Supplementary information for. Atomically resolved spectroscopic study of Sr 2 IrO 4 : Experiment and theory

Transcription

1 Supplementary information for Atomically resolved spectroscopic study of Sr 2 IrO 4 : Experiment and theory Qing Li 1,9,, Guixin Cao 2,3,, Satoshi Okamoto 3, Jieyu Yi 2,3, Wenzhi Lin 1, Brian C. Sales 3, Jiaqiang Yan 2,3, Ryotaro Arita 4,5, Jan Kunes 6, Anton V. Kozhevnikov 7, Adolfo G. Eguiluz 8, Masatoshi Imada 4,5, Zheng Gai 1, Minghu Pan 1,, David G. Mandrus 2,3, 1 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 2 Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA 3 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 4 Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, , Japan 5 JST-CREST, Hongo, Bunkyo-ku, Tokyo, , Japan 6 Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka 10, Praha 6, , Czech Republic 7 Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland 8 Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA 9 Institute of Functional Nano & Soft Materials (FUNSOM), Soochow University, Suzhou, Jiangsu , China These authors contributed equally to this work. panm@ornl.gov and dmandrus@utk.edu

2 1. Temperature dependented Low-Energy Electron Diffraction (LEED) Our LEED measurements at RT show clear 1 1 diffraction point, indicating a dominate (001) terminate surface. Additionally, 2 2 defraction point is also observed and it represents the RuO6 octahedral rotation of Sr 2 RuO 4. We also performed the temperature dependent LEED measurements (fig. S1) and did not find clear changes of the diffraction pattern from 166 K to RT (Neer Temperature is about 240 K). Therefore we can conclude that the metal to insulator transition of Sr 2 IrO 4 is not accompanied with structrual change. Fig. S1. LEED patterns acquired at different temperatures (166 K, 203 K, 225 K and 277 K).

3 2. Determination of high index facet in Sr 2 IrO 4 From the height profile along the blue line in fig. S2a, the angle between the orientations of the two surfaces is about 50. This help to find which plane this exposed high-index facet is. There are several reasons to assign this facet to (661); this plane orients in the angle about 47 with (001) surface, in good agreement with the experimental observation. Most important, atomic resolved STM image in this plane indicates a pseudo-hexagonal surface structure, which can only be found in this (661) surface. Tetragonal crystalline structure of Sr 2 IrO 4, make the hexagonal lattice only possible at special exposed plane. Besides that, the size of the pseudohexagonal lattice of (661) facet is in good agreement with the experimental value. Fig. S2. Determination of the (661) surface. (a), 3D landscape of the scan area, showing two different orientated surfaces after cleaving. The height profile across two surfaces is plotted at the bottom panel, displaying the angle between two surfaces is about 50. (b), Proposed (661) plane and (001) plane, both highlighted with purple color in the unit cell of Sr 2 IrO 4. The angle between these two planes is calculated as 47. The (661) plane has a clear pseudo-hexagonal surface structure.

4 3. Fiting the STS gap with different gap symmetries An STM tip collects electrons from all directions in the sample indiscriminatly. Therefore, the DOS curves meausred by an STM are an average over k-space. For many materials, e.g. conventional superconductor, the gap symmetry is isotropic s-wave. In such case, k-dependence of gap Δ(k) is constant as a function of angle. Therefore, when the STM averages over angle, the resultant DOS shows a square gap shape. For comparison, the gap in d-wave superconductor cuperates has four-fold symmetric k- dependence. An electron entering the tip from one direction may see a 30 mev square gap, while the electron from another direction may see no gap. The average of all the directions gives a V- shaped gap in tunneling spectrum. However, neither a isotropic, square gap nor v-shaped gap can be fitted to the inulating gap of Sr 2 IrO 4. The gap in Sr 2 IrO 4 has to be anisotropic, reflecting the d-symmetry of 5d electron nature. In ab plane (which is the (001) surface), gap Δ(k) is angle-dependent, having four-fold symmetry. However, distinct from d-wave superconducting gap in cuperates, k-denpendence of gap Δ(k) has non-zero minimum. A formula for the gap as a function of angle, can be described by: 2 1 cos 6 The lowest order terms consistent with d 2 x - 2 y symmetry are cos(2θ) and cos(6θ). A proposed Δ(k) for Sr 2 IrO 4 is shown in Fig. 2(d), which has d-symmetry and non-zero gap minimum. Such gap landscape can fit better to the experimental gap (Fig. 2(d)). For high-index facet, e.g. the (611) surface, various ansotropic gap landscapes were tested and a two-fold symmetric landscape (shown in Fig. 2(d)) was assigned to this facet. With such anglegap-dependence, the gap in the (611) surface can be fitted exceptionally well (Fig. 2(c)). 4. The tilt distortion of surface IrO 6 If the surface has the same symmetry as the bulk (bulk-truncated), the LEED pattern should look like Fig. 1(a), where circles represent pattern expected from tet - (1 1) structure, and solid dots are fractional spots with the appearance due to ( 2 2)R45 unit cell. Considering the structure factor, the fractional spots (circles) will extinct along the two glide lines, which are represented by dash lines in Fig. R3b and c, as observed on the surface of Sr 2 RuO 4. Under this

5 rotational distortion, the surface still maintains C4v symmetry. If there is the tilt distortion of surface octahedron, the C4v symmetry will be broken by inducing two domains, thus eliminating both glide lines. Therefore, the fractional spots will appear in such case. Here we show the LEED image taken both below and above T N. Both LEED patterns show weak fractional spots appearing along two glide lines, which suggest there is a slight tilt distortion of IrO6 octahedron on this surface. The effect of surface octahedron tilting on the electronic ground state remains unknown and such discussion is beyond the scope of this paper. At least in our STS results on (001) surface, such effect doesn t cause a dramatic change of electronic ground state of material. (As we know, the tilt distortion of IrO 6 octahedron lowers the symmetry of Sr 2 IrO 4 and results in a four times larger unit cell. Martins et al. 1 compared the band structure of Sr 2 IrO 4 with/without considering structural distortion, and found the structural distortions may help to form an insulating state.) Fig. S3: (a) A schematic view of LEED pattern expected with rotated octahedra without tilt. The tet - (1 1) real space periodicity generates the diffractional spots (solid dots) with a reciprocal unit cell marked in black square. The ( 2 2)R45 real space periodicity produces fractional spots (circles) as the reciprocal lattice with its unit cell marked in red dashed square. Two glides are indicated by dashed lines along which fractional spots (marked by arrows) are extinct. (b) and (c) Experimental images of LEED pattern taken at 166 K and RT at 225eV for Sr 2 IrO 4, respectively. 5. Comparision of gaps observed on different surfaces 1 Martins et al., Phys. Rev. Lett. 107, (2011)

6 Although the gap features are different, however, the observed gap in (661) has similar gap size as the one measured on (001) surface, as mentioned in the main text. The reason for showing STS on (661) facet instead of the curve on (001), is that the STS on (661) facet has well-defined gap feature. Here we present the STS curves showing gaps measured simultaneously on (001) terrace and (661) facet at different temperature points (4.2 K, 78 K, 135 K and 195 K). As shown in this figure (Fig. S4), we can see the gap on both two surfaces has similar size and temperature dependence. Fig. S4. Tunneling spectra taken simultaneously on (001) terrace and (661) facet at different temperature points (4.2 K, 78 K, 135 K and 195 K) 6. Band strucutre calculation

7 Fig. S5. Band structure of Sr 2 IrO 4 calculated by GGA+U with the spin-orbit coupling and the antiferromagneic ordering. Parameter values are indicated in the text.