Length scale of puddle formation in compensation-doped semiconductors and topological insulators

Abstract

In most semiconductors and insulators the presence of a small density of charged impurities cannot be avoided, but their effect can be reduced by compensation doping, i.e. by introducing defects of opposite charge. Screening in such a system leads to the formation of electron-hole puddles, which dominate bulk transport, as first recognized by Efros and Shklovskii. Metallic surface states of topological insulators (TI) contribute extra screening channels, suppressing puddles. We investigate the typical length $l_p$, which determines the distance between puddles and the suppression of puddle formation close to metallic surfaces in the limit where the gap $\Delta$ is much larger than the typical Coulomb energy $E_c$ of neighboring dopants, $\Delta \gg E_c$. In particular, this is relevant for three dimensional Bi-based topological insulators, where $\Delta /E_c\sim 100$. Scaling arguments predict $l_p\sim (\Delta /E_c{)}^2$. In contrast, we find numerically that $l_p$ is much smaller and grows in an extended crossover regime approximately linearly with $\Delta /E_c$ for numerically accessible values, $\Delta /E_c\lesssim 35$. We show how a quantitative scaling argument can be used to extrapolate to larger $\Delta /E_c$, where $l_p\sim (\Delta /E_c{)}^2/\ln (\Delta /E_c)$. Our results can be used to predict a characteristic thickness of TI thin films, below which the sample quality is strongly enhanced.

new version with substantially changed interpretation of numerical results, new first author

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• Fermi-liquid instabilities at magnetic quantum phase transitions
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• Majorana bound states in topological insulators without a vortex
• Current-induced breakdown of the quantum anomalous Hall effect
• Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
• Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder
• Metallization and proximity superconductivity in topological insulator nanowires
• Disorder effects in topological insulator nanowires
• Spatially varying electronic dephasing in three dimensional topological insulators
• Ionic and electronic properties of the topological insulator Bi${}_2$Te${}_2$Se investigated using $\beta$-detected nuclear magnetic relaxation and resonance of ${}^8$Li
• Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder
• Enhanced coherence and decoupled surface states in topological insulators through structural disorder
• Large positive magneto-conductivity at microwave frequencies in the compensated topological insulator BiSbTeSe2
• Nonlinear planar magnetotransport due to tilted Dirac cones in topological materials
• Characterizing the chemical potential disorder in the topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ thin films
• Tracing Dirac points of topological surface states by ferromagnetic resonance
• Plasmons in semiconductor and topological insulator wires with large dielectric constant