide perspectives on open challenges and potential developments in quantitative dielectric-function analyses.

• Elgvin, Cana; Hage, Fredrik Sydow; Prytz, Øystein; Elyas, Khairi; Höflich, Katja & Koch, Christoph T. [Show all 7 contributors for this article] (2026). Advances in momentum-resolved EELS of phonons, excitons and plasmons in 2D materials and their heterostructures. PHYSICAL REVIEW MATERIALS. 10. doi: 10.1103/8wwb-lxk2. Full text in Research Archive Show summary

  Momentum-resolved electron energy-loss spectroscopy (q-EELS) enables the study of 2D materials by simultaneously capturing energy and momentum transfer with nanometer spatial resolution, probing excitations beyond the light cone and outside the first Brillouin zone. This technique provides unrivaled detail in the investigation of plasmons, excitons, phonons, and their coupling in 2D materials and across interfaces in heterostructures. This review covers the fundamentals of q-EELS, including resolution limits and detectability challenges. Current applications in graphene, hexagonal boron nitride, and transition metal dichalcogenides are surveyed. Emerging frontiers including magnons, cryogenic operation, and in situ capabilities promise to advance our understanding of low-dimensional materials.

• Valido, Dario Alejandro Leon; Kuisma, Mikael; Sauer, Mikkel Ohm; Svaneborg, Jakob K.; Svendsen, Mark K. & Americo, Stefano [Show all 9 contributors for this article] (2025). Self-consistent layer-projected scissors operator for band structures of two-dimensional van der Waals materials with large unit cells. Physical review B (PRB). ISSN 2469-9950. 112(11). doi: https:/journals.aps.org/prb/abstract/10.1103/2y5s-qcw9. Full text in Research Archive Show summary

  We introduce a computationally efficient method to calculate the quasiparticle band structure of general van der Waals (vdW) heterostructures. A layer-projected scissors (LAPS) operator, which depends on the one-body density matrix, is added to the density functional theory Hamiltonian. The LAPS operator corrects the band edges of the individual layers for self-energy effects (both intralayer and interlayer) and unphysical strain fields stemming from the use of model supercells. The LAPS operator is treated self-consistently whereby charge redistribution and interlayer hybridization occurring in response to the band energy corrections are properly accounted for. We present several examples illustrating both the qualitative and quantitative performance of the method, including MoS2 films with up to 20 layers, bilayer MoS2 in an electric field, lattice-matched MoS2/WS2 and MoSe2/WSe2 bilayers, and MoSe2/WS2 moiré structures. Our work opens the way for predictive modeling of electronic, optical, and topological properties of experimentally relevant vdW materials, including twisted homobilayers and incommensurate heterostructures.

• Åsland, Anna Cecilie; Bakkelund, Johannes; Cooil, Simon Phillip; Røst, Håkon; Hu, Jinbang & Vescovo, E. [Show all 9 contributors for this article] (2025). Overcoming the challenges of accessing topological hallmarks in Sb(112). Electronic Structure. 7(3). doi: 10.1088/2516-1075/adf384. Full text in Research Archive Show summary

  Sb is topologically non-trivial and semi-metallic, but differs from many topological semi-metals because of its continuous band gap. By measuring its (112) surface using angle- and spin-resolved photoemission spectroscopy, Sb(112) was shown to have 1D spin-polarised surface states resembling those on vicinal Bi surfaces and many topological insulators and topological semi-metals. The shape and spin-polarisation of the measured features and the calculated bands agreed. However, the measured features had a slightly steeper energy dispersion and different Fermi-momenta than the calculated bands. Both theoretical and experimental methods were necessary when determining the topology of Sb(112). The presence of projected bulk states near the Fermi-level and varying surface localisation of the electronic states meant it was challenging to deduce the topology of Sb(112) from the number of bands crossing the Fermi-level or a continuous contour in the bulk band gap. Ultimately, the calculations and measurements suggest that there are topological surface states on the Sb(112) surface.

• Strand, Frode Sneve; Cooil, Simon Phillip; Campbell, Quinn T.; Flounders, John J.; Røst, Håkon & Åsland, Anna Cecilie [Show all 16 contributors for this article] (2025). Direct Observation of 2DEG States in Shallow Si:Sb δ-Layers. Journal of Physical Chemistry C. ISSN 1932-7447. 129(2), p. 1339–1347. doi: 10.1021/acs.jpcc.4c07331. Full text in Research Archive Show summary

  We investigate the electronic structure of high-density layers of Sb dopants in a silicon host, so-called Si:Sb δ-layers. We show that, in spite of the known challenges in producing highly confined Sb δ-layers, sufficient confinement is created such that the lowest conduction band states (Γ states, studied in depth in other silicon δ-layers), become occupied and can be observed using angle-resolved photoemission spectroscopy. The electronic structure of the Si:Sb δ-layers closely resembles that of Si:P systems, where the observed conduction band is near-parabolic and slightly anisotropic in the k∥ plane. The observed Γ state extends ∼1 nm in the out-of-plane direction, which is slightly wider than the 1/3 monolayer thick dopant distribution. This is caused by a small segregation of the dopant layer, which is nevertheless minimal when comparing with earlier published attempts. Our results serve to demonstrate that Sb is still a feasible dopant alternative for use in the semiconductor δ-layer platform, providing similar electronic functionality to Si:P systems. Additionally, it has the advantages of being less expensive, more controllable, safer to handle, and more compatible with industrial patterning techniques. Si:Sb is therefore a viable platform for emerging quantum device applications.

• Valido, Dario Alejandro Leon; Berland, Kristian & Cardoso, Claudia (2025). Spectral properties from an efficient analytical representation of the GW self-energy within a multipole approximation. Physical review B (PRB). ISSN 2469-9950. 111(19). doi: 10.1103/PhysRevB.111.195147. Full text in Research Archive Show summary

  We propose an efficient analytical representation of the frequency-dependent 𝐺⁡𝑊 self-energy Σ via a multipole approximation (MPA-Σ). The MPA self-energy model is interpolated from a small set of numerical evaluations of Σ in the complex frequency plane, similar to the MPA interpolation developed for the screened Coulomb interaction (MPA-𝑊) [D. A. Leon et al., Phys. Rev. B 104, 115157 (2021)]. Crucially, MPA-Σ enables a multipole representation for the interacting Green's function 𝐺 (MPA-𝐺) and, in turn, access to all the spectral properties, including quasiparticle energies (QP) and renormalization factors beyond the linearized QP equation. We validate the MPA-Σ and MPA-𝐺 approaches for a diverse set of systems: bulk Si, Na, and Cu, monolayer MoS2 , the NaCl ion pair, and the F2 molecule. We show that, just as for MPA-𝑊, an appropriate choice of frequency sampling in MPA-Σ is critical to guarantee computational efficiency and high accuracy. Moreover, the combined MPA-𝑊 and MPA-Σ scheme considerably reduces the cost of full-frequency self-energy calculations, especially for spectral band structures over a wide energy range.

• Guandalini, Alberto; Leon_Valido, Dario Alejandro; D'Amico, Pino; Cardoso, Claudia; Ferretti, Andrea & Rontani, Massimo [Show all 7 contributors for this article] (2024). Efficient GW calculations via interpolation of the screened interaction in momentum and frequency space: The case of graphene. Physical review B (PRB). ISSN 2469-9950. 109(7). doi: 10.1103/PhysRevB.109.075120. Full text in Research Archive
• Valido, Dario Alejandro Leon; Elgvin, Cana; Nguyen, Phuong Dan; Prytz, Øystein; Hage, Fredrik Sydow & Berland, Kristian (2024). Unraveling many-body effects in ZnO: Combined study using momentum-resolved electron energy-loss spectroscopy and first-principles calculations. Physical review B (PRB). ISSN 2469-9950. 109(11). doi: 10.1103/PhysRevB.109.115153. Full text in Research Archive Show summary

  We present a detailed study of the dielectric response of ZnO using a combination of low-loss momentum- resolved electron energy-loss spectroscopy (EELS) and first-principles calculations at several levels of theory, from the independent particle and the random phase approximation with different variants of density functional theory (DFT), including hybrid and DFT + U schemes; to the Bethe-Salpeter equation (BSE). We use a method based on the f -sum rule to obtain the momentum-resolved experimental loss function and absorption spectra from EELS measurements. We characterize the main features in the direct and inverse dielectric functions of ZnO and their dispersion, associating them to single-particle features in the electronic band structure, while highlighting the important role of many-body effects such as plasmons and excitons. We discuss different signatures of the high anisotropy in the response function of ZnO, including the symmetry of the excitonic wave functions.

• Røst, Håkon; Mazzola, Federico; Bakkelund, Johannes; Åsland, Anna Cecilie; Hu, Jinbang & Cooil, Simon Phillip [Show all 8 contributors for this article] (2024). Disentangling electron-boson interactions on the surface of a familiar ferromagnet. Physical review B (PRB). ISSN 2469-9950. 109, p. 1–9. doi: 10.1103/PhysRevB.109.035137. Full text in Research Archive Show summary

  We report energy renormalizations from electron-phonon and electron-magnon interactions in spin minority surface resonances on Ni(111). The different interactions are identified, disentangled, and quantified from the characteristic signatures they provide to the complex self-energy and the largely different binding energies at which they occur. The observed electron-magnon interactions exhibit a strong dependence on momentum and the electron energy band position in the bulk Brillouin zone. In contrast, electron-phonon interactions observed from the same bands appear to be relatively momentum and symmetry independent. Additionally, a moderately strong (λ>0.5) electron-phonon interaction is distinguished from a near-parabolic spin majority band not crossing the Fermi level.

• Røst, Håkon; Cooil, Simon Phillip; Åsland, Anna Cecilie; Hu, Jinbang; Ali, Ayaz & Taniguchi, Takashi [Show all 12 contributors for this article] (2023). Phonon-Mediated Quasiparticle Lifetime Renormalizations in Few-Layer Hexagonal Boron Nitride. Nano Letters. ISSN 1530-6984. 23(16), p. 7539–7545. doi: 10.1021/acs.nanolett.3c02086. Full text in Research Archive Show summary

  Understanding the collective behavior of the quasiparticles in solid-state systems underpins the field of non-volatile electronics, including the opportunity to control many-body effects for well-desired physical phenomena and their applications. Hexagonal boron nitride (hBN) is a wide energy bandgap semiconductor, showing immense potential as a platform for low-dimensional device heterostructures. It is an inert dielectric used for gated devices, having a negligible orbital hybridization when placed in contact with other systems. Despite its inertness, we discover a large electron mass enhancement in few-layer hBN affecting the lifetime of the pi-band states. We show that the renormalization is phonon-mediated and consistent with both single- and multiple-phonon scattering events. Our findings thus unveil a so-far unknown many-body state in a wide-bandgap insulator, having important implications for devices using hBN as one of their building blocks.

• Åsland, Anna Cecilie; Bakkelund, Johannes; Thingstad, Even; Røst, Håkon; Cooil, Simon Phillip & Hu, Jinbang [Show all 11 contributors for this article] (2023). One-dimensional spin-polarized surface states: A comparison of Bi(112) with other vicinal bismuth surfaces. Physical review B (PRB). ISSN 2469-9950. 108(20). doi: 10.1103/PhysRevB.108.205403. Full text in Research Archive Show summary

  Vicinal surfaces of bismuth are unique test beds for investigating one-dimensional (1D) spin-polarized surface states that may one day be used in spintronic devices. In this paper, such states have been observed for the (112) surface when measured using angle- and spin-resolved photoemission spectroscopy, and also when calculated using a tight-binding model and with density functional theory. The surface states appear as elongated Dirac-cones which are 1D and almost dispersionless in the ky direction, but disperse with energy in the orthogonal kx direction to form two ×-like features centered at the ky line through Γ. Unlike many materials considered for spintronic applications, their 1D nature suggests that conductivity and spin-transport properties are highly dependent on direction. The spin polarization of the surface states is mainly in plane and parallel to the 1D states, but there are signs of a tilted out-of-plane spin-vector component for one of the features. The Bi(112) surface states resemble those found for other vicinal surfaces of bismuth, strongly indicating that their existence and general properties are robust properties of vicinal bismuth surfaces. Furthermore, differences in the details of the states, particularly related to their spin polarization, suggest that the electronic band structure may be engineered simply by precise cutting and polishing of the crystal.

• Røst, Håkon; Tosi, Ezequiel; Strand, Frode Sneve; Åsland, Anna Cecilie; Lacovig, Paolo & Lizzit, Silvano [Show all 7 contributors for this article] (2023). Probing the Atomic Arrangement of Subsurface Dopants in a Silicon Quantum Device Platform. ACS Applied Materials & Interfaces. ISSN 1944-8244. 15(18), p. 22637–22643. doi: 10.1021/acsami.2c23011. Full text in Research Archive Show summary

  High-density structures of subsurface phosphorus dopants in silicon continue to garner interest as a silicon-based quantum computer platform; however, a much-needed confirmation of their dopant arrangement has been lacking. In this work, we take advantage of the chemical specificity of X-ray photoelectron diffraction to obtain the precise structural configuration of P dopants in subsurface Si:P δ-layers. The growth of δ-layer systems with different levels of doping is carefully studied and verified using X-ray photoelectron spectroscopy and low-energy electron diffraction. Subsequent diffraction measurements reveal that in all cases, the subsurface dopants primarily substitute with Si atoms from the host material. Furthermore, no signs of carrier-inhibiting P–P dimerization can be observed. Our observations not only settle a nearly decade-long debate about the dopant arrangement but also demonstrate how X-ray photoelectron diffraction is surprisingly well suited for studying subsurface dopant structure. This work thus provides valuable input for an updated understanding of the behavior of Si:P δ-layers and the modeling of their derived quantum devices.

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• Schenk, Richard Justin; Skarpeid, Alv; Røst, Håkon; Yadav, Rohit; Cooil, Simon Phillip & Wells, Justin William (2026). Modifying the Electronic Structure of Nickel with Antimony Surface Alloys. Full text in Research Archive
• Valido, Dario Alejandro Leon; Berland, Kristian & Cardoso, Claudia (2025). Bulk plasmons in elemental metals. http://arxiv.org/abs/cond-mat. doi: https:/arxiv.org/pdf/2510.07261. Full text in Research Archive Show summary

  The spectral properties, momentum dispersion, and broadening of bulk plasmonic excitations of 25 elemental metals are studied from first principles calculations in the random-phase approximation. Spectral band structures are constructed from the resulting momentum- and frequency-dependent inverse dielectric function. We develop an effective analytical representation of the main collective excitations in the dielectric response, by extending our earlier model based on multipole-Pad´e approximants (MPA) to incorporate both momentum and frequency dependence. With this tool, we identify plasmonic quasiparticle dispersions exhibiting complex features, including non-parabolic energy and intensity dispersions, discontinuities due to anisotropy, and overlapping effects that lead to band crossings and anti-crossings. We also find good agreement between computed results and available experiments in the optical limit. The results for elemental metals establish a reference point that can guide both fundamental studies and practical applications in plasmonics and spectroscopy.

• Valido, Dario Alejandro Leon (2024). A tour of many-body theory for modelling excitons in van der Waals heterostructures. Full text in Research Archive
• Leon_Valido, Dario Alejandro (2024). Unraveling many-body effects in ZnO: Combined study using momentum-resolved electron energy-loss spectroscopy and first-principles calculations. Full text in Research Archive
• Leon_Valido, Dario Alejandro (2024). Unraveling many-body effects in ZnO: Combined study using momentum-resolved electron energy-loss spectroscopy and first-principles calculations. Full text in Research Archive
• Elgvin, Cana; Leon, Dario A.; Hage, Fredrik Sydow; Nguyen, Phuong Dan; Berland, Kristian & Prytz, Øystein (2023). The effects of heavy doping on the band structure of zinc oxide obѕerνed using momentum-resolved EELS. Full text in Research Archive
• Elgvin, Cana; Leon, Dario A.; Hage, Fredrik Sydow; Nguyen, Phuong Dan; Berland, Kristian & Prytz, Øystein (2023). Anisotropy and nature of electronic excitations using ωq-mapping and ab initio calculations. Full text in Research Archive
• Tosi, Ezequiel; Strand, Frode Sneve; Åsland, Anna Cecilie; Lacovig, Paolo; Lizzit, Silvano & Wells, Justin William (2023). Probing the Atomic Arrangement of Sub-Surface Dopants in a Silicon Quantum Device Platform. Full text in Research Archive Show summary

  Recently, efforts to realize a silicon-based, CMOS-compatible quantum computer have been intensifying. Central to its development are so-called Si:P δ-layers: i.e., ultra-sharp layers of phosphorus atoms placed beneath the silicon surface. Until recently, one key property has remained elusive: the arrangement of the P dopants within the δ-layer. The answer to this question is of crucial importance, as the dopant arrangement will directly impact the energy separation (i.e., valley-splitting) of the supported quantum well states. In this talk, we will demonstrate how the local neighborhood around encapsulated dopants in a bulk semiconductor can be directly probed using X-ray photoelectron diffraction (XPD). By utilizing subtle core level energy shifts that are concomitant with the coordination of a dopant, chemically specific diffractive images can be formed. Through comparison with XPD simulations that are derived from models of the local atomic environment around the dopants, the true dopant atom placement can be ascertained. Typically, XPD is only used as a probe of surface structure. We demonstrate here that – under the right conditions, it also can be used to determine the local arrangement of sub-surface atoms. Therefore, XPD is well suited for solving the long-standing mystery of the Si:P δ-layer structure.

• Røst, Håkon; Tosi, Ezequiel; Strand, Frode Sneve; Åsland, Anna Cecilie; Lacovig, Paolo & Lizzit, Silvano [Show all 7 contributors for this article] (2023). Determining the Arrangement of Subsurface Dopants in a Silicon Quantum Device Platform. Full text in Research Archive
• Valido, Dario Alejandro Leon (2023). Frequency dependence in GW: origin, modelling and practical implementations. Full text in Research Archive
• Valido, Dario Alejandro Leon (2022). Efficient full frequency GW using a multipole approach for the dielectric screening. Full text in Research Archive
• Valido, Dario Alejandro Leon (2022). Electronic properties of wide-band-gap semiconductors resolved by low energy q-EELS. Full text in Research Archive
• Valido, Dario Alejandro Leon (2022). Many-body perturbation theory-based approaches to understand finite-momentum EELS spectra. Full text in Research Archive

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