Many electron systems exhibit entanglement, giving rise to macroscopic coherent quantum phenomena such as superconductivity, magnetism, and various types of quantum liquids. In my recent research, I have been specifically focused on studying a class of unconventional superconductors known as noncentrosymmetric materials, which lack inversion symmetry. Notable examples of these materials include monolayer transition metal dichalcogenides, artificial heterostructures, and the recently discovered compound CeRh2As2.

What piqued my interest in these materials is the presence of both spin-singlet and spin-triplet components in the superconducting state. The coexistence of these components is significant because they exhibit distinct responses to magnetic fields. Consequently, the application of a magnetic field can give rise to intriguing effects in these systems.

In my research, I specialize in conducting real-space simulations using a mean-field approach. While working with systems that possess translational symmetry, it is often convenient to utilize momentum-space. However, when studying the effects of interfaces, boundaries, topological defects, disorder, and similar phenomena, translational symmetry is absent, and it becomes necessary to directly solve the Hamiltonian in real-space. Similar to quantum Monte Carlo simulations, real-space methods are susceptible to finite-size effects.

Fortunately, recent advancements in ultrafast algorithms have enabled us to investigate real-space 3D systems or micrometer-sized 2D materials, effectively bypassing the limitations posed by finite-size effects. Inspired by these developments, I have conceived an ambitious project idea in this realm. If you share an interest in this direction, please do not hesitate to contact me.

I am interested in a variety of mathematical methods such as functional integrals, diagrammatics, quasi-classics, group theory, Ginzburg-Landau theory and Keldysh. If you draw satisfaction from the math alone, and feel that application to real materials is just an excuse - I have some project ideas in this direction.