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The Simulation of Quantum Transport in Topological Insulators (TIs) and TI Based Nanoscale Field Effect Transistors (TI FETs)

Project Description

The field of Nanoelectronics is concerned with the materials, devices, circuits and systems relevant to contemporary integrated circuits (ICs). Modern ICs which are the ‘electronic brain’ and memory, inside mobile phones, laptop and desktop PCs are comprised of billions of Field Effect Transistors (FETs). The gate length of such an FET ~ 10 nm, constituting an in service nano-device. The gate is the terminal that controls the current flow through the channel from the source to the drain, thus the FET acts as a switch. At this length scale, where a FET consists of few hundred atoms, quantum mechanics must be applied to decipher the operating principles and the engineer must draw upon the expertise from Condensed Matter Physics. In this project, the electron flow in exotic topological insulator materials, which can be incorporated in the channel of a FET, are investigated numerically.

Topological insulator (TI) materials have burst onto the scene to become a very important topic in condensed matter physics in the last decade {Qi & Zhang, 2011}. Topological insulators are insulators in the bulk but have topologically protected edge current carrying states at the surface. Quantum Transport properties of topologically protected states are also of strong contemporary electrical engineering interest as they act as perfect conducting channels, in potential nanoelectronic interconnects and quantum functional devices. A 2D topological insulator system such as a CdTe/HgTe/CdTe quantum well, above the critical well width shows the Quantum Spin Hall (QSH) effect {Qi & Zhang, 2011}. The conducting edge states are protected by time reversal symmetry and their carriers have their spin locked to the momentum.

In this PhD project the Kwant Quantum Transport Simulator {Groth et al. 2014}, which is written in Python, will be used to explore the effect of non-magnetic impurities, defects and vacancies, initially in 2D for QSH systems, described by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian {Qi & Zhang, 2011}. Non-magnetic impurities have spin conserving scattering which don’t destroy the topologically protected states. However, the presence of these impurities will alter the bulk conduction and will introduce quantum interference effects. Lattice vacancies can cause the formation of current vortices {Dang et al., 2015}. Kwant calculates the Scattering matrix for the system and gives the conductance through the Landauer - Buttiker formula. Kwant can also be used to examine the local density of states (DOS) and local current. Looking at the local DOS and currents will provide detailed information on the effects of impurities and vacancies on Quantum Transport. This work will then be extended by addressing the Quantum Transport in impure 3D topological insulators, from the Bi2Se3 family.

Then the extension of looking at the effect of magnetic gating on quantum transport, by a ferromagnetic adatom, in a TA, will be tackled {Dang et al., 2016}. Once getting a handle on quantum transport and its control by a single adatom gate, the next stage is to address the TI Field Effect Transistors (FETs) engineering device application, where the gate is now film of atoms. A ferromagnetic insulator layer is required to give the TI Dirac Cone a bandgap i.e. splitting the zero gap, essential for TI FET switching behaviour, with a high ratio of ‘on’ to ‘off’ current. The potential applied at the gate and source to drain bias gives a linear potential drop along the TI channel which can be treated in Kwant by discretising as a staircase potential. Kwant can then calculate the Scattering matrix for the system and then integrating the transmission coefficient, gives the channel current and consequently the transistor transfer characteristic. The next phase of the research would be to investigate a TI FET incorporating a quantum well resonant tunnelling region and to study the emerging 2D materials silicene and germanene, for the channel


The successful candidate should have (or expect to achieve) a minimum of a UK Upper Second Class Honours Undergraduate Degree in BSc Physics or BEng Electrical & Electronic Engineering or BSc Applied Mathematics with a strong interest in applied quantum mechanics, theory and computer simulation.

Application Procedure:

Initially interested candidates are encouraged to make an informal enquiry to the Principal Supervisor Dr Gerard Edwards () including a copy of a curriculum vitae and a covering letter, indicating your interest in this project.

Contact Details:

Dr Gerard Edwards
Tel. +44 1244 512314
Email -

Supervisory Team

Principal Supervisor (Director of Studies): Dr G. Edwards, Department of Electronic & Electrical Engineering
Second Supervisor: Dr T. Papadopoulos, Department of Natural Sciences

Funding Notes

There is no funding attached to this project. It is for self - funding students only.


X. Dang, J. D. Burton, & E. Y.Tsymbal, ‘Local currents in a 2D topological insulator’, J. Phys.: Condens. Matter, Volume 27, (2015), 505301.
X. Dang, J. D. Burton, & E. Y.Tsymbal, ‘Magnetic gating of a 2D topological insulator’ J. Phys.: Condens. Matter, 28, (2016), 38LT01.
C. W. Groth, M. Wimmer, A. R. Akhmerov, & X.Waintal ‘Kwant: a software package for quantum transport’ New Journal of Physics, 16, (2014), 063065.
X. L. Qi & S. C. Zhang,. Topological insulators and superconductors. Reviews of Modern Physics, 83, (2011), 1057.

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