Momentum microscopy of single crystals with detailed surface characterisation

Abstract

We report the in situ preparation of surfaces of the proposed topological Kondo insulator SmB by controlled cycles of Ar ion sputtering and annealing. The procedure provides a reproducible way for the preparation of Sm- or B-rich surface terminations by low (1080 C) or high (1200 C) temperature annealing. The surface quality and termination were checked by low energy electron diffraction and Auger electron spectroscopy. Photoemission studies were carried out using momentum microscopy and two laboratory light sources providing polarised radiation with an energy of 6 eV (fourth harmonic of a pulsed Ti:Sapphire laser) and unpolarised radiation with an energy of 21.2 eV (He–I line of a gas discharge lamp). Full dispersions of electronic states in a wide two-dimensional momentum space were obtained by momentum microscopy from the in situ prepared Sm-terminated surface. The shape of the Fermi surface is discussed based on the sections through the bulk Brillouin zone sampled by the different photon energies.

Keywords:

• Momentum microscopy
• 2D-ARPES
• SmB
• Sm termination
• surface preparation

Notes

No potential conflict of interest was reported by the authors.

Present address: Johannes-Gutenberg-Universität Mainz, Institut für Physik, 55128 Mainz, Germany.

1 In the A–B binary alloy system, the congruent melting compound of an A–B phase can coexist with its liquid state of the same composition. Therefore, a crystal with the same composition before melting is separated out with FZ scanning. The Sm-B phase diagram is given in [34].

2 For materials with incongruent melting properties, the composition in the molten zone is different from the stoichiometric ratio of the resulting crystal. For instance, in the case of the Kondo insulator YbB, the Yb/B ratio in the molten zone needs to be less than 1/12 [35].

3 and were measured by a commercial instrument (PPMS, Physical Property Measurement System, Quantum Design Inc. (QD)) and by a SQUID magnetometer, MPMS (Magnetic Property Measurement System, QD)

4 The pyrometer was used without a red filter, still obtaining visually equal colour and brightness of the filament in front of the sample, suggesting a wavelength-independent emissivity. An emissivity of 0.77 has been reported in [40]. As an upper bound for the error introduced by the neglect of the emissivity, we use the equation (5) given in [41] for spectral radiation pyrometers and obtain a relative error of 1% at 1070 K (wavelength 500 nm). We note, that in this case, a pyrometer working in the visible range introduces a smaller error than infrared pyrometers due to (1) the higher emissivity as compared to the infrared and (2) the error being directly proportional to the wavelength [41]. The precision of temperature readings by visually recognising the disappearing filament condition is assumed to be K.

5 We use the high-symmetry point labels pertaining to the surface Brillouin zone (marked by bars on top) regardless of bulk origin or surface origin of the discussed electronic states in order to indicate positions in our momentum images in a simple way. For labels such as , and , the component of the wave vector shall be understood to be unspecified.

6 The wave vectors for the k-path on the abscissa of Figure 7(e) and (f), along which the DFT-LDA band structure was evaluated, read for the points labelled , and , respectively.

7 Along the axis, the photoelectron state is even in , the photon operator for s-polarisation is odd in and the photoemission transition matrix element vanishes if the initial state is even in .

8 A recent review article [54], containing a detailed discussion of the work functions of hexaborides, still cites the value of 4.2 eV for SmB. One work [55] reported a value of 3.1 eV for the thermionic work function (measured at temperatures around 1100 C). However, thermionic work functions are typically lower (by up to 0.5 eV) than photoelectric work functions [56].

10 Deviating from the reference, we use a definition of which includes the number of electrons in the ionised subshell.

11 Input parameters for calculating from the database are the density of SmB (5.0733 g/cm), the band gap (0 eV), the number of valence electrons ( from the boron and samarium atoms, respectively), and the emission angle (30). The TPP-2M equation [71] has been chosen for evaluation of the inelastic mean free path.

Additional information

Funding

This work was supported by the BMBF [grant number 05K12EF1].