Topologically Non-trivial RTD: First Report
First proposed in 1973 by Chang and Esaki, resonant tunneling has since become a very well understood and well utilized property in devices(Chang 1974). Due to the fabrication capabilities at the time, the devices that could be created were too thick and defective to properly utilize this effect. Early experiments on this effect were promising, but only showed weak features at unrealistically low temperatures. However, since then fabrication techniques have greatly improved and tunneling effects can now be well observed and utilized. One of the primary uses of this property is in the resonant tunneling diode(RTD), in which the double potential barrier system allows for strong diode control(Mizuta 1995).
In this report, the analysis of a theoretical RTD composed of topological insulator material will be carried out and used to compare the properties of this topologically non-trivial RTD to those of a conventional RTD. Topological insulators will be discussed in the following sections, but these materials exhibit unique edge state transport properties and could be useful in an RTD.
As previously stated, an RTD is a tunneling device that makes use of resonances in the tunneling probability for diode control. This resonance arises from the interaction of the potential barriers, which can be thought of as a double potential barrier with adjustable positions relative to each other. When an electron tunnels through one barrier, it will be temporarily bound between the two barriers until it can tunnel out(Mizuta 1995). The relative positional adjustment of the barriers, which in actuality is the result of applying a bias to the device, results in adjustability of the amount of time the electron is bound. At a certain bias, the tunneling probability spikes and the electron sees virtually no barriers; this is the resonance condition, which can be seen in figure 1a. Using tunneling probability, current can be calculated and has been shown to exhibit unique properties that include a negative differential resistance region, which can be seen in figure 1b(Kluksdahl 1989). These properties have made RTD’s very useful for switching devices as well as a platform for studying the wave nature of electrons.
Although RTD’s have been extensively tested and studied for more than twenty years, the field of topological insulators has only come into focus in the past five years. Without going into excessive detail, a topological insulator is a material that can exhibit a unique quantum state of matter. This is known as the quantum spin hall(QSH) state and leads to numerous unique material and transport properties. Matter in this state is insulating in the bulk region, but has conducting edge states, which can be seen in figure 2a(Hasan 2010),(Qi 2011). Moreover, these conduction edge states are spin polarized and propagate in opposite directions. As shown in figure 2b, this state of matter has been experimentally observed in HgTe/CdTe quantum wells(Konig 2007),(Roth 2009). Unlike the quantum hall state, a magnetic field is not required to change to the QSH phase.