Topological superconductors have been a focus of intense research efforts, because of their po- tential application in building fault-tolerant topological quantum computers. One approach to seeking topological superconductivity is investigating topological materials that transition to superconductors. In this Thesis, I present a series of discoveries that concern interacting condensates in the bulk and the edge states of superconducting topological materials.

A type-II Weyl semimetal MoTe₂ hosts an intrinsic edge supercurrent. In a MoTe₂ device with gold electrodes, the critical current modulates periodically with respect to the applied magnetic field. The area associated with this period scales with increasing field and converges to the physical area of device, which suggest the fluoxid quantization by the one-dimensional superconducting edge mode as the origin.

When a superconducting MoTe₂ crystal is coupled to a s-wave superconductor, such as niobium, the incompatibility between the two condensates is manifested as various exper- imental anomalies. The phenomena include asymmetric noise content in fluoxid-induced oscillations, anti-hysteretic central peaks, and bimodal stochastic switching of critical cur- rent. Analyses of these observations reveal that the unique gap function of device, described by the correlation method of proximity effect, switches between different symmetries as the field changes the relative strengths of the pair condensates. The symmetry that dictates the edge pairing can be inferred from the noise content of edge oscillations, which also uncovers the novel blockade mechanism of s-wave condensate by the intrinsic one.

Nonlocal effects are observed in MoTe₂ devices, where niobium electrodes cover the entire edges. In such devices, the edge pairing always follows the s-wave symmetry. When the volume of niobium electrodes is reduced significantly, all pairings in the bulk are suppressed. The observed effects suggest that the bulk states are sensitive to the entirety of edge states.

Anomalous modulations of critical current are observed in a kagome superconductor CsV₃Sb₅ with niobium electrodes. The period of oscillations is unstable and changes during field scans. The area associated with this period is always larger than the physical area of device. The incompatibility between the intrinsic CsV₃Sb₅ and s-wave condensates appears as anti-hysteretic zero-bias differential resistance and central peaks.

Adviser: N. Phuan Ong