SUPPLEMENTARY INFORMATION

Transcription

1 Topological surface state in the Kondo insulator samarium hexaboride D. J. Kim, J. Xia and Z. Fisk 1 Sample quality and thickness reduction The key feature of SmB 6 resistance is an exponential rise with cooling with low temperature saturation. However, the order of magnitude, saturation rate, and saturation point of resistance rise are not sample independent for samples from different batches. Usually higher purity elements (Sm, B) including flux material, Al, make larger increase with slightly lower saturation temperature (see Fig. S1 a). The high quality sample and thickness reduction with well defined rectangular parallelipiped geometry are two important requirements for the resistance ratio measurement. We chose samples with well-defined facets for reference and shaped them with Al 2 O 3 polishing pads (usually starting from 30 µm and ending with 50 nm roughness pad) into parallelipipeds. Then, we used dilute HCl (50 HCL + 50 DI water) for 2 minutes to remove possible oxidation on the surface. After drying the sample, the electrical leads were made with thermocouple grade 25 µm thick platinum wires by spot welding. After measuring the thickness with microscope reticule, the resistance temperature dependence was precisely measured at each stabilized temperature with a high resolution AC resistance bridge and Quantum design PPMS. An important point is that the thermal cycle (cooling down and warming up), mounting sample on the polishing fixture with wax, and following chemical treatment (Acetone, IPA, HCL etching) should not change the resistance dependence with temperature for the same thickness sample to avoid any possible artifact from measurement setup (drift, offset, thermal cycling effect) and chemical reaction or contamination (see Fig. S1 b). Measuring resistance versus temperature for one thickness, the reduced thickness data was measured with exactly the same sample with the original leads. First, the same sample with the original leads was flipped to mount on the fixture, and the leads were carefully pressed so as not to be destroyed during the polishing. Figure S1 c shows the procedure for thickness reduction. NATURE MATERIALS 1

2 Figure S1 Sample quality, reproducibility, and thickness reduction. a, resistance versus temperature curves from two different batches. b, resistance ratio versus temperature, the first run is measured with the initial condition of c and the second run is measured with the final condition of c without polishing. c, sample thickness reduction procedure. 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION 2 Transition from positive to negative magneto-resistance Usually f-orbital Kondo insulators show negative magnetoresistance associated with Kondo screening breaking which eventually evolves to positive when they become a more metallic bulk conductor at higher temperature. One possible conjecture for TKI would be a sign change of magneto resistance with field, from positive at low field to negative at high field. This happens in high purity SmB6 samples (see Fig. S2 a). However, this transition is not unique to temperatures below the complete gap opening temperature. Even above 10 K with magnetic or non-magnetic impurity doped the samples show a similar transition (see Fig. S2 b). Thus this field dependence is not clear support for the TKI state. NATURE MATERIALS 3

4 Figure S2 Sign change of magneto-resistance. a, resistance versus external magnetic field curves for pure SmB 6 at 480 mk and 2 K. b, resistance versus external field of doping samples at 10 K. 3. Magnetic property of Yb doped SmB 6 Impurities with magnetic moments on Sm sites usually contribute to the magnetic properties of the doped samples significantly in magnetic susceptibility and magnetization curve,as in Gd doped samples. We find that divalent Yb, which has no magnetic moment in free ion form, does not show a magnetic moment in SmB 6 and does not disturb the insulating properties in host bulk as do Y and Gd impurities. Figure S3 shows magnetic susceptibility curve for 18% Yb doped SmB 6 at 1000 Oe and magnetization curve (inset) compared with pure SmB 6. Yb sites appear as a magnetic vacancy in those curves. The non-magnetic doping shifts the peak and valley positions as in other non-magnetic doped samples. The estimation of Yb concentration from the high temperature regime is very close the nominal concentration. 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION Figure S3 Magnetic properties of Yb doped SmB 6. Magnetic susceptibility (1000 Oe external field) and magnetization (inset) curves of high purity pure and 18% Yb doped SmB Physical properties of single crystal YbB 6 It is necessary to be clear whether or not Yb is divalent in the RB 6 crystal structure and to confirm that YbB6 does not converge to a topological insulator to support the nonmagnetic impurity model. Figure S4 a and b show resistivity and resistance ratio with thickness. Unlike SmB6, there is no clear evidence of bulk and surface separation, but rather behavior quite similar to BaB 6. The positive quadratic magnetoresistance in Fig S4 c without any oscillation supports bulk conduction. Finally, the temperature dependent magnetic susceptibility shows a tiny diamagnetism approaching zero at the base temperature. Thus, the role of Yb as a non-magnetic impurity in SmB 6 crystal is clear. Even if pure YbB 6 is a TI, it would be very bulk conductive one like Bi based TIs. NATURE MATERIALS 5

6 ρ (mω cm) Pure YbB 6 resistivity at zero field a Resistance Ratio YbB 6 resistance ratio (Thickness 170 μm / Thickness 440 μm) b Temperature (K) ρ (mω cm) Pure YbB 6 magnetoresistance at 2 K c χ (emu/mole) Pure YbB 6 d magnetic susceptibility at 0.1 T H ( T) Figure S4 Physical properties of YbB 6. a resistivity versus temperature. b, resistance ratio over thickness. c, magnetoresistance. d, magnetic susceptibility over temperature. 5. Effect of Gd doping level to the surface state in SmB 6 Magnetic impurities change both the bulk Kondo insulating state and the surface conduction state. 0.1% Gd doping SmB 6 exhibits virtually identical behavior in its resistance and resistance ratio curves to pure SmB6 as shown in Fig. S5 a. The right inset of Fig. S5 a shows that the same sample used in transport exhibits in the magnetometer that there is a small substitution of Gd on Sm sites. Figure. S5 b shows that 40% Gd doped sample no longer has insulating property, the resistance ratio being flat and the resistance itself no longer having an exponential dependence with temperature suggesting a bulk metallic state. 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION % Gd doped Sm B6 resistance ratio thickness 120 μm / thickness 250 μm a Resistance Ratio R (Ω) Ω at 500 mk 6.6 mω at 300 K χ (emu / mole) % Gd doped SmB6 resistance ratio thickness 150 μm / thickness 310 μm 0.1% Gd doping Pure SmB b Resistance Ratio R (Ω ) Figure S5 0.1% and 40% Gd doping. a, resistance ratio of 0.1% Gd doping SmB 6. the right inset is resistance versus temperature of the sample, the left inset is magnetic susceptibility of 0.1% Gd and pure SmB 6. b, resistance ratio of 40% Gd doped SmB 6, the inset is resistance vs temperature curve of the sample. 6. Reproducibility NATURE MATERIALS 7

8 resistance ratio % Y 3% Gd 4% Yb Figure S6 Reproducibility of Figure 2a. 8 NATURE MATERIALS