Quantum Transport and Interaction in Topological Materials

Restricted (Penn State Only)
- Author:
- Yang, Kaijie
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 29, 2024
- Committee Members:
- Mikael Rechtsman, Major Field Member
Chaoxing Liu, Chair & Dissertation Advisor
Nitin Samarth, Major Field Member
Joshua Robinson, Outside Unit & Field Member
Mauricio Terrones, Program Head/Chair - Keywords:
- topological material
moire system
quasi symmetry
Coulomb interaction
spin transport - Abstract:
- Theoretical quantum matter describes a class of materials characterized by certain nontrivial topological invariant in their bulk electronic band structures and the electronic modes localized at the boundary of a finite sample. In this dissertation, I implement theoretical studies on the transport and interaction effect in topological states of matter. My research includes the spin transport in a variety of topological insulator and semimetal materials (Chapter 2), the theoretical proposal of topologically nontrivial moir\'e minibands in a class of topological insulator based moir\'e heterostructures and the interaction effects (Chapter 3), and a new class of topological semimetals originating from the low-energy effective models rather than protected by crystalline symmetries (Chapter 4). Chapter 2 focuses on the spin transport in topological insulators and topological semimetals. First, we propose that a topologically stable spin texture, spin antivortex, in momentum space can appear in 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of spin antivortex is guaranteed by the Poincar\'e-Hopf theorem and thus topologically stable. The existence of spin antivortex can be featured by rapid variations in current induced spin polarization and spin Hall conductivity when the Fermi energy is tuned across the spin antivortex. Second, We investigate the archetypal Dirac semimetal Cd$_3$As$_2$ interfaced with In$_{1-x}$Mn$_x$As, a ferromagnetic semiconductor with perpendicular magnetic anisotropy. Our calculation reveals a nonzero off-diagonal spin susceptibility in the Cd$_3$As$_2$ thin film due to the Rashba spin-orbit coupling from broken inversion symmetry, which can mediate local moments in the neighboring In$_{1-x}$Mn$_x$As layer by the presence of a Dzyaloshinskii-Moriya interaction and implies a real space chiral spin texture with topological Hall effects in transport measurement. This shows the heterostructure as a promising electrostatically tunable platform with the interplay between the helical Dirac fermions and chiral real space spin textures in a ferromagnet. Third, we study the electrical switch of edge state chirality in the quantum anomalous Hall insulator by a current pulse. We obtain spin polarization induced by the longitudinal and Hall currents of the surface states in the quantum anomalous Hall insulator and simulate the magnetization flipping dynamics with the spin-orbit torques from the spin polarization, which proves in principle the easy and instantaneous manipulation of the quantum anomalous Hall state by the interplay between magnetism and topological phases. Chapter 3 discusses about the search of topological phases in moir\'e materials with strong Coulomb interaction. First, we predict the topological insulator under a hexagonal moir\'e superlattice potential can have $\mathbb Z_2$ nontrivial minibands, interaction-driven quantum anomalous Hall state, and monolayer Sb$_2$ on top of Sb$_2$Te$_3$ films as a candidate heterostructure. Second, we introduce a new mechanism, which originates from the band folding induced by moir\'e superlattice, for topological mini-bands in moir\'e materials and use the Rashba model under a moir\'e superlattice for illustration. A general theory based on symmetry representations has also been developed for a generalization of this mechanism to other space groups. In Chapter 4, we generalize the symmetry principle to the quasi-symmetry in low-energy effective Hamiltonian, obtain a range of nodal structures in 230 space groups beyond the representation theory of crystal symmetries, and identify a class of potential topological semimetals in the topological material database. A notable example is that the existence of nodal points or nodal lines between two states with opposite mirror symmetry eigenvalue in certain space group is guaranteed by the $k \cdot p$ Hamiltonian linear or quadratic in momentum for all Hamiltonian parameters and robust against high order perturbations in momentum even though the mirror symmetry can only lead to accidental degeneracy, which shows the quasi-symmetry as a new principle in search of topological materials.