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We introduce a new resistance measurement method that is useful in characterizing materials with both surface and bulk conduction, such as three-dimensional topological insulators. The transport geometry for this new resistance measurement configuration consists of one current lead as a closed loop that fully encloses the other current lead on the surface, and two voltage leads that are both placed outside the loop. We show that in the limit where the transport is dominated by the surface conductivity of the material, the four-terminal resistance measured from such a transport geometry is proportional to $\sigma_b/\sigma_s^2$, where $\sigma_b$ and $\sigma_s$ are the bulk and surface conductivities of the material, respectively. We call this new type of measurement \textit{inverted resistance measurement}, as the resistance scales inversely with the bulk resistivity. We discuss possible implementations of this new method by performing numerical calculations on different geometries and introduce strategies to extract the bulk and surface conductivities. We also demonstrate inverted resistance measurements on SmB$_6$, a topological Kondo insulator, using both single-sided and coaxially-aligned double-sided Corbino disk transport geometries. Using this new method, we are able to measure the bulk conductivity, even at low temperatures, where the bulk conduction is much smaller than the surface conduction in this material.

SmB$_6$ exhibits a small (15-20 meV) bandgap at low temperatures due to hybridized $d$ and $f$ electrons, a tiny (3 meV) transport activation energy $(E_{A})$ above 4 K, and surface states accessible to transport below 2 K. We study its magnetoresistance in 60-T pulsed fields between 1.5 K and 4 K. The response of the nearly $T$-independent surface states (which show no Shubnikov-de Haas oscillations) is distinct from that of the activated bulk. $E_{A}$ shrinks by 50% under fields up to 60 T. Data up to 93 T suggest that this trend continues beyond 100 T, in contrast with previous explanations. It rules out emerging theories to explain observed exotic magnetic quantum oscillations., Comment: 12 pages, 3 figures

The mixed valent compound SmB6 is of high current interest as the first candidate example of topologically protected surface states in a strongly correlated insulator and also as a possible host for an exotic bulk many-body state that would manifest properties of both an insulator and a metal. Two different de Haas van Alphen (dHvA) experiments have each supported one of these possibilities, while angle resolved photoemission spectroscopy (ARPES) for the (001) surface has supported the first, but without quantitative agreement to the dHvA results. We present new ARPES data for the (110) surface and a new analysis of all published dHvA data and thereby bring ARPES and dHvA into substantial consistency around the basic narrative of two dimensional surface states., Comment: 5 pages, 4 figures + supplement (12 pages, 6 figures)

Topological insulators (TIs) have the singular distinction of being electronic insulators while harboring metallic, conductive surfaces. In ordinary materials, defects such as cracks and deformations are barriers to electrical conduction, intuitively making the material more electrically resistive. Peculiarly, 3D TIs should become better conductors when they are cracked because the cracks themselves, which act as conductive topological surfaces, provide additional paths for the electrical current. Significantly, for a TI material, any surface or extended defect harbors such conduction. In this letter, we demonstrate that small subsurface cracks formed within the predicted 3D TI samarium hexaboride (SmB$_{6}$) via systematic scratching or sanding results in such an increase in the electrical conduction. SmB$_{6}$ is in a unique position among TIs to exhibit this effect because its single-crystals are thick enough to harbor cracks, and because it remarkably does not appear to suffer from conduction through bulk impurities. Our results not only strengthen the building case for SmB$_{6}$'s topological nature, but are relevant to all TIs with cracks, including TI films with grain boundaries., Comment: 10 pages, 2 figures

In Kondo insulator samarium hexaboride SmB$_6$, strong correlation and band hybridization lead to an insulating gap and a diverging resistance at low temperature. The resistance divergence ends at about 5 Kelvin, a behavior recently demonstrated to arise from the surface conductance. However, questions remain whether and where a topological surface state exists. Quantum oscillations have not been observed to map the Fermi surface. We solve the problem by resolving the Landau Level quantization and Fermi surface topology using torque magnetometry. The observed Fermi surface suggests a two dimensional surface state on the (101) plane. Furthermore, the tracking of the Landau Levels in the infinite magnetic field limit points to -1/2, which indicates a 2D Dirac electronic state.

We studied the persistent photoconductivity (PPC) effect in AlGaN/AlN/GaN heterostructures with two different Al-compositions (x=0.15 and x=0.25). The two-dimensional electron gas formed at the AlN/GaN heterointerface was characterized by Shubnikov-de Haas and Hall measurements. Using optical illumination, we were able to increase the carrier density of the Al0.15Ga0.85N/AlN/GaN sample from 1.6x10^{12} cm^{-2} to 5.9x1012 cm^{-2}, while the electron mobility was enhanced from 9540 cm2/Vs to 21400 cm2/Vs at T = 1.6 K. The persistent photocurrent in both samples exhibited a strong dependence on illumination wavelength, being highest close to the bandgap and decreasing at longer wavelengths. The PPC effect became fairly weak for illumination wavelengths longer than 530 nm and showed a more complex response with an initial negative photoconductivity in the infrared region of the spectrum (>700 nm). The maximum PPC-efficiency for 390 nm illumination was 0.011% and 0.005% for Al0.25Ga0.75N/AlN/GaN and Al0.15Ga0.85N/AlN/GaN samples, respectively. After illumination, the carrier density could be reduced by annealing the sample. Annealing characteristics of the PPC effect were studied in the 20-280 K temperature range. We found that annealing at 280 K was not sufficient for full recovery of the carrier density. In fact, the PPC effect occurs in these samples even at room temperature. Comparing the measurement results of two samples, the Al0.25Ga0.75N/AlN/GaN sample had a larger response to illumination and displayed a smaller recovery with thermal annealing. This result suggests that the energy scales of the defect configuration-coordinate diagrams for these samples are different, depending on their Al-composition., Comment: 27 pages, 8 figures

Spin-orbit coupling is studied using the quantum interference corrections to conductance in AlGaN/AlN/GaN two-dimensional electron systems where the carrier density is controlled by the persistent photoconductivity effect. All the samples studied exhibit a weak antilocalization feature with a spin-orbit field of around 1.8 mT. The zero-field electron spin splitting energies extracted from the weak antilocalization measurements are found to scale linearly with the Fermi wavevector with an effective linear spin-orbit coupling parameter 5.5x10^{-13} eV m. The spin-orbit times extracted from our measurements varied from 0.74 to 8.24 ps within the carrier density range of this experiment., Comment: 16 pages, 4 figures