A main goal of our research is to understand the underlying mechanisms of long range order in materials. Microscopically, long range order often bears a close relation to low-energy excitations. In particular, superconductivity arises when low energy excitations about the Fermi level are forbidden; this occurs when a superconducting gap is formed as Cooper pairs condense. As the typical energy scale for such excitations is around a few meV, high energy and momentum resolution in ARPES is necessary to resolve the gap. The modern high-repetition rate UV laser is an excellent light source for this application. Through the cumulative effort of many generations of our group members, we have developed a laser ARPES system with modern laser technique.
7 eV Laser
In our lab, 7 eV (177.3 nm) laser light is produced by frequency-doubling light from a 3.5 eV (354.7 nm) laser (Coherent, Palladin) using a KBe2BO3F2 (KBBF) device. The 3.5 eV laser in turn comes from frequency-tripling of a Nd:YAG oscillator (1064 nm). The set up schematic of the 7 eV laser , where we have fully exploited the characteristic nonlinear process of frequency doubling in a KBBF crystal, is shown below. A significant proportion of incident 3.5 eV seed laser doubles the frequency, as an extraordinary light beam which differs from the path of the residual 3.5 eV laser due to different refraction in crystal. Furthermore, we designed several optical components to deflect the beam into the chamber.
11 eV Laser
While the 7 eV laser can in principle provide the highest possible resolution, it cannot cover a large area of momentum space due to its low energy. This constraint makes it challenging for us to obtain a systematic physical picture of electronic behavior in the entire first Brillouin zone. In the cuprates, for example, we have still not obtained a high-quality dataset on the nodal-antinodal dichotomy of the pseudogap using laser ARPES because the 7 eV laser will not enable us to reach the antinodal set for many cuprate species. Therefore, we are also developing an 11 eV laser technique to overcome this deficiency. Our Coherent 11 eV laser light source utilizes three cascaded stages of nonlinear frequency conversion of a quasi-continuous-wave, pulsed 1024 nm IR solid-state laser. A schematic energy level diagram and the experimental setup is shown below. 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. By mixing this local atomic oscillation with a fundamental IR photon (ω), light at the ninth harmonic (9ω) is generated (10.897 eV/113.778 nm) .
One distinct advantage of using photons with lower energy from a laser source (as opposed to other, higher energy sources) is an inherently higher momentum resolution, as detector-angle-to-momentum conversion scales directly with photoelectron kinetic energy. In the figure on the right, we plot the corresponding 1° × 1° detector region (in units of Å-1) at different excitation photon energies. The first quadrant of the Brillouin zone showing the Fermi surface of optimally doped Bi2212, measured by laser ARPES, is overlaid. It is clear that at lower photon energies, one can sample momentum space in a much finer grid, given an identical angular range of the detector.
A trade-off when low-energy photons are used is the shrunken momentum space accessible by ARPES. For example, the 7 eV laser source is unable to reach the antinodal region of Bi2212, where interesting physics such as the pseudogap could be expected to manifest in ARPES spectra. Hence, in addition to our 7 eV laser source, we have recently commissioned an 11 eV laser source that largely preserves superior momentum resolution, but has also been shown to cover a much larger momentum space, including the entire first Brillouin zone of Bi2212. These two laser sources hold promising possibilities for investigating finer details that were previously missed due to low resolution.
The laser sources we use are at least an order of magnitude brighter than a similarly monochromatized line from a synchrotron source or Helium lamp, which in turn allows us to work at finer energy resolutions and collect higher quality data in a shorter amount of time. The figure on the right shows the nodal spectra of the optimally-doped high-Tc cuprate Bi2212, which were taken by our 7 eV laser ARPES system. In this measurement, energy and momentum resolution used are 3 meV and <0.003 Å-1 respectively. Because of the high resolution of the experiment, sharp quasi-particle peaks in both momentum space (MDC) and energy space (EDC) were be obtained. These high resolution spectra will be crucial for quantitative analyses of cuprate physics.
It has been shown that electron mean free path inside a solid increases dramatically with decreasing kinetic energy . As mean free path determines the depth at which ARPES can probe into the sample, the lower photon energy afforded by laser ARPES thus imparts a measure of bulk-sensitivity to this heretofore surface-sensitive measurement.
Laser ARPES enables us to take high-quality datasets in many systems we are interested in and has provided important experimental evidence to advance our understanding of condensed matter physics.
Renormalization of Nodal Fermi Velocity in Bi2212
A project that has significantly benefited from the high resolution of laser ARPES is our discovery and interpretation of doping-dependent nodal Fermi velocity. In this project, I. M. Vishik et al. performed a systematic, doping-dependent study of the low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O8+δ (Bi2212). Renormalization of the nodal velocity due to this kink was showed to become stronger in the underdoped phase, contrasting with previous assumed phenomenology where the nodal velocity was universal through the whole cuprate superconducting dome .
Our observation of the doping-dependent renormalization of Fermi velocity benefited from the high-quality laser-ARPES data, and provided a solid foundation for further theoretical discussion in the cuprates. Prior to the discovery of this low-energy kink, the prevalent view of the high-temperature cuprates was that their essential low-energy physics is captured by local Coulomb interactions. However, local Coulomb interactions themselves were insufficient to capture the doping-dependent strong renormalization of nodal velocity, which motivated us to consider more candidate interactions. Theoretical work following the above experimental observations was accomplished by S. Johnson and I. M. Vishik et al., in which they demonstrated further evidence for the importance of extended Coulomb interactions and forward scattering in cuprate superconductors .
One of the key observations in our experimental data is that the low-energy renormalization typically happens at a binding energy scale of 8 – 15 meV, below the maximum of the superconducting gap. This implied a strong momentum dependence on the electron-phonon coupling vertex g(k,q) for quasiparticle scattering from the momentum state |k〉to |k+q〉. To capture the essence of this short-range, momentum-dependent electron-phonon scattering vertex, we adopted a simple Thomas-Fermi wave vector, leading to an overall momentum dependence peaked at q ~ qTF. Based on this model, we simulated the corresponding ARPES spectrum, which was showed to agree excellently with the experimental data in doping, energy and momentum dependence. This result indicated that electron-phonon coupling and extended Coulomb interactions are strongly intertwined, both playing important roles in establishing the low-energy physics of the cuprates.
Phase competition in trisected superconducting dome
A detailed investigation on low-energy excitations is crucial for microscopic understanding of the superconducting phenomena in cuprates. Using the high energy resolution of our laser ARPES system, I. M. Vishik et al. performed a thorough doping- and temperature-dependent study of spectral gaps in superconducing Bi2Sr2CaCu2O8+δ (Bi2212). The superconducting dome is divided into three regions characterized by the different phenomenology of their near-nodal gaps. Region A (p < 0.076) features a fully gapped Fermi surface and a gap anisotropy that decreased with underdoping. Region B (0.076 < p < 0.19) was identified as a regime where superconductivity coexists with the pesudogap in the ground state, because gaps at the near-nodal and intermediate momenta were independent of doping. Region C (p > 0.19) was identified as a pure superconducting ground state, as the d-wave superconducting gap shrunk as Tc decreased. Tracking the temperature dependence of the gaps revealed phase competition between the pseudogap and superconductivity, in which pseudogap physics dominated a smaller region of the Fermi surface at lower temperatures and larger dopings. For more detailed discussion, please refer to . High temperature behavior and nature of the gap above Tc in the overdoped regime has recently been updated , while critical behavior at 19% remained robust.
 I. M. Vishik, Low energy excitations in cuprate high-temperature superconductors: angle-resolved photoemission spectroscopy studies [Thesis work]
 Yu He et al., Review of Scientific Instruments 87, 011301 (2016)
 I. M. Vishik, Phys. Rev. Lett. 104, 207002 (2010)
 S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
 I. M. Vishik et al., PNAS, 109 (45) 18332-18337 (2012)
 Su-Di Chen, Makoto Hashimoto, et al., Science 366, 1099-1102 (2019)