Observation of Landau quantization and standing waves in HfSiS

L. Jiao, Q. N. Xu, Y. P. Qi, S.-C. Wu, Y. Sun, C. Felser, and S. Wirth

Phys. Rev. B 97, 195137 – Published 21 May 2018

Abstract

Recently, HfSiS was found to be a new type of Dirac semimetal with a line of Dirac nodes in the band structure. Meanwhile, Rashba-split surface states are also pronounced in this compound. Here we report a systematic study of HfSiS by scanning tunneling microscopy/spectroscopy at low temperature and high magnetic field. The Rashba-split surface states are characterized by measuring Landau quantization and standing waves, which reveal a quasilinear dispersive band structure. First-principles calculations based on density-functional theory are conducted and compared with the experimental results. Based on these investigations, the properties of the Rashba-split surface states and their interplay with defects and collective modes are discussed.

Received 17 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.195137

Physics Subject Headings (PhySH)

Landau levels Rashba coupling

Node-line semimetals

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Jiao¹, Q. N. Xu¹, Y. P. Qi^1,2, S.-C. Wu¹, Y. Sun¹, C. Felser¹, and S. Wirth^1,*

¹Max-Planck-Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany
²School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China

^*Steffen.Wirth@cpfs.mpg.de

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Vol. 97, Iss. 19 — 15 May 2018

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Images

Figure 1
(a) Crystal structure of HfSiS. The green plane indicates the cleavage position. (b) $18 \times 18 {nm}^{2}$ STM topography of the cleaved S-terminated surface of HfSiS. The image was taken at a tunneling condition of bias voltage $V_{b} = 300$ mV, current set point $I_{set} = 0.8$ pA, and sample temperature $T = 0.35$ K. (c) Typical STS spectra measured on a clean site in a magnetic field of 0 and 12 T with $B ∥ c$ . The spectrum measured at 12 T is offset by 2 a.u. Tunneling conditions used for all the STS measurements are $V_{b} = 0.1$ V and $I_{set} = 0.5$ nA, while the modulation voltage $V_{mod} = 3$ mV. The inset shows the spectrum obtained at 12 T after subtracting a background signal.
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Figure 2
(a) Slab calculation of the band structure of HfSiS along certain high-symmetry directions. The red and blue bands are surface and bulk states, respectively. Black arrow indicates the van Hove singularities corresponding to peak (a) in the bottom panel. (b) Calculated DOS of the slab structure of HfSiS from $- 0.3$ to 0.2 eV.
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Figure 3
(a) Topography of the surface of HfSiS with three different types of defects (marked as $⨁, □$ , and $✠$ in the main text). (b) Contour plot of the 20 $d I / d V$ curves measured along the 20 nm white dotted line in (a). The spectra were obtained at 0.35 K and 12 T. (c) Selected $d I / d V$ curves with a background signal subtracted. Curves are equally offset for clarity. (d) The Landau level number vs bias voltage for the spectra obtained at different conditions as noted in the legend. The solid red line is an expected curve calculated by Eq. (1). The black dashed line is a guide to the eye.
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Figure 4
Magnetic-field-dependent $d I / d V$ curves with a smooth background subtracted. These curves are measured at a clean surface from 7 to 12 T at $T = 0.35$ K. Curves are offset vertically for clarity.
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Figure 5
(a) $25 \times 10 {nm}^{2}$ topography of HfSiS with a sharp step edge. $θ \approx 55^{\circ}$ is the angle between the crystal axis (red dashed line) and the normal of the step edge (white arrow). (b) A line scan [the blue dotted line in (a)] shows the height of the step edge is one unit cell (8 Å). (c) $d I / d V$ curves measured at selected bias voltages along the white dashed line in (a). Data were taken at 0.35 K and 0 T with $V_{b} = 0.2$ V and $I_{set} = 0.4$ nA. Curves are equally shifted for clarity. (d) A contour plot of the $d I / d V$ map measured along the white dashed line at various bias voltages. (e) A Fourier transform of the $d I / d V$ map in (d). The black dashed line is a linear extrapolation of the frequencies of the standing waves. (f) Reproduced Fermi surface of HfSiS reported in our previous calculation [19]. Bulk states (BS) and Rashba surface states (SS) are marked in the plot. (g) A sketched Fermi surface of the Rashba-split surface bands around one of the four $\bar{X}$ points, which is based on the calculation in (f). The pink arrow indicates a possible scattering vector on the Fermi surface with $55^{\circ}$ off the $k_{x}$ direction. Red and green mark the opposite spin orientations of the outer and inner surface-state bands.
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