Resolving unoccupied electronic states with laser ARPES in bismuth-based cuprate superconductors

Abstract

Angle-resolved photoemission spectroscopy (ARPES) is typically used to study only the occupied electronic band structure of a material. Here we use laser-based ARPES to observe a feature in bismuth-based superconductors that, in contrast, is related to the unoccupied states. Specifically, we observe a dispersive suppression of intensity cutting across the valence band, which, when compared with relativistic one-step calculations, can be traced to two final-state gaps in the bands 6 eV above the Fermi level. This finding opens up possibilities to bring the ultra-high momentum resolution of existing laser-ARPES instruments to the unoccupied electron states. For cases where the finalstate gap is not the object of study, we find that its effects can be made to vanish under certain experimental conditions.Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental probe that has been used extensively to image the occupied electronic states of materials in an energy-and momentum-resolved manner [1,2]. Since it is based on Einstein's photoelectric effect, it cannot directly probe a material's unoccupied electronic states, but it has nevertheless provided signatures of gaps in the unoccupied states [3][4][5][6]. According to the one-step model [7], some electrons, after absorbing photons, may have energies which lie between two unoccupied bands. We call the space between the unoccupied bands a finalstate gap, although this gap may be confined to a limited momentum range, and disperse within that range. The photoemission intensity of these electrons is suppressed, but not suppressed completely, due to the finite widths of the final states. These finite widths represent the small chance that electrons interacting with the medium, primarily through electron-hole pair creation and plasmonic interaction, will have energy within the final-state gap. Typically, this final-state effect in ARPES is not used to measure unoccupied states, which are instead mapped by inverse photoemission[8] or very-low-energy electron diffraction [5,[9][10][11][12].Here we show that laser-based ARPES [13][14][15], under certain conditions, can be used to map final-state gaps in the electronic states of a material. This method provides the following advantages with respect to standard synchrotron-based ARPES: (a) improved momentum resolution and greater bulk sensitivity, due to the lower photon energy range available in laser-ARPES (6-7 eV)[13], * alanzara@lbl.gov and (b) access to unoccupied electron states closer to the Fermi level.Data are shown for cuprate superconductors Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) and Bi 2 Sr 2−x La x CuO 6 (La-Bi2201) along the Γ-Y direction of the Brillouin zone, using ∼6 eV laser ARPES. In these measurements, a final-state gap can be seen as a line of suppressed intensity that disperses in momentum.When the final-state gap crosses the photoemitted valence band, it creates a distortion 100-140 meV below the Fermi level, depending on the photon energy. A second distortion is seen at 20-50 meV, indicating...

Revealing the Coulomb interaction strength in a cuprate superconductor

“…Numerical techniques such as division by the Fermi-Dirac distribution have been used to reveal the states slightly above E F [10], yet this method is confined to an energy range on the order of the sample temperature. A recent ARPES study on Bi-based cuprates identified features contributed by unbound states at 6 eV above E F [11]. However, the key quantities of the strong correlation physics in cuprates -the energy scale of the UHB and the Coulomb interaction strength -remain underexplored.…”

Three-dimensional nature of the band structure of ZrTe5 measured by high-momentum-resolution photoemission spectroscopy

“…The resulting dispersions cannot be well described as two distinct bands, as the bands "twist" around each other (as guided by the red dashed curves), and seem to "switch momenta" at certain binding energies (as indicated by the yellow arrows), which change roughly by the same amount as the difference in photon energy. This behavior suggests that the spectrum is modulated by the structure of final states 32 , and therefore cannot be understood solely in the context of a well-defined initial state dispersion. More detailed calculations involving electron final-states are required to fully understand this complexity 33 .…”

Laser angle-resolved photoemission as a probe of initial statekzdispersion, final-state band gaps, and spin texture of Dirac states in theBi2Te3topolog

“…Accessing spin-textures of the TSSs via spin-resolved ARPES (SARPES), on the other hand, has generally proven to be more challenging. For example, circular-dichroism ARPES (CD-ARPES) experiments, where one measures the difference in ARPES intensities for right-and left-circularly polarized light, show that the CD-ARPES spectrum changes sign with photon energy from the same sample of a Bi 2 Te 3 single crystal, making it clear that CD-ARPES cannot provide a probe of the initial state spin structure [15][16][17] . These results are not surprising since it is well-known that spectral intensities in highly resolved spectroscopies such as ARPES depend sensitively on matrix element effects, which in the case of ARPES involve not only the properties of the initial state but also of the final state wave functions [18][19][20] .…”

“…As in our previous laser ARPES studies, we chose a small value of the imaginary part, Σ f " = 0.1 eV (full-width-at-halfmaximum of 0.2 eV), for the final state self-energy 16,17,24 . This value of Σ f " is comparable to the value of 0.2 eV for low photon energies suggested by Strocov et al 25 .…”

“…An ideal Te-terminated surface was assumed. For further details of our methodology for ARPES computations we refer to our earlier publications [15][16][17][18][19][20]26,27 .…”