Two degenerate topological paired states that can be naturally favored in monolayer transition metal dichalcogenides.
Topological superconductivity in Van der Waals materials
Topological superconductors (Tsc) are exotic phases of matter that host exotic Majorana modes on different dimensional boundaries, and are proposed to be promising platforms for topological quantum computation. The main challenge in the field is the rareness of actual materials exhibiting any type of Tsc. The PI has been theoretically predicting material candidates for different Tsc phases using various analytical and numerical techniques, with emphasis on Van der Waals materials. See examples: Nat. Commun. 8 14983 (2017), Phys. Rev. Lett. 125, 097001 (2020). In collaboration with various ab initio and experimental groups, our current direction is to systematically design and identify more material candidates, as well as predicting experimental signatures in the presence of defects and external fields.
Topological invariants for higher-order Tsc protected by crystalline symmetries
Under the protection of certain crystalline symmetries, 2D and 3D superconductors can host Majorana corner or hinge modes. These crystalline Tsc are dubbed higher-order Tsc (HOTsc). One key challenge in understanding these phases is how to diagnose the Majorana boundary type in the real space from the normal band information in the momentum space, especially in the cases where the non-trivial topology occurs away from the high-symmetry points. The PI with collaborator(s) have developed a systematic method to obtain explicit expressions of topological invariants for crystalline Tsc, including invariants beyond symmetry indicators. The method establishes bulk-boundary correspondence for HOTsc using classification techniques in the real and momentum spaces. From the resulting topological invariants, we derive general recipes that can guide material searches and designs for higher-order Tsc. See examples: Phys. Rev. Research 3, 013243 (2021), Phys. Rev. B 105, 094518 (2022).
Derived invariants for 2D inversion-protected Tsc and the corresponding Majorana boundary types (upper panel). The numerically found Majorana corner modes in monolayer WTe2, a material that satisfies our recipe for HOTsc (lower panel).
RG flows and the obtained phase diagram for twisted bilayer transition metal dichalcogenides with spin-valley locking.
Correlated electronic phases in twisted few-layer VdW systems
Recent experimental breakthroughs in fabricating twisted few-layer Van der Waals systems have led to new platforms that can be designed to realize rare exotic phases. This is because the twist angle between adjacent layers is in fact a tuning knob that can tune the relative strengths between the kinetic energy and electronic interactions. Focusing on the weak-to-intermediate coupling regime, the PI has investigated how various interaction-driven phases could be favored by tuning twist angle and other experimental knobs using a renormalization group (RG) technique. Under this framework, different material systems can be understood in a unified way in terms of their van Hove fermiology. See examples in graphene and TMD-based Moire systems: Phys. Rev. B 102, 085103 (2020) Editor's suggestion, Phys. Rev. B 104, 195134 (2021). Our current goal is to study the non-interacting and interacting phases in different types of Moire systems.
Machine learning in quantum dynamics
Machine learning (ML) techniques have offered a unique tool box that could answer questions difficult for conventional methods in condensed matter theory. One example question is how to define "phases" in isolated quantum systems without a heat bath, which can be realized in cold atom experiments. In such systems, order parameters cannot be defined in the usual way since statistical mechanics is not straightforwardly applicable. On the other hand, simple-minded supervised learning does not come to help since the number of phases is unknown. The PI has developed an unsupervised ML approach that can identify the number of manybody quantum phases in such systems based on the entanglement spectra. The approach was successfully applied to case studies of quasiperiodic systems with single-particle mobility edges, where the number of manybody phases was under debate. See Phys. Rev. Lett. 121, 245701 (2018). Our current direction is to apply this method as well as developing new ML methods to characterize quantum dynamics in various Hermitian and non-Hermitian systems.
Phase diagram for a quasi-periodic 1D chain with a single-particle mobility edge, produced using our ML approach.