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Inverted Resistance Measurements as a Method for Characterizing the Bulk and Surface Conductivities of Three-Dimensional Topological Insulators
Phys. Rev. Applied 9, 044006 – Published 5 April, 2018
DOI: https://doi.org/10.1103/PhysRevApplied.9.044006
Abstract
We introduce a 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 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 , where and are the bulk and surface conductivities of the material, respectively. We call this type of measurement inverted resistance measurement, as the resistance scales inversely with the bulk resistivity. We discuss possible implementations of this 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 , a topological Kondo insulator, using both single-sided and coaxially aligned double-sided Corbino disk transport geometries. Using this 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.
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References (17)
- E. H. Hall, On a new action of the magnet on electric currents, Am. J. Math. 2, 287 (1879).
- O. M. Corbino, Electromagnetic actions due to ions in a metal deflected from the normal trajectory as a result of field, Nuovo Cimento 1, 397 (1911).
- D. A. Kleinman and A. L. Schawlow, Corbino disk, J. Appl. Phys. 31, 2176 (1960).
- L. J. van der Pauw, A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape, Philips Tech. Rev. 20, 220 (1958).
- I. Vurgaftman, J. Meyer, C. Hoffman, D. Redfern, J. Antoszewski, L. Faraone, and J. Lindemuth, Improved quantitative mobility spectrum analysis for Hall characterization, J. Appl. Phys. 84, 4966 (1998).
- L. Fu, C. L. Kane, and E. J. Mele, Topological Insulators in Three Dimensions, Phys. Rev. Lett. 98, 106803 (2007).
- J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75, 121306 (2007).
- D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature (London) 452, 970 (2008).
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5, 398 (2009).
- Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Experimental realization of a three-dimensional topological insulator, , Science 325, 178 (2009).
- M. Brahlek, N. Koirala, N. Bansal, and S. Oh, Transport properties of topological insulators: Band bending, bulk metal-to-insulator transition, and weak anti-localization, Solid State Commun. 215, 54 (2015).
- M. Dzero, K. Sun, V. Galitski, and P. Coleman, Topological Kondo Insulators, Phys. Rev. Lett. 104, 106408 (2010).
- T. Takimoto, : A promising candidate for a topological insulator, J. Phys. Soc. Jpn. 80, 123710 (2011).
- R. M. Martin and J. Allen, Theory of mixed valence: Metals or small gap insulators, J. Appl. Phys. 50, 7561 (1979).
- J. W. Allen, B. Batlogg, and P. Wachter, Large low-temperature Hall effect and resistivity in mixed-valent , Phys. Rev. B 20, 4807 (1979).
- S. Wolgast, C. Kurdak, K. Sun, J. W. Allen, D.-J. Kim, and Z. Fisk, Low-temperature surface conduction in the Kondo insulator , Phys. Rev. B 88, 180405 (2013).
- Y. S. Eo, A. Rakoski, J. Lucien, D. Mihaliov, C. Kurdak, P. R. Rosa, D.-J. Kim, and Z. Fisk, Robustness of the insulating bulk in the topological Kondo insulator, , arXiv:1803.00959.
