UC Riverside

Half-integer conductance, the signature of Majorana edge

modes, was recently observed in a thin-film

magnetic topological insulator/superconductor bilayer.

Chapter 2 of this thesis analyzes a scheme for gate control of Majorana zero modes in such systems. Gating the top surface of the thin-film magnetic topological insulator controls the topological phase in the region underneath the gate. The voltage of the transition depends on the gate width, and narrower gates require larger voltages. Relatively long gates are required, on the order of 2 µm, to prevent hybridization of the end modes and to allow the creation of Majorana zero modes at low gate voltages. Applying voltage to T-shaped and I-shaped gates localizes the Majorana zero modes at their ends. This scheme may provide a facile method for implementing quantum gates for topological quantum computing.

The extremely small energy splitting of Majorana zero modes caused by s-wave pairing makes identifying them experimentally very challenging.

A heterostructure between a magnetic TI and a high Tc superconductor, which has an order of magnitude enhancement in the induced pairing gap, may offer a more feasible approach.

In Chapter 3, we study the effect of top surface electrical gating on a TI / high-Tc-superconductor with dx2-y2 pairing.

We calculated the phase diagram using the Kubo formula to find the required condition for the topological superconductivity Chern number ±1, which is necessary for obtaining Majorana modes.

We show that chiral Majorana modes appear by applying the gating potential to the top surface of the TI. We also show that we are able to change their propagation direction by only changing the top gating potential. In the end, we apply the gating potential locally to create localized Majorana zero modes. Although bound states appear at zero energy, and they are robust against an increasing gating potential,

we find that the wave functions of these zero-energy modes

do not fulfill the wavefunction condition of a Majorana zero mode,

namely that a Majorana mode is its own anti-particle.

In Chapter 4, the effect of an antiferromagnetic Skyrmion on the tunneling magnetoresistance of a ferromagnet/insulator/antiferromagnet/ferromagnet heterostructure is numerically investigated.

The tunneling magnetoresistance in the presence of a Bloch type antiferromagnetic Skyrmion is significantly reduced when the polarization of the ferromagnetic leads is anti-parallel.

The amplitude of the output signal, caused by the transmission of current in the presence of Skyrmion, depends on the resistance change induced by the Skyrmion. The change in the resistance can be engineered by changing the thickness of the insulator and magnetization strength of the ferromagnetic leads. This scheme can be used for electrical detection, and the read-out of antiferromagnetic Skyrmions in the future of Skyrmion based antiferromagnetic memories.