# Fileset

[Ueda_APEX2024.pdf](https://mdr.nims.go.jp/filesets/fcd1fa3d-7626-40a0-a979-13ff024ad6fe/download)

## Creator

[Shigenori Ueda](https://orcid.org/0000-0001-9425-0614), [Masaki Mizuguchi](https://orcid.org/0000-0003-1090-0179)

## Rights

free to: Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
Adapt — remix, transform, and build upon the material for any purpose, even commercially.[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Probing buried interface band dispersion of a MgO/Fe heterostructure with hard X-ray angle-resolved photoemission](https://mdr.nims.go.jp/datasets/625c9b2f-0293-4df0-a257-17b73fca998c)

## Fulltext

Probing buried interface band dispersion of a MgO/Fe heterostructure with hard X-ray angle-resolved photoemissionApplied Physics Express     LETTER • OPEN ACCESSProbing buried interface band dispersion of aMgO/Fe heterostructure with hard X-ray angle-resolved photoemissionTo cite this article: Shigenori Ueda and Masaki Mizuguchi 2024 Appl. Phys. Express 17 075501 View the article online for updates and enhancements.You may also likeSoft X-ray angle-resolved photoemissionspectroscopy of heavily boron-dopedsuperconducting diamond filmsT. Yokoya, T. Nakamura, T. Matushita etal.-Electronic structure of (In,Mn)As quantumdots buried in GaAs investigated by soft-x-ray ARPESA D Bouravleuv, L L Lev, C Piamonteze etal.-Electronic signatures of successiveitinerant, antiferromagnetic transitions inhexagonal La2Ni7Kyungchan Lee, Na Hyun Jo, Lin-LinWang et al.-This content was downloaded from IP address 144.213.253.16 on 18/07/2024 at 04:02https://doi.org/10.35848/1882-0786/ad5e33/article/10.1016/j.stam.2006.02.014/article/10.1016/j.stam.2006.02.014/article/10.1016/j.stam.2006.02.014/article/10.1088/0957-4484/27/42/425706/article/10.1088/0957-4484/27/42/425706/article/10.1088/0957-4484/27/42/425706/article/10.1088/1361-648X/acc629/article/10.1088/1361-648X/acc629/article/10.1088/1361-648X/acc629/article/10.1088/1361-648X/acc629Probing buried interface band dispersion of a MgO/Fe heterostructure with hardX-ray angle-resolved photoemissionShigenori Ueda1,2* and Masaki Mizuguchi3,4,5,61Research Center for Electronic and Optical Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan2Synchotron X-ray Station at SPring-8, NIMS, Sayo, Hyogo 679-5148, Japan3Institute of Materials and Systems for Sustainability, Nagoya University, Nagoya, Aichi 464-8603, Japan4Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan5Cutting-edge, International Research Units, Nagoya University Institute for Advanced Study, Nagoya University, Nagoya, Aichi 464-8603, Japan6Center for Spintronics Research Network, Osaka University, Toyonaka, Osaka 560-8531, Japan*E-mail: UEDA.Shigenori@nims.go.jpReceived June 28, 2024; accepted July 1, 2024; published online July 16, 2024Interface band dispersion of a MgO(2 nm)/Fe(50 nm) heterostructure was detected by hard X-ray angle-resolved photoemission spectroscopy(HARPES) with the excitation photon energy of 3.29 keV by utilizing X-ray total reflection (TR). By subtracting bulk-sensitive band dispersion of theburied Fe(001) obtained by HARPES in the non-TR condition from near-interface-sensitive Fe(001) band dispersion obtained by TR-HARPES, theband-folding of Fe and the O 2p -Fe 3d hybridization at the heterointerface were clearly unveiled. These results suggest that HARPES can probenot only the bulk band but also the buried interface band of heterojunctions. © 2024 The Author(s). Published on behalf of The Japan Society ofApplied Physics by IOP Publishing LtdRecently, hard X-ray photoemission spectroscopy(HAXPES) has been developed for the measure-ments of bulk-sensitive electronic and magneticstates of solids1–9) owing to a large inelastic mean-free-pathof electrons (λe) with several-keV inside solids.10) HAXPESwith an angular resolution (HARPES) for the band dispersionmeasurements of single crystals or epitaxial thin films11–14)has also been a powerful tool for detecting bulk banddispersion of materials. The band dispersion measurementsfor epitaxial films covered by thin protection layers (e.g.AlOx) by using HARPES are very useful since the surfacetreatment of the samples is not required in many cases.Although the HARPES measurements are limited by thephotoemission Debye–Waller factor (DWF), which is afraction of the momentum-conserved transition,2,11,13) obser-vations of band dispersion are expected to be possible inmany cases at low-temperature and approximately 3 keVphotoexcitation conditions.In the HAXPES experiments combined with X-ray totalreflection (TR), it has been reported that the effective λe (λeff)can be tuned by the incidence angle of X-ray (θin) withrespect to the sample surface and that the depth-dependentelectronic (and magnetic) states can be obtained.5,9) It seemsthat HARPES combined with TR has a capability forexploring band dispersion of heterointerfaces as well asburied layers, while TR-HARPES has not been reportedyet. Here, we focused on a MgO/Fe heterojunction todemonstrate the capability of TR-HARPES, since the inter-facial electronic states between the MgO and Fe layers in Fe/MgO/Fe tunnel magnetoresistance (TMR) junctions15) arestill important; differences in band dispersion betweeninterfacial and buried bulk Fe layers are present or not.Very recently it has been reported that the TMR ratio of Fe/MgO/Fe-based junctions reaches 631%, which is the highestvalue in the TMR junctions at room temperature.16) In thiswork, we have performed HARPES measurements for aMgO-capped Fe(001) thin film to observe the band disper-sion of near-interface and buried Fe layers in TR and non-TR(NTR) conditions, respectively. In the TR-HARPES mea-surement, a clear band dispersion from the buried Fe(001)film with the enhanced MgO-derived O 2p states was found,while the O 2p states were quite weak in the NTR-HARPESmeasurement. We also found that the band-folding of Fe(001) and the formation of the O 2p-Fe 3d anti-bonding stateat the MgO/Fe heterojunction, which were obtained by thesubtraction of bulk band dispersion (NTR condition) fromnear-interface one (TR condition), suggesting the usefulnessof the combination of TR- and NTR-HARPES for probinginterface electronic band states.The HARPES measurements for the MgO(2 nm)/Fe(50 nm)/MgO(001) structure at the temperature (T) of 22 Kwere performed with the excitation photon energy (hν) of3.29 keV at the undulator beamline BL15XU ofSPring-8.3,17) The sample growth procedure was describedelsewhere.6) Although we used a helical undulator as a lightsource, circularly polarized X-rays were converted to hor-izontal linear polarized X-rays due to the Bragg reflections18)in a four-bounce Si 111 monochromator, leading to thedegree of linear polarization calculated to be ∼0.98. Theenergy and angle of photoelectrons were analyzed anddetected by a hemispherical electron analyzer (VG ScientaR4000). The angular resolution of the electron analyzer was∼0.3° in HARPES.11) The energy resolution was set to290 meV, and the binding energy (EB) was calibrated by theFermi level (EF) of the Au film. The spot size of X-rays at thesample position was 25 μm (vertical)× 35 μm (horizontal) inFWHM. The experimental geometry was describedelsewhere.3,11) To control λeff (depth in Fe with respect tothe interface), the relationship of λeff = λpλe/(λp+λe) wasused, where λp was X-ray attenuation length in Fe anddepended on θin.5,19) λe for Fe was obtained from the TPP-2M equation.10)Figure 1(a) shows the Fe 2p core-level HAXPES spectra ofthe MgO(2 nm)/Fe(50 nm) film measured in the TR and NTRconditions. In the TR condition (λeff ∼1.7 nm), θin was set tothe TR critical angle (θC= 0.817°) for Fe, which wasContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of thiswork must maintain attribution to the author(s) and the title of the work, journal citation and DOI.075501-1© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 17, 075501 (2024) LETTERhttps://doi.org/10.35848/1882-0786/ad5e33https://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/ad5e33&domain=pdf&date_stamp=2024-07-16https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0003-1090-0179https://orcid.org/0000-0003-1090-0179mailto:UEDA.Shigenori@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/ad5e33detected by the intensity maximum of the Fe 2p core-levelphotoemission as a function of the incidence angle (see Ref. 5for details), while θin was set to 2.6° in the NTR condition(λeff ∼3.4 nm). The reduction of the background intensity inthe higher EB side for the TR spectrum compared to the NTRone was found as proof of TR. The similarity of eachspectrum indicates that oxidation of Fe near the interface isnegligibly weak, since the spectrum obtained in the TRcondition is sensitive to the MgO/Fe interface compared tothe NTR condition.Figure 1(b) shows the valence band HAXPES spectra ofthe MgO(2 nm)/Fe(50 nm) film measured in the TR and NTRconditions, where the spectra have been obtained from theangle-integrated HARPES data shown in Figs. 2(a) and 2(e).Both the TR and NTR spectra (ITR and INTR) were normal-ized by the peak intensity at EB = 0.65 eV. The NTRspectrum is roughly classified into two parts: dominant Fe 3dstates in the EB range between EF and ∼2 eV and dominantFe 4s states in the range between ∼2 and ∼9 eV as referred tothe previously reported HAXPES spectra for bulk Fe20) dueto the large photoionization cross-section of 4s orbitalrelative to 3d one in HAXPES for 3d transition metals.21)For the TR spectrum, additional O 2p states originating fromthe MgO layer are visible in the range between ∼4 and∼9 eV according to Ref. 22. A hump structure at around13 eV is due to carbon contamination on the MgO layeraccording to Ref. 23. The enhanced MgO-derived states inthe TR spectrum is again proof of TR. The intensitydifference spectrum (Idiff), which is defined by Idiff =ITR− INTR, clearly shows the O 2p states of MgO in theEB > 4 eV region, while the in-gap of MgO (EB <4 eV)shows structures, which would reflect the difference in theelectronic structures of Fe between the near-interface andbulk regions. In fact, the theoretical calculations for the MgO(001)/Fe(001) multilayer structure indicate that the nearest-neighbor Fe atomic layer from the MgO layer shows thedecrease of the density of states (DOS) at around EF and theincrease of DOS at EB ∼2 eV originated from the Fe 3d -O2p hybridization at the interface.6,24) These changes in theelectronic structure near the interface are reported in theinterface-emphasized HAXPES measurement for the MgO(2 nm)/Fe(1.5 nm)/MgO(001) structure.6)Figures 2(a) and 2(e), symbolized by IMTR and IMNTR,respectively, show the HARPES intensity maps for the MgO(2 nm)/Fe(50 nm) film measured in the TR and NTR condi-tions. Each intensity map was divided by the energy-integrated angular distribution curve (ADC) to partly reducea detector inhomogeneity along the detector angle. In Fig. 3,the final state wave-vector (kf) passing through the mo-mentum space in the extended Brillouin zone (BZ) for thekinetic energy (EK) of photoelectrons with 3288 eV excitedfrom EF for Fe(001) in our experimental geometry is shown.The final state wave-vector corrected by the photon wave-vector (kf—khν) is also shown in Fig. 3, since khν cannot benegligible in HARPES as can be seen in the figure. One seesthat kf—khν passes through near the Γ–H direction.Figures 2(b) and 2(f), symbolized by IMTR_BG andIMNTR_BG, respectively, show the intensity maps of theangle-integrated energy distribution curves (EDCs) obtainedfrom Figs. 2(a) and 2(e) with no angular dependence, toassume the non-momentum-conserved transition intensitymaps as a background for simplicity. Here, the intensitymaps of Figs. 2(a) and 2(b) [Figs. 2(e) and 2(f)] werenormalized by their angle-integrated EDCs at EB = 0.65 eV.Figures 2(c) and 2(g), symbolized by IMTR_C and IMNTR_C,respectively, show the HARPES intensity maps for TR andNTR after subtracting the background intensity maps shownin Figs. 2(b) and 2(f). These intensity maps are obtained byIMTR_C=IMTR – α×IMTR_BG and IMNTR_C= IMNTR –β×IMNTR_BG, where α and β are coefficients. One seesthat the clear band dispersion features in Figs. 2(c) and 2(g)compared to those in Figs. 2(a) and 2(e) are apparent. Thissubtraction process also gives DWF of Fe in our experimentalcondition. The DWFs given by 1–α for the TR condition and1–β for the NTR condition for Fe at T = 22 K andEK = 3288 eV are ∼0.40. This value is close to the calculatedDWF of 0.37 based on Refs. 2 and 11. Thus, this subtractionprocess can roughly estimate DWF from the experimentalHARPES results.Figures 2(d) and 2(h) compare the experimental banddispersion with the theoretical calculation based on the local-spin-density approximation (LSDA).25) Although the experi-mentally probed momentum region slightly deviates from theΓ–H direction, the experimental results of both TR and NTRconditions are similar to the LSDA calculations along theΓ–H direction. One sees that the intensity at EB of ∼2 eV(a)(b)Fig. 1. (a) Fe 2p core-level HAXPES spectra of the MgO(2 nm)/Fe(50 nm)/MgO(001) structure measured with the TR (λeff∼1.7 nm) and NTR(λeff∼3.4 nm) conditions at T = 22 K. (b) Valence band spectra of the MgO(2 nm)/Fe(50 nm)/MgO(001) structure measured in the TR (λeff∼1.9 nm)and NTR (λeff∼4.0 nm) conditions at T = 22 K. The intensity differencebetween the TR and NTR spectra is indicated by the green line. The insetshows the enlarged view of the difference spectrum around EF.075501-2© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 075501 (2024) S. Ueda and M. Mizuguchiaround the Γ point in the experiment damps in both TR andNTR conditions, while the flat-band-like majority spin bandstates are present in the calculation. The damping andbroadening of the majority spin band has been reported insurface-sensitive spin-resolved ARPES for Fe(110),26) andthe importance of many-body correlation effects in ARPEShas been discussed in the theoretical calculations for Fe.26–30)To emphasize the interface sensitivity in HARPES, theintensity difference map (IMdiff= IMTR_C–IMNTR_C) of theHARPES maps between Figs. 2(d) and 2(h) in the Γ–Hregion, indicated by black arrows, is shown in Fig. 4(a),where IMTR_C and IMNTR_C are normalized by their angle-integrated EDCs at EB = 0.65 eV within the Γ–H region. Onesees that the negative and positive intensity regions are foundeven after the subtraction process and that the intensitydifference map is antisymmetric to the X̅ point. Here, thepositive (negative) intensity mainly arises from the interface(bulk) electronic states. In Fig. 4(b), the difference map wascompared with the band dispersion along the Γ–H directionof Fe. The negative intensity area partly agrees with the Δ1majority and minority spin band and the majority spin bandaround the H point at ∼EF, while the positive intensity areadoes not show a similarity to the band dispersion curves.When we applied the band-folding at the X̅ point as shown inFig. 4(c), the positive intensity area partly agreed with thefolded majority and minority spin band, although the band-folding does not occur in the ideal interface structure forMgO/Fe as described in Ref. 31. The absence of the band-folding in the ideal MgO/Fe interface is due to the in-planelattice period of Fe is the same as that of MgO at the interfaceas seen in Fig. 4(d). If oxygen defects at the interface asshown in Fig. 4(e) are present as an example, the in-planelattice period of Fe is half of that of O-deficient MgO, leadingto the band-folding at the X̅ point in Fe at the interface. TheO-deficient MgO at the interface might relate to a depositioncondition and/or a large lattice mismatch between Fe andMgO and is a possible origin of the band-folding of Fearound the interface. Finally, we note that the intensityintegration in the region enclosed by the dashed line at EB(a) (b) (c) (d)(e) (f) (g) (h)Fig. 2. (a) and (e) Experimental HARPES intensity maps for the MgO(2 nm)/Fe(50 nm)/MgO(001) structure in the TR and NTR conditions, respectively,measured at T = 22 K. In the valence band region, λeff is ∼1.9 (∼4.0) nm in the TR (NTR) condition. (b) and (f) Background intensity map obtained from theangle-integrated EDC in each map. No angular-dependent intensity distribution is assumed. (c) and (g) Corrected HARPES intensity maps for TR and NTRconditions, respectively. (d) and (h) same as (c) and (g), but the theoretical spin-resolved band dispersions along the Γ–H direction are overlaid, where themajority (minority) spin band is indicated by the red (light blue) lines, where the band dispersion data are taken from Ref. 25.Fig. 3. Extended BZ in HARPES for Fe(001) in our experimental setup.The center (corner) of black squares corresponds to Γ (H) point. The graydashed and green solid curves correspond to the trace of kf and kf–khν forEK = 3288 eV, respectively. The red (blue) thick lines indicate the maximumdetector field of view for |kf–khν| in the TR (NTR) conditions. The red (blue)thin line indicates the center of the detector field of view in the TR (NTR)conditions.075501-3© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 075501 (2024) S. Ueda and M. Mizuguchiof ∼2 eV in Fig. 4(a) shows the positive value as similar tothe intensity difference spectrum in Fig. 1(b), suggesting thatthis region is considered to originate from the Fe 3d-O 2phybridized states formed at the MgO/Fe interface.6,24)In summary, buried interface band dispersion of the MgO/Fe heterostructure was detected by HARPES combinedwith the NTR and TR conditions. By subtracting bulk-sensitive band dispersion of the buried Fe(001) obtained byNTR-HARPES from near-interface-sensitive Fe(001) banddispersion obtained by TR-HARPES, the band-folding of Feand the Fe 3d-O 2p hybridized state at around the interfacewere clearly unveiled. These results suggest that HARPEScan probe not only the bulk band but also the buried interfaceband of heterojunctions.Acknowledgments The HARPES measurements at SPring-8 were per-formed under the approval of NIMS Synchrotron X-ray Station (Proposal No.2018B4606). This work was partially supported by Tokodai Institute forElemental Strategy and Data Creation and Utilization Type Material Research andDevelopment Project from MEXT, Japan [Grant Nos. JPMXP0112101001 andJPMXP1122683430].ORCID iDs Shigenori Ueda https://orcid.org/0000-0001-9425-0614 Masaki Mizuguchi https://orcid.org/0000-0003-1090-01791) S. Hüfner, Very High Resolution Photoelectron Spectroscopy, Lecture Notesin Physics (Springer, Berlin, 2007) Vol. 715, Chap.14.2) C. S. Fadley, J. Electron Spectrosc. Rel. Phenom. 190, 165 (2013).3) S. Ueda, J. Electron Spectrosc. Rel. Phenom. 190, 235 (2013).4) S. Ueda et al., Appl. Phys. Express 1, 077003 (2008).5) S. Ueda, Appl. Phys. Express 11, 105701 (2018).6) S. Ueda, M. Mizuguchi, M. Tsujikawa, and M. Shirai, Sci. Technol. Adv.Mater. 20, 796 (2019).7) S. Ueda and Y. Sakuraba, Sci. Technol. Adv. Mater. 22, 317 (2021).8) S. Ueda, Y. Miura, Y. Fujita, and Y. Sakuraba, Phys. Rev. B 106, 075101(2023).9) S. Ueda, Y. Fujita, and Y. Sakuraba, Phys. Rev. B 109, 085109 (2024).10) S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interf. Anal. 21, 165 (1994).11) A. X. Gray et al., Nat. Mater. 10, 759 (2011).12) S. Nemšák et al., Nat. Commun. 9, 3306 (2018).13) S. Banenkov et al., Commun. Phys. 2, 107 (2019).14) S. Chernov, C. Lidig, O. Fedchenko, K. Medjianik, S. Babenkov,D. Vasilyev, M. Jourdan, G. Schönhense, and H. J. Elmers, Phys. Rev. B103, 054407 (2021).15) S. Yuasa and D. D. Djayaprawira, J. Phys. D: Appl. Phys. 40, R337 (2007).16) T. Scheike, Z. Wen, H. Sukegawa, and S. Mitani, Appl. Phys. Lett. 112,112404 (2023).17) S. Ueda, Y. Katsuya, M. Tanaka, H. Yoshikawa, Y. Yamashita, S. Ishimaru,Y. Matsushita, and K. Kobayashi, AIP Conf. Proc. 1234, 403 (2010).18) T. Ishikawa, K. Tamasaku, and M. Yabashi, Nucl. Instrum. Methods Phys.Res., Sect. A 547, 42 (2005).19) B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables54, 181 (1993).20) S. Ueda and I. Hamada, J. Phys. Soc. Jpn. 86, 124706 (2017).21) M. B. Trzhaskovskaya and V. G. Yarzhemsky, At. Data Nucl. Data Tables119, 99 (2018).22) G. H. Fecher et al., Appl. Phys. Lett. 92, 193513 (2008).23) L. H. Tjeng, A. R. Vos, and G. A. Sawatzky, Surf. Sci. 235, 269 (1990).24) H. X. Yang, M. Chshiev, B. Dieny, J. H. Lee, A. Manchon, and K. H. Shin,Phys. Rev. B 84, 054401 (2011).25) J. Schäfer, M. Hoinkis, E. Rotenberg, P. Blaha, and R. Claessen, Phys. Rev.B 72, 155115 (2005).26) J. Sánchez-Barriga et al., Phys. Rev. Lett. 103, 267203 (2009).27) A. Grechnev, I. Di Marco, M. I. Katsnelson, A. I. Lichtenstein, J. Wills, andO. Eriksson, Phys. Rev. B 76, 035107 (2007).28) J. Minár, J. Phys.: Condens, Matter 23, 253201.29) A. L. Walter, J. D. Riley, and O. Rader, New J. Phys. 12, 013007 (2010).30) M. C.-T. D. Müller, S. Blügel, and C. Friedrich, Phys. Rev. B 100, 045130(2019).31) K. Nawa, K. Masuda, and Y. Miura, Phys. Rev. Appl. 16, 044037 (2021).(a) (b)(c)(d) (e)Fig. 4. (a) Intensity difference map obtained by the subtraction of NTR-HARPES [Fig. 2(h)] from TR-HARPES [Fig. 2(d)]. (b) Same as (a), but thespin-resolved band dispersions along the Γ–H direction are overlaid. The red(blue) lines indicate the majority (minority) spin band. (c) Same as (b), butthe folding at the X̅ point is considered. The folded bands are indicated bythe dashed lines. (d) Ideal interface structure of MgO(001)/Fe(001). (e) Sameas (d), but O-deficient interface structure.075501-4© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 075501 (2024) S. Ueda and M. Mizuguchihttps://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0001-9425-0614https://orcid.org/0000-0003-1090-0179https://orcid.org/0000-0003-1090-0179https://orcid.org/0000-0003-1090-0179https://doi.org/10.1016/j.elspec.2013.06.008https://doi.org/10.1016/j.elspec.2013.01.009https://doi.org/10.1143/APEX.1.077003https://doi.org/10.7567/APEX.11.105701https://doi.org/10.1080/14686996.2019.1633687https://doi.org/10.1080/14686996.2019.1633687https://doi.org/10.1080/14686996.2021.1912576https://doi.org/10.1103/PhysRevB.106.075101https://doi.org/10.1103/PhysRevB.106.075101https://doi.org/10.1103/PhysRevB.109.085109https://doi.org/10.1002/sia.740210302https://doi.org/10.1038/nmat3089https://doi.org/10.1038/s41467-018-05823-zhttps://doi.org/10.1038/s42005-019-0208-7https://doi.org/10.1103/PhysRevB.103.054407https://doi.org/10.1103/PhysRevB.103.054407https://doi.org/10.1088/0022-3727/40/21/R01https://doi.org/10.1063/5.0145873https://doi.org/10.1063/5.0145873https://doi.org/10.1016/j.nima.2005.05.010https://doi.org/10.1016/j.nima.2005.05.010https://doi.org/10.1006/adnd.1993.1013https://doi.org/10.1006/adnd.1993.1013https://doi.org/10.7566/JPSJ.86.124706https://doi.org/10.1016/j.adt.2017.04.003https://doi.org/10.1016/j.adt.2017.04.003https://doi.org/10.1063/1.2931089https://doi.org/10.1016/0039-6028(90)90802-Fhttps://doi.org/10.1103/PhysRevB.84.054401https://doi.org/10.1103/PhysRevB.72.155115https://doi.org/10.1103/PhysRevB.72.155115https://doi.org/10.1103/PhysRevLett.103.267203https://doi.org/10.1103/PhysRevB.76.035107https://doi.org/10.1088/0953-8984/23/25/253201https://doi.org/10.1088/1367-2630/12/1/013007https://doi.org/10.1103/PhysRevB.100.045130https://doi.org/10.1103/PhysRevB.100.045130https://doi.org/10.1103/PhysRevApplied.16.044037 Acknowledgments A2