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Surface hall effect and nonlocal transport in SmB₆: evidence for surface conduction.

Kim DJ, Thomas S, Grant T, Botimer J, Fisk Z, Xia J - Sci Rep (2013)

Bottom Line: A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations.We report in large crystals of topological Kondo insulator (TKI) candidate material SmB₆ the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations.These results serve as proof that at low temperatures SmB₆ has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

View Article: PubMed Central - PubMed

Affiliation: 1] Dept. of Physics and Astronomy, University of California, Irvine, California 92697, USA [2].

ABSTRACT
A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. The surface transport, however, remains difficult to isolate from the bulk conduction in most existing TI crystals (particularly Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB₆ the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations. These results serve as proof that at low temperatures SmB₆ has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

No MeSH data available.


Related in: MedlinePlus

Surface Hall effect.(a), Markers, Hall resistances Rxy divided by magnetic field B versus temperature T at three different thicknesses d in a wedge shaped sample S1. Lines are simulations using a two conduction channel model (see text). Left inset, picture of the crystal before wiring. Right inset, measurement schematic. (b), Markers, ratios between Hall resistances Rxy at different d, showing the transition from bulk to surface conduction as temperature is lowered. Lines are calculated from simulations as in (a). (c), Rxy versus B at various T for d = 120 μm, showing nonlinearity at around 5 K. (d), Rxy/B normalized to small field values to demonstrate the nonlinearity.
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f1: Surface Hall effect.(a), Markers, Hall resistances Rxy divided by magnetic field B versus temperature T at three different thicknesses d in a wedge shaped sample S1. Lines are simulations using a two conduction channel model (see text). Left inset, picture of the crystal before wiring. Right inset, measurement schematic. (b), Markers, ratios between Hall resistances Rxy at different d, showing the transition from bulk to surface conduction as temperature is lowered. Lines are calculated from simulations as in (a). (c), Rxy versus B at various T for d = 120 μm, showing nonlinearity at around 5 K. (d), Rxy/B normalized to small field values to demonstrate the nonlinearity.

Mentions: Hall effect measurements were carried out in wedge-shaped SmB6 crystals. As depicted in the inset in Fig. 1(a), the sample is placed in a perpendicular magnetic field and current I flows between the two ends of the wedge. The Hall resistances Rxy = Vxy/I are measured at different thicknesses d to distinguish between surface and bulk conduction. For bulk conduction, while Rxy/B is d-independent if surface conduction dominates. In both cases, one can define a Hall coefficient RH = Ey/jxB independent of B, where jx is the current density (surface or bulk) and Ey is the transverse electric field. The Hall voltage Vxy is found to be linear with B (Fig. 1(c) (d)) at small fields at all temperatures, but becomes significantly nonlinear for larger fields around 5 K, indicating a temperature regime of multichannel conduction. At high (20 K) or low (2 K) temperatures, the extreme linearity of the Hall effect indicates single channel conduction, either from the bulk or surface. For the simplest case of one surface conduction channel (top and bottom surfaces combined) and one bulk channel with Hall coefficients RHS, RHB and resistivity ρS, ρB respectively, the Hall resistance Rxy at magnetic field B is . Nonlinearity is expected at large B, but at small fields it simplifies to , which indeed gives thickness-independent Rxy/B = RHS if the surface channel dominates (i.e. ρB ≫ ρSd). From B < 1 T data we extract the value Rxy/B at various temperatures T. Representative results in sample S1 are plotted in Fig. 1(a) for d = 120, 270, and 320 μm respectively, showing clearly that while at high temperatures Rxy/B differ at different d, they converge to a same universal value of 0.3 Ω/T below 4 Kelvin, consistent with surface conduction. Since more than one surface channels may exist, as predicted by theory2829, it is difficult to quantitatively extract the surface carrier density and mobility at this stage. Replotting the Hall resistance ratios Rxy(d1)/Rxy(d2) in Fig. 1(b), we found these ratios to be equal to d2/d1 at high T and become unity at low T, proving the crossover from 3D to 2D Hall effects when T is lowered. The temperature dependence is well described by a two-channel (bulk and surface) conduction model in which the bulk carrier density decreases exponentially with temperature with an activation gap Δ = 38 K. Using this simple model, we could reproduce the curious “peak” in Rxy/B at 4 K (solid lines in Fig. 1(a)), which lacks31 a good explanation until now. Low temperature surface-dominated conduction would also give rise to a longitudinal resistance Rxx that is independent of sample thickness, which we have demonstrated recently32.


Surface hall effect and nonlocal transport in SmB₆: evidence for surface conduction.

Kim DJ, Thomas S, Grant T, Botimer J, Fisk Z, Xia J - Sci Rep (2013)

Surface Hall effect.(a), Markers, Hall resistances Rxy divided by magnetic field B versus temperature T at three different thicknesses d in a wedge shaped sample S1. Lines are simulations using a two conduction channel model (see text). Left inset, picture of the crystal before wiring. Right inset, measurement schematic. (b), Markers, ratios between Hall resistances Rxy at different d, showing the transition from bulk to surface conduction as temperature is lowered. Lines are calculated from simulations as in (a). (c), Rxy versus B at various T for d = 120 μm, showing nonlinearity at around 5 K. (d), Rxy/B normalized to small field values to demonstrate the nonlinearity.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3818682&req=5

f1: Surface Hall effect.(a), Markers, Hall resistances Rxy divided by magnetic field B versus temperature T at three different thicknesses d in a wedge shaped sample S1. Lines are simulations using a two conduction channel model (see text). Left inset, picture of the crystal before wiring. Right inset, measurement schematic. (b), Markers, ratios between Hall resistances Rxy at different d, showing the transition from bulk to surface conduction as temperature is lowered. Lines are calculated from simulations as in (a). (c), Rxy versus B at various T for d = 120 μm, showing nonlinearity at around 5 K. (d), Rxy/B normalized to small field values to demonstrate the nonlinearity.
Mentions: Hall effect measurements were carried out in wedge-shaped SmB6 crystals. As depicted in the inset in Fig. 1(a), the sample is placed in a perpendicular magnetic field and current I flows between the two ends of the wedge. The Hall resistances Rxy = Vxy/I are measured at different thicknesses d to distinguish between surface and bulk conduction. For bulk conduction, while Rxy/B is d-independent if surface conduction dominates. In both cases, one can define a Hall coefficient RH = Ey/jxB independent of B, where jx is the current density (surface or bulk) and Ey is the transverse electric field. The Hall voltage Vxy is found to be linear with B (Fig. 1(c) (d)) at small fields at all temperatures, but becomes significantly nonlinear for larger fields around 5 K, indicating a temperature regime of multichannel conduction. At high (20 K) or low (2 K) temperatures, the extreme linearity of the Hall effect indicates single channel conduction, either from the bulk or surface. For the simplest case of one surface conduction channel (top and bottom surfaces combined) and one bulk channel with Hall coefficients RHS, RHB and resistivity ρS, ρB respectively, the Hall resistance Rxy at magnetic field B is . Nonlinearity is expected at large B, but at small fields it simplifies to , which indeed gives thickness-independent Rxy/B = RHS if the surface channel dominates (i.e. ρB ≫ ρSd). From B < 1 T data we extract the value Rxy/B at various temperatures T. Representative results in sample S1 are plotted in Fig. 1(a) for d = 120, 270, and 320 μm respectively, showing clearly that while at high temperatures Rxy/B differ at different d, they converge to a same universal value of 0.3 Ω/T below 4 Kelvin, consistent with surface conduction. Since more than one surface channels may exist, as predicted by theory2829, it is difficult to quantitatively extract the surface carrier density and mobility at this stage. Replotting the Hall resistance ratios Rxy(d1)/Rxy(d2) in Fig. 1(b), we found these ratios to be equal to d2/d1 at high T and become unity at low T, proving the crossover from 3D to 2D Hall effects when T is lowered. The temperature dependence is well described by a two-channel (bulk and surface) conduction model in which the bulk carrier density decreases exponentially with temperature with an activation gap Δ = 38 K. Using this simple model, we could reproduce the curious “peak” in Rxy/B at 4 K (solid lines in Fig. 1(a)), which lacks31 a good explanation until now. Low temperature surface-dominated conduction would also give rise to a longitudinal resistance Rxx that is independent of sample thickness, which we have demonstrated recently32.

Bottom Line: A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations.We report in large crystals of topological Kondo insulator (TKI) candidate material SmB₆ the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations.These results serve as proof that at low temperatures SmB₆ has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

View Article: PubMed Central - PubMed

Affiliation: 1] Dept. of Physics and Astronomy, University of California, Irvine, California 92697, USA [2].

ABSTRACT
A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. The surface transport, however, remains difficult to isolate from the bulk conduction in most existing TI crystals (particularly Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB₆ the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations. These results serve as proof that at low temperatures SmB₆ has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

No MeSH data available.


Related in: MedlinePlus