Massive Dirac surface states in topological insulator/magnetic insulator heterostructures

Topological insulators are new states of matter with a bulk gap and robust gapless surface states protected by time-reversal symmetry. When time-reversal symmetry is broken, the surface states are gapped, which induces a topological response of the system to electromagnetic field--the topological magnetoelectric effect. In this paper we study the behavior of topological surface states in heterostructures formed by a topological insulator and a magnetic insulator. Several magnetic insulators with compatible magnetic structure and relatively good lattice matching with topological insulators ${\rm Bi_2Se_3}, {\rm Bi_2Se_3}, {\rm Sb_2Te_3}$ are identified, and the best candidate material is found to be MnSe, an anti-ferromagnetic insulator. We perform first-principles calculation in ${\rm Bi_2Se_3/MnSe}$ superlattices and obtain the surface state bandstructure. The magnetic exchange coupling with MnSe induces a gap of $\sim$54 meV at the surface states. In addition we tune the distance between Mn ions and TI surface to study the distance dependence of the exchange coupling.Comment: 8 pages, 7 figure

Parameterized Complexity of Domination Problems Using Restricted Modular Partitions

For a graph class ?, we define the ?-modular cardinality of a graph G as the minimum size of a vertex partition of G into modules that each induces a graph in ?. This generalizes other module-based graph parameters such as neighborhood diversity and iterated type partition. Moreover, if ? has bounded modular-width, the W[1]-hardness of a problem in ?-modular cardinality implies hardness on modular-width, clique-width, and other related parameters. Several FPT algorithms based on modular partitions compute a solution table in each module, then combine each table into a global solution. This works well when each table has a succinct representation, but as we argue, when no such representation exists, the problem is typically W[1]-hard. We illustrate these ideas on the generic (?, ?)-domination problem, which is a generalization of known domination problems such as Bounded Degree Deletion, k-Domination, and ?-Domination. We show that for graph classes ? that require arbitrarily large solution tables, these problems are W[1]-hard in the ?-modular cardinality, whereas they are fixed-parameter tractable when they admit succinct solution tables. This leads to several new positive and negative results for many domination problems parameterized by known and novel structural graph parameters such as clique-width, modular-width, and cluster-modular cardinality

Preprocessing Complexity for Some Graph Problems Parameterized by Structural Parameters

Structural graph parameters play an important role in parameterized complexity, including in kernelization. Notably, vertex cover, neighborhood diversity, twin-cover, and modular-width have been studied extensively in the last few years. However, there are many fundamental problems whose preprocessing complexity is not fully understood under these parameters. Indeed, the existence of polynomial kernels or polynomial Turing kernels for famous problems such as Clique, Chromatic Number, and Steiner Tree has only been established for a subset of structural parameters. In this work, we use several techniques to obtain a complete preprocessing complexity landscape for over a dozen of fundamental algorithmic problems.Comment: 24 pages, 1 table, 1 figur

A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true $s$-sparse precision matrix under the spectral norm is $s\sqrt{\log p/n}$ when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise $L_{\infty}$ norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implementable by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.Comment: To appear in Journal of the American Statistical Associatio

Symmetry-dependent antiferromagnetic proximity effects on valley splitting

Various physical phenomena have been discovered by tuning degrees of freedom, among which there is the degree of freedom (DOF) -- "valley". The typical valley materials are characterized by two degenerate valley states protected by time-reversal symmetry (TS). These states indexed by valley DOF have been measured and manipulated for emergent valley-contrasting physics with the broken valley degeneracy. To achieve the valley splitting resulted from TS breaking, previous studies mainly focused on magnetic proximity effect provided by ferromagnetic (FM) layer. Nevertheless, the anti-ferromagnetic (AFM) proximity effect on the valley degeneracy has never been investigated systematically. In this work, we construct the composites consisting of a transitionmetal dichalcogenide (TMD) monolayer and a proximity layer with specific intra-plane AFM configurations. We extend the three-band model to describe the valley states of such systems. It is shown that either "time-reversal + fractional translation" or "mirror" symmetry has been proved to protect valley degeneracy. Additionally, first-principles calculations based on density functional theory (DFT) have been performed to verify the results obtained from the extended tight-binding (TB) model. The TB method introduced in the present work can properly describe the low-energy physics of valley materials that couple to the proximity with complex magnetic configurations. The results expand the range of qualified proximity layers for valley splitting, enabling more flexible manipulation of valley degree