Fermi Surface Mapping Research Articles

Emergence of multiple Fermi surface maps in angle-resolved photoemission fromBi2Sr2CaCu2O8+δ

We report angle-resolved photoemission spectra (ARPES) for emission from the Fermi energy ${(E}_{F})$ over a large area of the ${(k}_{x}{,k}_{y})$ plane using 21.2 and 32 eV photon energies in two distinct polarizations from an optimally doped single crystal of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi2212), together with extensive first-principles simulations of the ARPES intensities. The results display a wide-ranging level of accord between theory and experiment, demonstrating that the ARPES matrix elements can produce a striking variety of Fermi surface maps, especially in the presence of secondary features arising from modulations of the underlying tetragonal system. Our analysis demonstrates how the energy and polarization dependency of the ARPES matrix element can help to disentangle the primary contributions to the spectrum from the secondary features and indicates that secondary features reflect a direct modulation of the ${\mathrm{CuO}}_{2}$ planes.

High resolution angle-resolved photoemission study of high temperature superconductors: charge-ordering, bilayer splitting and electron–phonon coupling

The latest development of angle-resolved photoemission spectroscopy (ARPES) technique has seen extremely high energy resolution and momentum resolution, as well as multiple angle detection. These advancements have led to new findings through efficient Fermi surface mapping, fine electronic structure resolving, and direct determination of electron self-energy. In this paper, we will highlight some recent high resolution ARPES work on high temperature superconductors. These include: (1) charge-ordering and evolution of electronic structure with doping; (2) bilayer splitting and Fermi surface topology of Bi2212; and (3) strong electron–phonon coupling and electron–electron interaction in high temperature superconductors.

First principles simulations of energy and polarization dependent angle-resolved photoemission spectra of Bi2212

We discuss first-principles simulations of angle-resolved photoemission (ARPES) intensity in Bi2212 where the photoexcitation process is modeled realistically by taking into account the full crystal wavefunctions of the initial and final states in the presence of the surface. Some recent results aimed at understanding the effects of the energy and polarization dependencies of the ARPES matrix element are presented. The nature of the Fermi surface (FS) maps obtained via ARPES by holding the initial state energy fixed at the Fermi energy ( E F) is clarified. The theoretically predicted FS map at 21 eV photon energy displays a remarkable level of agreement with the corresponding ARPES spectrum taken over a large area of the ( k x , k y ) plane. Our analysis shows how the ARPES matrix element can help disentangle closely spaced energy levels and FS sheets and highlight different aspects of the electronic spectrum in complex materials under various experimental conditions.

Spin-polarized Fermi surface mapping

The magnetic and electronic properties of itinerant ferromagnets and their interplay have been studied in the last few years by spin resolved electron spectroscopy on one hand and by high-resolution angle-resolved photoemission experiments on the other. We discuss how the two approaches can be combined in a high resolution electron spectrometer with spin resolution for angle-scanned Fermi surface mapping experiments. We have built this new instrument, which allows an advance into a deeper understanding of magnetic thin film or multilayer systems, where band structures become intricately dense in momentum space and where the magnetization direction can change from layer to layer. Spin-resolution is thus required to arrive at a correct assignment of spectral features. A fully three-dimensional polarimeter makes the instrument ‘complete’ in the sense that all properties of the photoelectron are measured. First experiments on Ni(111) conclusively confirm previous band and spin assignments at the Fermi level and demonstrate the correct functioning of the apparatus.

THE FERMI SURFACE IN A MAGNETIC METAL–INSULATOR INTERFACE

Nickel (111) and the interface of hexagonal boron nitride on Ni(111) serve as model systems for an itinerant ferromagnet that is truncated with vacuum or a single layer insulator. These systems are investigated with angle-scanned He I and He II photoemission. Upon formation of the h-BN/Ni(111) interface the work function drops by 1.8 eV and the minority Ni Λ3d-band shifts by 0.13 eV to higher binding energy. This indicates that the Ni magnetic moment decreases in the interface. Spin-polarized band structure calculations from bulk nickel identify the observed minority and majority bands. The experimental Fermi surface maps show that h-BN distorts a minority d-band in a way which is consistent with the decreasing magnetic moment. It can be seen that h-BN affects the scattering of the electrons. Effects in the photoemission final and initial state are recognized.

Photoelectron imaging using an ellipsoidal display analyzer

We have built an ellipsoidal display analyzer (EDA) for angle-resolved photoelectron spectroscopy and related techniques. The instrument is an improved version of a design by Eastman et al. [Nucl. Instrum. Methods 172, 327 (1980)] and measures the angle-resolved intensity distribution of photoelectrons at fixed energy I(θ,φ)|E=const.. Such two-dimensional cuts through the Brillouin zone are recorded using a position-sensitive detector. The large acceptance angle (Δθ=43° in the polar direction and Δφ=360° in the azimuthal direction) leads to a collection efficiency which exceeds that of conventional hemispherical analyzers by a factor of about 3000. Using ray-tracing calculations we analyze the electron optical properties of the various analyzer components and optimize their arrangement. This minimizes distortions and aberrations in the recorded images and greatly improves the performance compared to previous realizations of this analyzer. We present examples demonstrating the performance of the analyzer and its versatility. Using a commercial He-discharge lamp we are able to measure complete angular distribution patterns in less than 5 s. The energy and angular resolution are ΔEEDA=85 meV and Δθ=1.2°, respectively. Complete stacks of such cuts through the Brillouin zone at different kinetic energies E can be acquired automatically using custom software. The raw data are processed leading to a three-dimensional set (I(EB,k∥) of photoelectron intensity versus binding energy E and wave vector k∥. From this all relevant information, like the dispersion relations EB(k∥) along arbitrary directions of the Brillouin zone or Fermi-surface maps, can then be computed. An additional electron gun enables low-energy electron diffraction, Auger electron spectroscopy, and electron energy-loss spectroscopy. Switching between electrons and photons as the excitation source is possible without any movement of the sample or analyzer. Because of the high acquisition speed it is possible to study the electronic structure of solids as a function of an external parameter (i.e., temperature) or to make animated movies showing, for example, the evolution of electronic states in reciprocal space. After installation of this EDA at a synchrotron providing tunable photon energy, the full power of the instrument will come into play by adding techniques like constant final state or constant initial state spectroscopy, and x-ray photoelectron diffraction.

Correlation effects and magnetism in 3d transition metals

Abstract Over the last few years the electronic structure of nickel metal has been investigated in quite some detail using high resolution photoemission spectroscopy. Important results from these studies are (i) that regions in momentum space could be identified where the exchange splitting for both d and sp bands could be measured directly in the vicinity of the Fermi level, and (ii) that these magnetic splittings continuously vanish as the Curie temperature T c is approached. Spectral functions calculated using a multiorbital Hubbard model [Manghi et al., Phys. Rev. B, 59 (1999) R10409] provide an almost quantitative description of the data, marking the importance of spin- and momentum-dependent correlation effects on the energy scale of 100 meV. The behaviour of band magnetism in the vicinity of an interface is illustrated by discussing two adsorbate systems: hydrogen on Ni(110) and one monolayer of hexagonal boron nitride (h-BN) on Ni(111). There is evidence emerging that the bulk-like bands that are formed by the Ni atoms adjacent to the interface are strongly affected by the chemical bonding. In the photoemission data this results in a spectral weight transfer away from the bulk bands, in the formation of strong surface umklapp bands, and in slight energy and/or momentum shifts. For cobalt, the picture is not so complete, yet. A high-resolution Fermi surface map is presented for a thick Co film on Cu(111), and the relation to band structure calculations and correlation effects are discussed.

Fermi Surface Map of the Single-Layer Bi-Cuprate Bi2Sr2 − xLaxCuO6 + δ at Optimal Doping

A first Fermi surface map of a single-layer high-Tc superconductor is presented. The experiments were carried out on optimally doped Bi2Sr2 − xLaxCuO6 + δ (x = 0.40) with synchrotron radiation which allow to discuss in detail the strong polarization dependence of the emissions near the Fermi edge. For the cuprates, only little is known about the impact of the electron–photon matrix element determining the photoelectron intensity. For the example of the model layered superconductor Bi2Sr2 − xLaxCuO6 + δ, it will be demonstrated that the polarization geometry has significant influence on the energy distribution curves at EF, and consequently also for the determination of the topology and character of the Fermi surface (FS) by angle-resolved photoemission. For further clarification also, a FS map of the n = 2 material Bi-2212 has been measured applying a different polarization geometry as previously used by Saini et al. In the context of the current debate on the character of the FS of Bi-cuprates, our results confirm a hole-like FS for n = 1 as well as for n = 2 material, what might be the universal FS for high-Tc superconductors.

The topology of the Fermi surface of Bi 2Sr 2CaCu 2O 8−δ from angle resolved photoemission

We present a study of the topology of the normal state Fermi surface (FS) of the high T c superconductor Bi 2Sr 2CaCu 2O 8−δ (Bi2212) using angle-resolved photoemission. We present FS mapping experiments, recorded using unpolarised radiation with high (E, k) resolution, and an extremely dense sampling of k-space. In addition, synchrotron radiation-based ARPES has been used to prove the energy independence of the FS as seen by photoemission. We resolve the current controversy regarding the normal state FS in Bi2212. The true picture is simple, self-consistent and robust: the FS is hole-like, with the form of rounded tubes centred on the corners of the Brillouin zone. Two further types of features are also clearly observed: shadow FSs, and diffraction replicas of the main FS caused by passage of the photoelectrons through the modulated BiO planes.

Normal-state Fermi surface of pristine and Pb-doped Bi2Sr2CaCu2O8+δ from angle-resolved photoemission measurements and its photon energy independence

We address the question as to whether the topology of the normal state Fermi surface of Bi2212 - as seen in angle resolved photoemission - depends on the photon energy used to measure it. High resolution photoemission spectra and Fermi surface maps from pristine and Pb-doped Bi2212 are presented, recorded using both polarised and unpolarised radiation of differing energies. The data show clearly that no main band crosses the Fermi surface along the GMZ direction in reciprocal space, even for a photon energy of 32 eV, thus ruling out the existence of a G-centred, electron-like Fermi surface in this archetypal high Tc superconductor. The true topology of the normal state Fermi surface remains that of hole-like barrels centred at the X,Y points of the Brillouin zone.

Fermi surface contours of p(2×2)O/Mo(110): an angle-resolved photoelectron spectroscopy study

We present the Fermi surface map of p(2×2)O/Mo(110) at room temperature. Changes with respect to the clean surface are discussed. Three surface-state contours (‘hole pockets’) that exist on the clean surface are found to persist on the oxygen-covered surface with slightly changed volumes. The large ‘electron pocket’ shows no significant shift. In combination with a previous electron energy-loss spectroscopy experiment measuring the surface phonon dispersion curves, these data put into question the recently postulated driving force for stabilizing the p(2×2) superstructure in the low-coverage regime.

Full hemispherical photoelectron diffraction and Fermi surface mapping

The routine measurement of full hemispherical photoemission intensity maps gives us the possibility for the combined investigation of structural and electronic phenomena at surfaces. As an example the growth of ultrathin films of Co on Cu(111) is studied as a function of film thickness. While X-ray photoelectron diffraction (XPD) shows the early appearance of stacking faults as a precursor of the hcp structure, Fermi surface maps reveal the very fast evolution of the Co Fermi surface that can be compared to measurements on a clean Co(0001) crystal. For the system O/Rh(111), XPD brings up important structural clues, relating changes in surface reactivity to small amounts of subsurface oxygen, which forces adjacent oxygen atoms to occupy new and more reactive adsorption sites. In the course of this last study we observed for the first time the weak backscattering signals in the angular pattern of adsorbate emission. These cone-like features are extremely sensitive to the adsorbate–substrate bond length.

Joys and Pitfalls of Fermi Surface Mapping inBi2Sr2CaCu2O8+δUsing Angle Resolved Photoemission

On the basis of angle-scanned photoemission data recorded using unpolarized radiation, with high (E,k) resolution, and an extremely dense sampling of k space, we resolve the current controversy regarding the normal state Fermi surface (FS) in Bi(2)Sr(2)CaCu(2)O(8+delta). The true picture is simple, self-consistent, and robust: the FS is holelike, with the form of rounded tubes centered on the corners of the Brillouin zone. Two further types of features are also clearly observed: shadow FSs, which are most likely to be due to short range antiferromagnetic spin correlations, and diffraction replicas of the main FS caused by passage of the photoelectrons through the modulated Bi-O planes.

Remnant Fermi Surface in the Presence of an Underlying Instability in Layered1T–TaS2

We report high resolution angle-scanned photoemission and Fermi surface (FS) mapping experiments on the layered transition-metal dichalcogenide $1T\ensuremath{-}{\mathrm{TaS}}_{2}$ in the quasicommensurate (metallic) and the commensurate (insulating) charge-density-wave (CDW) phase. Instead of a nesting induced partially removed FS in the CDW phase we find a pseudogap over large portions of the FS. This remnant FS exhibits the symmetry of the one-particle normal state FS. Possibly, this Mott localization induced transition represents the underlying instability responsible for the pseudogapped FS.

Photoemission spectroscopy in metals:

Angular resolved photoelectron spectroscopy plays a key role in the study of the electronic structure of solids. We discuss recent methodical developments in its application to metallic systems. These include a new procedure for absolute E(k) band structure determination, which allows complete control of the three-dimensional wave-vector k, as well as a method for Fermi surface mapping based on measurements of the angular photoelectron intensity distribution. Going beyond a simple one-electron picture, we examine under which conditions the photoemission signal can be interpreted in terms of the electron removal spectrum of an interacting electron system and discuss an experimental test on a suitable Fermi liquid metal, which supports this many-body interpretation.

Fermi surface study of pseudomorphic Fe1−xNix and Co1−xNix thin films on Cu(100)

We report angle resolved photoemission studies of the electronic behavior of ultrathin epitaxial layers of fcc structured binary alloys, Fe1−xNix and Co1−xNix, deposited by molecular beam epitaxy on Cu(100) substrates. In particular, we have used Fermi surface mapping to monitor changes in the Fermi surface with increasing magnetization density. Fe1−xNix and Co1−xNix binary alloys show a different behavior in the bulk. Co1−xNix is structurally and magnetically well-behaved. In particular, the magnetic moment varies linearly as a function of concentration. This is in sharp contrast to fcc Fe1−xNix which displays a magnetic instability at ∼65% Fe content. An extended regime of fcc stability is possible via epitaxy on Cu(100). The changes in the Fermi surfaces of Fe1−xNix and Co1−xNix pseudomorphic film alloys depending on various concentrations of Ni have been investigated in a large photon energy regime. We address the following question: To what degree is the Fermi surface sharply preserved in substitutional alloys?

New aspects of the QC-phase in layered 1T-TaS2

Abstract We present Fermi surface (FS) mapping measurements obtained by photoemission for the quasi-commensurate charge density wave (CDW) phase of layered 1T-TaS2. The topology of the FS is rather dominated by the undistorted (1×1) symmetry than by the CDW-induced ( 13 × 13 ) phase. CDW effects can be seen in terms of nesting properties of the FS. Compared to one-electron band structure calculations we observe changed FS contours of Ta 5d-derived electron pockets around the M,M′ points of the (1×1) Brillouin zone. Low energy electron diffraction measurements support the view of a quasi-commensurate CDW.

Complete k-space mappings of cuprates at different doping levels

We present full Fermi surface maps of differently doped Bi 2Sr 2CaCu 2O 8+ x crystals measured with angle-resolved photoemission. We find, for overdoped and optimally doped samples, a large Fermi surface centered at ( π, π). For an underdoped sample with a T c of 30K the contours of a large Fermi surface are still visible, but the photoelectron intensity is strongly reduced around ( π,0). The valence band maximum of the undoped antiferromagnetic insulator Sr 2CuO 2Cl 2 forms maxima at ( π/2, π/2) and equivalent points.

Temperature-dependent electronic structure of nickel metal

An extended set of temperature-dependent ARUPS data from Ni(111) is presented. The ferromagnetic and the paramagnetic state as well as the phase transition are examined in great detail. Rather new and unconventional modes of data acquisition in ARUPS are applied with high angular and energy resolution, exhibiting great power near the Fermi energy ${E}_{F}.$ Even up to ${5k}_{B}T$ above ${E}_{F}$ energy bands are readily observed. The understanding of these ARUPS data is strongly enhanced by spin-polarized band structure calculations. Exchange-split bands of both, $\mathrm{sp}$- and $d$-character, are resolved in angular scans and in photoemission Fermi-surface maps. From two-dimensional data sets in energy and angle the dispersion and the exchange splitting are obtained with high precision. All the observed $\mathrm{sp}$- and $d$-bands clearly exhibit a Stoner-like collapsing-band behavior. The exchange splitting $\ensuremath{\Delta}{E}_{\mathrm{ex}}$ vanishes above ${T}_{C}$ in all cases, and $\ensuremath{\Delta}{E}_{\mathrm{ex}}$ closely follows the temperature dependence of the macroscopic magnetization. The apparent deviations from the Stoner-like band behavior stated in P. Aebi et al., Phys. Rev. Lett. 76, 1150 (1996) are explained. Furthermore we detect anomalously high intensity from a minority $d$-band close to an $\mathrm{sp}$-band. This strongly suggests that $sp\ensuremath{-}d$-fluctuations at the Fermi level are a driving force for the magnetic phase transition of nickel.

Quasi-particle spectra and Fermi surface mapping

Abstract The low-lying electronic excitations of conventional metals can be described as quasi-particles with characteristic spectral properties which can in principle be probed by angle-resolved photoelectron spectroscopy (ARPES). Data taken on a suitable Fermi liquid (FL) material are discussed in terms of quasi-particle energy renormalization and lifetime width narrowing towards the Fermi level. In contrast, the unusual behavior observed in the spectra of a quasi-one-dimensional metal indicates a possible breakdown of the quasi-particle picture. I further discuss the mapping of Fermi surfaces using ARPES in the constant energy mode and suggest a method for precise Fermi vector determination based on FL properties.