Electrically Tunable Quantum Spin Hall State in Topological Crystalline Insulator Thin films

Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum spin Hall phase in a wide range of thickness. The nontrivial topology originates from the inter-surface coupling of the topological surface states of TCI in the 3D limit. The inter-surface coupling changes sign and gives rise to topological phase transitions as a function of film thickness. Furthermore, this coupling can be strongly affected by an external electric field, hence the quantum spin Hall phase can be effectively tuned under experimentally accessible the electric field. Our results show that (111) thin films of SnTe-class TCI can be an ideal platform to realize the novel applications of quantum spin Hall insulators.Comment: Minor revision with updated reference

Topological Crystalline Insulators and Dirac Octets in Anti-perovskites

We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.Comment: Accepted as PRB Rapid Communication. 4 pages, 3 figures, 3 pages of Supplementary Material. Typos fixe

Topological semimetals with Riemann surface states

Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological semimetals can be represented by Riemann surfaces generated by holomorphic functions in the two-dimensional momentum space, whose constant height contours correspond to Fermi arcs. This correspondence is demonstrated in the recently discovered Weyl semimetals and leads us to predict new types of topological semimetals, whose surface states are represented by double- and quad-helicoid Riemann surfaces. The intersection of multiple helicoids, or the branch cut of the generating function, appears on high-symmetry lines in the surface Brillouin zone, where surface states are guaranteed to be doubly degenerate by a glide reflection symmetry. We predict the heterostructure superlattice [(SrIrO$_3$)$_2$(CaIrO$_3$)$_2$] to be a topological semimetal with double-helicoid Riemann surface states.Comment: Four pages, four figures and two pages of appendice

Self-Learning Monte Carlo Method

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.Comment: add more refs and correct some typo

The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

Weak Topological Insulators in PbTe/SnTe Superlattices

It is desirable to realize topological phases in artificial structures by engineering electronic band structures. In this paper, we investigate $(PbTe)_m(SnTe)_{2n-m}$ superlattices along [001] direction and find a robust weak topological insulator phase for a large variety of layer numbers m and 2n-m. We confirm this topologically non-trivial phase by calculating Z2 topological invariants and topological surface states based on the first-principles calculations. We show that the folding of Brillouin zone due to the superlattice structure plays an essential role in inducing topologically non-trivial phases in this system. This mechanism can be generalized to other systems in which band inversion occurs at multiple momenta, and gives us a brand-new way to engineer topological materials in artificial structures.Comment: 6 pages, 4 figures, another author adde

Self-Learning Monte Carlo Method: Continuous-Time Algorithm

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of continuous time Monte Carlo method with auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. By using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.Comment: 6 pages, 5 figures + 2 page supplemental materials, to be published in Phys. Rev. B Rapid communication sectio