# Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

## Abstract

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TImore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22210466

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Experimental and Theoretical Physics

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 3; Other Information: Copyright (c) 2013 Pleiades Publishing, Inc.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTIVATION ENERGY; COMPUTERIZED SIMULATION; DENSITY; DOPED MATERIALS; IMPURITIES; POTENTIALS; RELATIVISTIC RANGE; SCREENING; SEMICONDUCTOR MATERIALS; SURFACES; SYMMETRY BREAKING; TEMPERATURE RANGE 0065-0273 K; THREE-DIMENSIONAL CALCULATIONS; TITANIUM SULFIDES; TOPOLOGY; TRANSPORT THEORY

### Citation Formats

```
Skinner, B., Chen, T., and Shklovskii, B. I., E-mail: shklovsk@physics.spa.umn.edu.
```*Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators*. United States: N. p., 2013.
Web. doi:10.1134/S1063776113110150.

```
Skinner, B., Chen, T., & Shklovskii, B. I., E-mail: shklovsk@physics.spa.umn.edu.
```*Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators*. United States. doi:10.1134/S1063776113110150.

```
Skinner, B., Chen, T., and Shklovskii, B. I., E-mail: shklovsk@physics.spa.umn.edu. Sun .
"Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators". United States. doi:10.1134/S1063776113110150.
```

```
@article{osti_22210466,
```

title = {Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators},

author = {Skinner, B. and Chen, T. and Shklovskii, B. I., E-mail: shklovsk@physics.spa.umn.edu},

abstractNote = {In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.},

doi = {10.1134/S1063776113110150},

journal = {Journal of Experimental and Theoretical Physics},

issn = {1063-7761},

number = 3,

volume = 117,

place = {United States},

year = {2013},

month = {9}

}