Advanced Techniques

To enable cutting edge science, the lab develops state of the art tabletop spectroscopy and microscopy techniques and collaborates with programs at LBNL's Advanced Light Source and the Molecular Foundry.

Angle Resolved Photoemission Spectroscopy

Angle-Resolved Photoemission Spectroscopy (ARPES) is an experimental technique based on several refinements of the photoelectric effect initially observed by Heinrich Hertz in 1887. When a monochromatic beam of photons of energy hνh\nu are incident upon a sample, measurement of the electron's kinetic energy and exit angle gives information about the momentum and energy ("band structure") of the electron state in the studied material. Directly, ARPES gives the binding energy (Eb\text{E}_\text{b}) of the emitted electrons and the components of momentum parallel to the sample surface (k\textbf{k}_\parallel). Crystalline translational symmetry is broken by the vacuum interface, so less information is available for the out of plane momentum (kz\textbf{k}_\text{z}) without varying the incident photon energy.

Experiment

Hemispherical Energy Analyzer
Figure 1. ARPES experimental geometry with hemispherical energy analyzer
From simple energy and momentum conservation arguments, we can explain the process by which ARPES makes available the electronic band structure. In typical ARPES experiments, a hemispherical energy analyzer simultaneously measures the intensity distribution of photoelectrons along a one dimensional linecut of angle—defined by an entrance slit on the analyzer—and resolved by the photoelectron kinetic energy. Briefly, photoelectrons emitted from different angles (green, blue, and orange in the above depiction) are incident at different locations on the entrance slit and follow different circular trajectories between the analyzer plates. Meanwhile, more and less energetic electrons follow longer and shorter paths (depicted as a spread in blue, green, and orange curves) due to their different bend radii in the constant E-field produced by the analyzer. The analyzer therefore spatially filters the electrons to produce an image of the photoemitted beam. A final electron sensitive detector, typically a channel plate paired with a phosphor screen + CCD or delay line + timing hardware, turns the spatially filtered electron signal into a digital one. If a photoemitted electron leaves the sample with an energy Ekin\text{E}_\text{kin} at an angle (θ,ϕ)(\theta, \phi) to the sample normal, z^\hat{\text{\textbf{z}}}, the binding energy and k\textbf{k}_\parallel are given by conservation: Eb=hνknownφEkinmeasured \text{E}_{\text{b}} = \underbrace{h\nu}_\text{known} - \varphi - \underbrace{\text{E}_\text{kin}}_\text{measured} p=2mEkinsinθ(cosϕx^+sinϕy^). \textbf{p}_\parallel = \sqrt{2 m \text{E}_\text{kin}}\sin{\theta} \left(\cos \phi \hat{\mathbf{x}} + \sin \phi \hat{\mathbf{y}} \right). The sample workfunction φ\varphi, giving the different between the Fermi and vacuum levels, may or may not be known. The Fermi edge of a metallic sample (actual or reference), nevertheless links the kinetic energy to the electron binding energy. By turning the sample, z^\hat{\text{\textbf{z}}} can be rastered perpendicular to the analyzer entrance, making available the photoemission intensity over all values of k\textbf{k}_\parallel. Consideration must be given to the difference between experimentally measured angles and the spherical polar angles relative to z^\hat{\text{\textbf{z}}}. To obtain high-quality data, ARPES experiments are conducted in an ultra-high vacuum chamber which minimizes surface contamination and interactions between the photoemitted electrons and any potential interference between the emission and detection processes. Additionally, ARPES experiments are often performed at cryogenic temperatures to minimize thermal broadening of the data. This capability also allows for the study of high-temperature superconductors below their critical temperatures, where the electrons take on a fundamentally different structure. ## Single + Many Body Physics ARPES provides a direct measurement of the angle resolved photocurrent I(k,ω)I(\textbf{k}, \omega). This can be expressed in terms of a dipole interaction matrix element MM, the Fermi-Dirac distribution for state occupancy, and the single-particle spectral function A(k,ω)A(\mathbf{k}, \omega): I(k,ω)=M(k,ω,kA)f(ω)A(k,ω). I(\textbf{k}, \omega) = M\left(\textbf{k}, \omega, \mathbf{k}\cdot\mathbf{A}\right)f(\omega)A(\mathbf{k}, \omega). Although matrix element contribution can in general be difficult to disentangle, it is typically slowly varying in momentum and photon energy, and therefore ARPES can be thought of as measuring also A(k,ω)A(\textbf{k}, \omega). A(k,ω)=1πΣ(k,ω)[ωϵ0(k)Bare bandΣ(k,ω)E-renormalization]2+[Σ(k,ω)Lifetimes]2 \textbf{A}(\mathbf{k}, \omega) = -\frac{1}{\pi} \frac{\textcolor{blue}{\Sigma''(\textcolor{black}{\mathbf{k}, \omega})}} {[\omega - \hspace{-0.25em}\underbrace{\textcolor{green}{\epsilon_0(\textcolor{black}{\mathbf{k}})}}_{\textcolor{green}{\text{Bare band}}}\hspace{-0.25em} - \hspace{-0.4em}\underbrace{\textcolor{red}{\Sigma'\left(\textcolor{black}{\mathbf{k},\omega}\right)}}_{\textcolor{red}{\text{E-renormalization}}}\hspace{-0.9em}]^2 + [\underbrace{\textcolor{blue}{\Sigma''\left(\textcolor{black}{\mathbf{k},\omega}\right)}}_{ \textcolor{blue}{\text{Lifetimes}} }]^2} From this quantity much can be extracted, including single-particle band structure, energy renormalization by interaction, and measurement of the quasiparticle lifetimes. ARPES therefore makes available momentum resolved information on electron-electron and electron-boson interaction in real material systems. ## Laser ARPES From the conservation equations, we can see that given a fixed angular resolution of Δθ\Delta \theta of our analyzer, we may obtain a higher momentum resolution for smaller photoelectron kinetic energy, ΔkEkinΔθ\Delta\mathbf{k}\propto\sqrt{\text{E}_\text{kin}}\Delta\theta. UV and VUV lasers based on frequency doubling in BBO or KBBF and operating at very high photon fluxes with narrow spectral linewidths of a few meV allow ARPES studies of materials at a much higher resolution than is possible at synchrotron sources. Pulsed laser sources also enable [ARPES studies of materials perturbed out of equilibrium](/tr-arpes) by a strong visible to IR pulse, at the penalty of larger bandwidth Δν\Delta \nu and therefore worse energy resolution.

Spin-Resolved Photoemission Spectroscopy

In our laboratory we have developed a novel analyzer for Spin-ARPES experiments (see photo at right). This analyzer employs a new concept for spin detection, based on a Time-of-Flight analyzer (which is 10 times more efficient than dispersive analyzers) coupled with a high-efficiency spin detector utilizing exchange scattering (about 50-100 times more efficient for spin detection than using spin-orbit interaction as in Mott detectors). Spin-ARPES is the only experimental tool that can directly probe the spin-resolved bandstructure of materials. Our “Spin-TOF” system allows us to perform experiments with energy resolution, momentum resolution, and collection efficiency unprecedented for a Spin-ARPES system. It has been used at the Advanced Light Source for measurements in wide energy and momentum ranges and with with the tabletop laser in our laboratory for high resolution measurements. The high efficiency of data collection allows for experimental scope never before possible with spin resolution. For example, the spin-TOF system mapped the spin-dependence of the bandstructure of Au(111) surface states, shown at right. These data, which would take prohibitively long to accumulate on most spin-ARPES systems, were taken in just two hours. The Spin-TOF system collects data rapidly enough to test a wide range of experimental parameters such as sample temperature or photon polarization. It can be a crucial probe for understanding topological insulators, Rashba systems, and magnetic materials.
Hemispherical Energy Analyzer
Figure 1. ARPES experimental geometry with hemispherical energy analyzer

Photoemission Microscopy

The technological frontier of our century lies in our ability to deal with very small samples (obtained by various combinations of 2D materials) or with quantum materials, where heterogeneity is the key to many of the novel observed behaviors. Tools that provide spatial resolution, in addition to energy and are becoming a must to advance the frontier of this field. In our laboratory we are developing a new ‘momentum space microscope’ that will allow us to measure energy and momentum of electrons in solids with nanometer spatial resolution. The new spectrometer is based on an entirely new concept for microscopy and is posed to revolutionized our understanding of quantum materials while pushing the frontiers for novel technologies.

AI Driven Analysis and Acquisition

We developed PyARPES, an open data analysis toolkit and framework designed specifically for the workflows of angle-resolved photoemission spectroscopy. With PyARPES, scientists can integrate with industry standard libraries for machine learning and image processing, work with specialized models for ARPES, and automate typical workflows.

Terahertz and Mid-Infrared Spectroscopy

# Time-domain THz Spectroscopy The THz wavelength regime encompasses the far-infrared range of 0.1-100 THz, or about 33300cm13-3300 \text{cm}^{-1}. The THz regime is especially interesting for condensed matter physics. This is the energy scale (0.4-400 meV) of many collective processes, like phonon and magnetic modes, superconducting gaps, and spin and charge ordering gaps, to name a few. It's also the energy scale of surface states in topological insulators and the Dirac cones of graphene. Time-domain THz spectroscopy is an integral tool for optical characterization of solids. The advantage of using femtosecond-scale pulses for THz generation is the ability to map the full phase and amplitude information of the THz electric field using electro-optic sampling. After a THz pulse has passed through or been reflected by the material of interest, the material's complex optical response can be reconstructed from the THz field, without requiring a broadband spectrum and Kramers-Kronig transformation.
Pump probe THz Spectroscopy by Electro-optic Sampling
Figure 1. Schematic beampath for ultrafast THz-spectroscopy by EOS
Our THz probe source relies on frequency conversion from the near-infrared (800 nm femtosecond pulses output by an amplified Ti:Sapphire laser) into single-cycle THz pulses via optical rectification in ZnTe. The bandwidth of the resulting THz pulses can probe between 0.3-2.5 THz (1085cm110-85 \text{cm}^{-1}). We combine our THz spectroscopy probe with a variable wavelength pump generated by optical parametric amplification and difference frequency generation (OPA+DFG) of 800 nm light. Our system has a state-of-the-art pulse energy range in the mid-infrared of 50-150 uJ for wavelengths between 4-15 um. This translates to large excitation fields, on order 10 MV/cm.