Invited Article: High resolution angle resolved photoemission with tabletop 11 eV laser Free

Angle-resolved photoemission spectroscopy (ARPES) directly accesses electronic band structures and electronic self-energies in a momentum-resolved manner, which makes it a powerful and unique technique in condensed matter research. This momentum resolution allows one to distinguish multiple electronic band dispersions in multiband systems, to assess the symmetry of order parameters, and to characterize electronic anisotropy in solid state systems. Recent progress in the ARPES technique has pushed energy resolutions down to meV scales, which gives unprecedented access to low energy excitations in quantum materials. With its unique combination of energy and momentum resolution, ARPES contributes significantly to the understanding of many two-dimensional quantum materials,^1–4 in particular, high T_c superconducting cuprates,^5,6 iron based superconductors,^7–9 and topological states of matter.^10,11

ARPES collects photoemitted electrons as a function of kinetic energy E_k and emission angle θ with respect to the sample surface normal. The conservation of energy and in-plane momentum of each electron¹² allows the calculation of the electron’s binding energy with respect to the Fermi level E_F and its parallel momentum ħ k_∥,⁵ 

Here, ϕ denotes the work function of the material and hν the photon energy. Eq. (1) describes how larger photon energies provide access to states with higher binding energy. Eq. (2) shows that the accessible electron momenta are limited by the electron kinetic energy, which scales monotonically with the photon energy. For typical values of θ = 50° and ϕ = 4.5 eV, the minimum photon energy required to capture the entire first Brillouin zone (BZ) of a material with 3.5 Å lattice constant is hν = 9.7 eV.¹³ 

The relation between photon energy hν and parallel momentum resolution Δk_∥ is given by

As indicated in Eqs. (2) and (3), for a given detector angular resolution Δθ and momentum feature, higher photon energies degrade the momentum resolution due to increasing hν and decreasing θ.

When employing pulsed photon sources, Coulomb repulsion of electrons photoemitted by a single pulse can lead to space charging effects, which both shift and broaden the spectrum.^14,15 The effects of space charging can be mitigated by higher repetition rates while maintaining a constant photon flux. Therefore, to achieve ultimate resolution and applicability, a light source optimized for high-resolution ARPES studies of complex materials should satisfy several requirements as follows:

1. sufficiently high photon energy (>10 eV) to access the first BZ and probe valence bands (Eqs. (1) and (2));

2. sufficiently low photon energy (<20 eV) to facilitate high momentum resolution (Eq. (3));

3. sufficiently high repetition rate (≫100 kHz) to limit the loss of energy and momentum resolutions due to space-charge effects while maintaining sufficiently high signal-to-noise ratio;

4. sub-meV bandwidth, high flux, and long term stability;

5. variable polarization for control over photoemission matrix elements; and

6. additional requirements may include a small (<1 mm) beam spot and short (≤100 ps) pulse duration for time-of-flight detection schemes.

While it is challenging to integrate all these properties into one single light source, existing light sources successfully capture different aspects of the requirements listed in Table I. Noble gas discharge lamps, helium and xenon, in particular, were among the earliest photoemission light sources with photon energies in the range of 8.4–41 eV.^16–19 These pioneering experiments established ARPES as a valuable tool for the analysis of electronic structures in solids.

Continuous advances of synchrotron technology provided bright and tunable light sources that were pivotal to the tremendous success of ARPES in the last two decades. Comparing with gas discharge lamps, synchrotron-based ARPES features small (<0.5 mm) beam spots which improve momentum resolution and avoids reduced sample lifetimes due to gas molecules effusing from the light source.^16,17 Additionally, third generation synchrotron sources feature low photon energies in combination with excellent energy-momentum resolution.^20,21 Despite the outstanding capabilities of synchrotron-based ARPES, the demand for accessible, table-top ultraviolet light sources with higher photon flux and improved energy stability remains high.

Laser-based ARPES commonly utilizes non-linear optical crystals to up-convert infrared (IR) light pulses into the UV spectral region.²² The generated low photon energies of 6-7 eV result in the excellent energy and momentum resolution required for studies of detailed band dispersions and subtle low-energy excitations.^23–26 Yet, these low photon energies limit the access to high momenta and valence bands.

Although highly desirable, frequency up-conversion to sub-170 nm wavelengths is not feasible in nonlinear optical crystals due to the re-absorption in the vacuum UV (VUV) range in any material. Instead, these short wavelengths can be generated via high-harmonic generation in polarizable gases. Tjernberg and coworkers built a 10.5 eV light source dedicated to ARPES by frequency tripling the third harmonic of a pulsed IR laser in Xe gas,²⁷ which, when integrated with a time-of-flight detector, for the first time made laser-based photoemission study possible at many materials’ BZ boundaries. Such non-resonant XUV generation schemes usually require MW peak power, which in turn typically limit the laser repetition rate to <1 MHz.²⁷ The capabilities of commonly used light sources for ARPES are summarized in Table I.

In this article, we describe a table-top pulsed VUV light source optimized for high resolution ARPES studies of quantum materials. Its photon energy of ∼11 eV is sufficient to cover the complete BZ in most materials, while maintaining exceptional energy and momentum resolution at high photon flux. We demonstrate its capabilities for high resolution ARPES on a number of materials, including antimony, rare earth metal tritelluride, unconventional copper and iron-based high temperature superconductors, and single unit cell FeSe film.

Our coherent VUV light source utilizes three cascaded stages of nonlinear frequency conversion of a quasi-continuous wave pulsed, 1024 nm IR solid-state laser. As shown schematically in Fig. 1, the first two conversion stages occur in birefringent nonlinear crystals; VUV flux is generated via two-photon resonant, sum-frequency generation in xenon gas using the fundamental (ω) and fourth-harmonic (4ω) of this laser system.

The VUV light source is driven by a fiber-coupled wavelength-tunable (1024 nm) IR seed source with variable repetition rate and sub-nanosecond pulse duration. Its output is amplified by a Yb-doped fiber amplifier to an average power of 10 W and a peak power of ∼10 kW. The amplified IR light is up-converted to the second harmonic (512 nm) using a first second harmonics crystal (SHG1) with 50% efficiency. The second harmonic light is separated from the fundamental using a dichroic beam splitter (BS) and refocused into a second nonlinear crystal (SHG2) to generate UV light (256 nm). By controlling the polarization of the 512 nm beam, the output power of the frequency quadrupled UV light can be continuously modulated. This attenuation method provides VUV (114 nm) flux control, without change to the alignment or beam profile.

Following the beam splitter, the polarization of the residual IR beam is controlled by a second half-wave plate (HWP) to achieve any given VUV beam polarization. Then, the IR and UV beams are overlapped in time and space using dichroic dielectric-coated beam-combiner mirrors and focused by a single lens into a xenon-filled gas cell. The energy-level diagram of the specific nonlinear process in atomic xenon, and the control of the final VUV polarization, is shown in Fig. 2. Two UV photons (4ω) with wavelengths of 256.015 nm resonantly drive the dipole forbidden 5p^6 1S₀–5p⁵6p transition.^33–35 By mixing this local atomic oscillator with a fundamental IR photon (ω), light at the 9th harmonic (9ω) is generated (10.897 eV or 113.778 nm). By driving the two-photon transition with linearly polarized UV light, the polarization of the VUV photon is determined by the optical polarization of the IR photon.

Traditional gas-phase nonlinear optical systems have typically required MW-scale peak-power driving lasers for efficient conversion, thereby severely limiting the achievable repetition rates. However, by operating at a two-photon resonance condition, the peak optical powers required for efficient up-conversion are reduced to the kW level, which is a necessary condition for increasing the repetition rate of the source to the MHz range²⁷ and for reducing the overall source size to a table-top device.

Atomic xenon is negatively dispersive for degenerate two-photon-resonant sum-frequency generation, which enables a tightly focussed geometry for VUV generation.³⁶ Fig. 3(a) demonstrates typical variation of generated VUV flux on the xenon gas pressure. The single-peaked curve, with a maximum at approximately 12 Torr xenon pressure, is typical of tightly focussed sum-frequency generation.³⁷ 

Due to the intermediate resonance step in the frequency-conversion process, the generated VUV flux is particularly sensitive to the absolute frequency of the UV beam. As shown in Fig. 3(b) for the 1 MHz repetition rate, 1 ns pulsewidth laser setup, detuning of the UV wave from the two-photon resonance results in a rapid reduction in VUV generation efficiency.³⁸ The width of this resonance profile is set by the convolution of the laser linewidth and the natural linewidth (including isotopic and Doppler broadening) of the two-photon transition. In order to maintain peak flux, the central frequency of the UV beam must be maintained to within 1 GHz; the IR frequency must therefore be stabilized to the central frequency within 250 MHz uncertainty. In comparison, the total width of the resonance curve for the case of the broader-bandwidth excitation laser pulses produced in the 10 MHz, 100 ps laser configuration reaches ∼8 GHz. This provides a lower bound on both the energy resolution and the absolute energy stability of the 11 eV laser of ∼30 μeV.

VUV light is absorbed strongly by several atmospheric constituents, most notably oxygen and water vapor.^39,40 The 1/e attenuation length for 11 eV photons in air is approximately 3 mm.⁴¹ Therefore, the entire beam path for the 11 eV light must be either evacuated or purged to remove the absorbing species.

The xenon-filled gas converter is connected directly to a N₂-purged dispersion chamber using an uncoated LiF window. The 11 eV light is generated inside the xenon gas cell as a nearly diffraction-limited beam that propagates collinearly with the driving IR and UV beams. The IR and UV photons have energies of 1.21 eV and 4.84 eV, respectively, and Watt-level average powers. Illumination of the sample with these IR and UV beams can cause heating and photoemission and must be avoided. We employ an equilateral LiF prism to refractively disperse the 11 eV flux from the lower-energy photons prior to photoemission. The prism is operated in a minimum-deviation condition, so that the incidence angle is near the Brewster angle for the VUV light, thus minimizing reflective losses for horizontal-linearly polarized 11 eV flux.⁴² 

Under normal photoemission measurement conditions, the prism is positioned to refract the co-propagating beams; both the front-surface reflections, and the refracted IR and UV beams, are trapped by beam dumps to minimize scattered light. In order to measure the 11 eV source power, the prism may be automatically retracted to allow the three laser beams to propagate to the opposite port of the dispersion chamber (dashed line in Fig. 4(b)). The photocurrent produced by an ionization chamber mounted to this port (Lumeras model IC-LF-C, with a LiF entrance window and filled with isopropanol vapor) provides solar-blind measurements of the 11 eV flux.

The 11 eV light is then focused onto the ARPES sample using a single concave reflective MgF₂-overcoated aluminum mirror. This mirror images the laser waists in the xenon converter onto the ARPES sample with a magnification factor of approximately 3. The 11 eV photons propagate through a second, uncoated 2 mm-thick LiF window into the UHV chamber. Photoelectrons are collected by a Scienta R8000 hemispherical electron analyzer.

Fig. 5(a) shows the momentum-integrated spectrum of an evaporated polycrystalline gold film. The angle integrated Energy distribution curves (EDCs) was fit with a Fermi-Dirac function convolved with a Gaussian instrument energy-resolution function (red lines), giving 0.9 meV as an upper bound of the experimental energy resolution for the raw spectrum (open markers). A similar analysis was carried out after correcting the spectrum for detector nonlinearity (solid markers). The correction gives an experimental resolution of 2.2 meV. The origin and correction procedure of the detector nonlinear effect were detailed in Ref. 40. As shown in Fig. 5(b), by continuously varying the laser power, the detector count rate was measured as a function of total photoemission current over a large photon flux range. To remove the nonlinearity, detector count rates were mapped to the corresponding photoemission current (incident laser power) for every pixel.⁴³ 

Antimony is known to host a metallic surface state on the (111) surface,⁴⁵ which we can use to estimate the upper bound of the setup’s momentum resolution as shown in Fig. 6. A bulk Sb crystal is cleaved in vacuo on the (111) surface with Fig. 6(c) showing the band dispersion along the Γ-M cut. The angular distribution curve of the surface state from inner Γ pocket at E_F reaches a FWHM of 0.53° or 0.012 Å⁻¹ when converted to parallel momentum. It should be noted that this is a combined effect from both instrument resolution and intrinsic sample-dependent electron scattering at E_F. In comparison, high quality measurements on optimally doped Bi-2212 can yield 0.37° angular or 0.0039 Å⁻¹ momentum FWHM at E_F with 7 eV laser-ARPES.⁴⁶ 

We employ two systems with comparable flux but different repetition rates to calibrate the system’s space-charging effect. For our control experiment setup, at 1 MHz repetition rate, 500 ps pulse duration, and 2 × 10¹² photons/s, space charging caused the measured Fermi level (on evaporated polycrystalline gold) to shift by 6 meV.

In order to mitigate the space charging induced spectral changes, we reduce the pulse duration to 100 ps while maintaining the peak pulse intensity of the IR beam, which is crucial to preserve high conversion efficiency of VUV photon generation.⁴⁷ The repetition rate is boosted up to 10 MHz to compensate for the reduced photon count within every single pulse comparing to 1 MHz setup.

Fig. 7 shows the photon-intensity dependence of space charging for both the 1 MHz and the 10 MHz setups. The severity of space charging is quantified both by the shift in E_F (Fig. 7(a)) and the broadening of the Fermi edge (Fig. 7(b)). The broadening is defined as the fitted instrument resolution as is adapted in Fig. 5(a). Electron count/(pixel/s) from the Scienta R8000 detector camera is used as a measure of beam intensity. We find that up to 10¹² photons/s or 1 electron count/(pixel/s), space charging can be limited to 2 meV E_F shift and 4 meV broadening for the 10 MHz configuration. In the control experiment (blue markers), the 1 MHz setup gives worse space charging with a decade lower photon flux. In typical high resolution ARPES experiment operating at 0.1-1 count/(pixel/s), space charging effects are almost absent in the 10 MHz setup.

Rare earth metal tritellurides have been a model system to study charge density wave (CDW) formation, where a large CDW gap extends over the entire BZ.^48,49 11 eV photons provide access to the entire first folded BZ (Fig. 8(a)). When the system is warmed up from 20 K to 314 K, the CDW order weakens. This manifests as a shrinking CDW gap below E_F (Figs. 8(b1)-8(b3)), which is observed in our experiment as an uplifting gap edge in the integrated EDC (Fig. 8(c)).

We then apply the 11 eV laser-ARPES to cuprate high temperature superconductors, namely, bilayer Pb-doped Bi₂Sr₂CaCu₂O_8+δ with a T_c of 80 K (overdoped). Previous laser-based ARPES studies at both 6 eV and 7 eV photon excitation energies have provided tremendous insights towards near-nodal excitation, yet the antinodal region near the BZ boundary was not accessible with these low photon energies.^50–53 Fig. 9(a) compares the Fermi surface in the superconducting state obtained by 11 eV (upper left quadrant) and 7 eV (upper right quadrant) photoemission. The grey dashed lines are superstructures related to Bi-O sublattice distortion.^54,55

With 11 eV photons, the entire BZ can be mapped with high energy and momentum resolution. Notably, the 11 eV system can measure an antinodal (near (π, 0)) spectrum (Figs. 9(d2) and 9(d3)), whereas measurements with 7 eV laser can barely reach the antinode and have poor cross section there.⁵⁶ EDCs with clear quasiparticle peaks from node to antinode are shown in panel (b) and (c) with two different analyzer slit orientations to account for different matrix element effects.⁵⁷ Here, we adopted photon flux of ∼10¹¹ photons/s during data collection to ensure the absence of space-charging.

Another advantage is the ability to access valence bands (Fig. 9(e)). While a 7 eV laser barely reaches over the copper 3d_xy band (grey arrow), the 11 eV system enables access all the way down in binding energy including non-interacting oxygen 2p_z band (purple arrow). This is a significant advancement compared to previous laser ARPES setups in addressing materials’ chemical potential evolution, and it provides opportunities for the application of a full 5-band treatment in cuprate superconductors.^58–60 

Previous laser-based ARPES studies on iron-based high temperature superconductors^61–64 were limited by the small cross section of 7 eV photons when compared to higher energy synchrotron light sources.^65,66 In addition, as a multi-band system, iron based superconductors have a rich Fermi surface structure, which has significant contributions from both the BZ center and corner, as the nesting-driven spin fluctuations are considered to govern the physics in these materials.^8,67 The importance of the corner pockets has recently been highlighted in K_xFe_2−ySe₂^63,68–70 and the superconducting monolayer FeSe/SrTiO₃ film systems, which have only Fermi surfaces at the BZ corner.^9,71,72 For ARPES studies on these systems, access to the full BZ with high resolution and flux is required.

The 11 eV laser-based ARPES system is ideal to tackle these questions. Here, we demonstrate the much improved cross section and extended momentum range in both (Ba,K)Fe₂As₂ (T_c ∼ 38 K, Figs. 10(a)-10(c)) bulk crystal system at 10 K and monolayer FeSe/STO film system (T_gap ∼ 65 K, Figs. 10(d)-10(f)) at 10 K. The VUV light is polarized along the Γ-M direction and is kept perpendicular to the cut direction.

In (Ba,K)Fe₂As₂, two hole pockets with different k_F’s centered around Γ (Fig. 10(b))⁷³ are identified, with the inner pocket (red arrows) showing a bigger superconducting gap (7.2 meV) than the outer pocket (blue arrows, 2.4 meV). For the two bands, the Bogoliubov quasiparticle band backbending is observed in the superconducting state. For the zone corner cut (Fig. 10(c)), the d_xz/d_yz band shows a shallow band bottom and forms an electron-like Fermi surface, consistent with previous observations from synchrotron studies.^72,74,75

The single unit cell FeSe film is grown on Nb-doped SrTiO₃ substrate and is transferred to the ARPES measurement chamber in situ. The Fermi surface shows that Fermi pockets only exist at the BZ corner (Fig. 10(f)), and the hole band does not cross E_F at the Γ point (Fig. 10(e)). The superconducting backbending of the d_xz electron band as well as its hybridization gap with the strongly renormalized d_xy band is observed, consistent with previous measurements at higher photon energy.^71,76,77 The measurements also show evidence, although weaker than synchrotron data, of the shadow band due to the strong coupling to the substrate’s out-of-plane phonon, which could play a decisive role in boosting T_c by as much as 50% from its K_xFe_2−ySe₂ counterpart.⁹ The polarization control and improved cross section of our 11 eV laser facilitate resolving gap functions with high resolution on multiple bands across the entire BZ. This is essential to understand the pairing symmetry and superconducting mechanism of this multi-band system.

We have presented a table-top 11 eV laser-based ARPES system. The system utilizes the 9th harmonics of a 1024 nm IR laser to produce the 113.778 nm VUV radiation for photoemission. Combined with a Scienta R8000 hemispherical electron analyzer, we demonstrate the system’s energy resolution of 2 meV and momentum resolution of 0.012 Å⁻¹ under realistic experimental conditions. The system is capable of reaching to k_∥ = 1.2 Å⁻¹ parallel momenta as well as 5 eV in binding energy (assuming 4.5 eV material work function). Space charging effects are reduced at high repetition rates of 10 MHz. On the other hand, short pulses (≤100 ps) can be utilized for time-of-flight applications where time resolution is more prioritized.

This system provides a long desired solution to bridging the gap between the existing high-resolution small-momentum-coverage laser-based ARPES and large-momentum-coverage synchrotron-based ARPES. It is capable of producing high resolution spectra in many correlated electron systems and reaching their BZ boundaries as well as valence bands, including the temperature dependent CDW gap in rare earth metal tritelluride, the antinode and oxygen 2p band spectrum in cuprate superconductor, and superconducting gap measurements in iron-pnictide and iron-chalcogenide film.

The authors acknowledge enlightening discussions with Donghui Lu and Makoto Hashimoto. Samples are kindly provided by Wei Li, Ian Fisher, and Hiroshi Eisaki. A.J.M. acknowledges partial support for the VUV light source development from the National Science Foundation under SBIR Grant No. 0848526. S.L.Y. acknowledges Stanford Graduate Fellowship for support. This work is a collaboration between Lumeras LLC and Stanford Institute for Materials and Energy Sciences (SIMES). The photoemission studies were supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering.