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Register a new userLocal marker for interacting topological insulators
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Topological states of matter were first introduced for non-interacting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have been developed that can describe the topological state of systems without translational symmetry and well-defined gap. However, no local marker for interacting matter has been proposed yet that is capable of directly addressing an interacting system. Here we suggest such a many-body local marker based on the single-particle Greens function. Using this marker we identify topological transitions in finite lattices of a Chern insulator with Anderson disorder and Hubbard interactions. Importantly, our proposal can be straightforwardly generalised to non-equilibrium systems.
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Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.
We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite sign for electrons with opposite spin. Assuming density-density contact interactions, we find superconducting and anomalous (quantum) Hall phases for attractive and repulsive interactions, respectively, as well as chiral fermion and chiral Majorana fermion boundary modes between different phases. Our setup is preeminently adapted to the search for topologically ordered surface terminations that could be microscopically stabilized by tailored surface interaction profiles.
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emery-Luther mapping. The gapless glassy edge state spontaneously breaks time-reversal symmetry in a `spin glass fashion, and may be viewed as a localized state of solitons which carry half integer charge. Such a qualitatively distinct edge state provides a simple explanation for heretofore puzzling experimental observations. This phase exhibits a striking non-monotonicity, with the edge growing less localized in both the weak and strong disorder limits.
The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.
Motivated by the discovery of the quantum anomalous Hall effect in Cr-doped ce{(Bi,Sb)2Te3} thin films, we study the generic states for magnetic topological insulators and explore the physical properties for both magnetism and itinerant electrons. First-principles calculations are exploited to investigate the magnetic interactions between magnetic Co atoms adsorbed on the ce{Bi2Se3} (111) surface. Due to the absence of inversion symmetry on the surface, there are Dzyaloshinskii-Moriya-like twisted spin interactions between the local moments of Co ions. These nonferromagnetic interactions twist the collinear spin configuration of the ferromagnet and generate various magnetic orders beyond a simple ferromagnet. Among them, the spin spiral state generates alternating counterpropagating modes across each period of spin states, and the skyrmion lattice even supports a chiral mode around the core of each skyrmion. The skyrmion lattice opens a gap at the surface Dirac point, resulting in the anomalous Hall effect. These results may inspire further experimental investigation of magnetic topological insulators.
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