A New Method for Characterizing Bulk and Surface Conductivities of Three-Dimensional Topological Insulators: Inverted Resistance Measurements

Abstract

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.

References in corpus (3)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Transport Properties of Topological Insulators: Band Bending, Bulk Metal-to-Insulator Transition, and Weak Anti-Localization

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• Bulk transport paths through defects in floating zone and Al flux grown SmB${}_6$
• Correlation-driven organic 3D topological insulator with relativistic fermions
• Extraordinary Bulk Insulating Behavior in the Strongly Correlated Materials FeSi and FeSb${}_2$
• Correlated Topological Mixed-Valence Insulators in Moiré Hetero-Bilayers
• An STM perspective on hexaborides: Surface states of the Kondo insulator SmB${}_6$
• Observation of the superconducting proximity effect from surface states in SmB${}_6$/YB${}_6$ thin film heterostructures via terahertz spectroscopy