Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Nowadays ARPES is widely used to determine the electronic structure of solids. Usually, different variations of this method are defined by the source of the radiation needed to excite the electrons. We use synchrotron radiation since it offers a unique opportunity to tune the polarization and the excitation photon energy in a wide energy range and is characterized by high intensity, small bandwidth (uncertainty in energy hn) and it can be focused to a narrow beam to collect photoelectrons from a spot of a few tens of microns. Synchrotron radiation is generated in electron storage rings forcing electrons circulating in the ring with an energy of the order of 2 GeV ** to pass through periodic arrangements of strong magnets (undulators). The magnetic field deflects the electrons and when such fast electrons change their direction they emit radiation. Exactly this radiation is then directed into the so called beamline where it is further monochromatized by a diffraction grating and focused on the surface of the sample by several mirrors. There are many such facilities around the world. Our end-station is located at one of the beamlines of the BESSY storage ring which belongs to the Helmholtz-Zentrum Berlin.

The heart of this ARPES facility is the electron-energy analyzer (Figure 1). Since we are interested in both the kinetic energy and angle at which electrons leave the surface, it is very convenient to detect them in one measurement. A very simple principle makes this approach a reality. As in a basic experiment with an optical lens, which focuses a plane wave into the point in the back focal plane thus performing spatial Fourier transformation, the electron optical lens projects electrons which left the surface at particular angle to a point in the focal plane (Figure 1). In such a way we gain access to the reciprocal, i.e. momentum, space. The distance from the forward direction in the focal plane corresponds to the angle and thus to the momentum of the photoelectron. Now the electrons have to be analyzed in terms of energy. For this purpose the entrance slit of the hemispherical analyzer is placed exactly in the focal plane of the electron optical lens. Voltages on two hemispheres are chosen such that only electrons with particular kinetic energy (pass energy) will be guided exactly in the middle of two hemispheres and land on the central line of the two dimensional detector. Those which are faster will hit the detector closer to the outer hemisphere; those which are slower will be deflected towards the inner hemisphere. In such a way we can get the photoemission intensity distribution as a function of angle and kinetic energy simultaneously.

The main advantage of our approach over existing methods is the use of the He³ cryomanipulator. There are at least two reasons to carry out the measurements at low temperatures. The higher the temperature of the material, the more smeared out the electronic states become in energy and momentum. To determine the electronic structure with high precision this temperature broadening has to be avoided. Also, many physical properties are temperature dependent, some ordering phenomena set in at low temperatures and the knowledge of the electronic structure in the ground state of the system, i.e. at T=0, is of fundamental importance. One of the most effective ways to cool down the sample down to tenths of a Kelvin is to liquefy He³ gas. In many experiments reaching sub-Kelvin temperatures is not a problem, since thermal radiation, the main enemy of ultra-low temperatures, can be effectively shielded. Unfortunately, this is not the case in photoemission experiments. We need to provide free access for the incoming light and outgoing electrons. This is realized by specially designed slits in three radiation shields, having different temperatures. In order to compensate for the heat load caused by the photon beam and room-temperature radiation, the cooling power of the cryostat should be very high. This is achieved by the very large pumping speed of two pumps which reduce the vapor pressure above the liquid He³, thus cooling the cold finger and sample. The design specifications of our He³ system make it the most powerful worldwide. It is perhaps the only place on the planet where one can see a 1 K cold surface through a room temperature window, the "coldest visible".

The sketch of the modern photoemission experiment is shown in Figure 1. The synchrotron beam (dashed green line) illuminates the 1 K cold surface of the sample and excites photoelectrons. Electrons are projected to the entrance slit of the hemispherical analyzer, sorted in terms of angle (yellow, magenta and cyan traces correspond to different tilt angles) and then are analyzed in terms of kinetic energy. Figure 2 shows the typical intensity distribution as a function of tilt angle and kinetic energy. Such an intensity distribution is indeed expected as the comparison with band structure calculations of this material shows (right panel). This is our window into reciprocal space.

By scanning voltages on the lens and hemispheres and rotating the sample around the vertical axis (polar angle) we can explore the broad binding energy range as well as wide regions of the reciprocal space with unprecedented detail. In particular, plotting intensity at the Fermi level as a function of both components of the in-plane momentum, calculated from tilt and polar angles, we have direct access to the Fermi surface (FS).

* Under "uncertainty" we understand the experimenter's best estimate of how far an experimental quantity might be from the "true value."

** The low-energy ring can have an energy of ~0.8 GeV, the high-energy one - up to 8 GeV.