Designer Topological Insulators in Superlattices

Gapless Dirac surface states are protected at the interface of topological and normal band insulators. In a binary superlattice bearing such interfaces, we establish that valley-dependent dimerization of symmetry-unrelated Dirac surface states can be exploited to induce topological quantum phase transitions. This mechanism leads to a rich phase diagram that allows us to design strong, weak, and crystalline topological insulators. Our ab initio simulations further demonstrate this mechanism in [111] and [110] superlattices of calcium and tin tellurides.Comment: 5 pages, 4 figure

Giant and tunable valley degeneracy splitting in MoTe2

Monolayer transition-metal dichalcogenides possess a pair of degenerate helical valleys in the band structure that exhibit fascinating optical valley polarization. Optical valley polarization, however, is limited by carrier lifetimes of these materials. Lifting the valley degeneracy is therefore an attractive route for achieving valley polarization. It is very challenging to achieve appreciable valley degeneracy splitting with applied magnetic field. We propose a strategy to create giant splitting of the valley degeneracy by proximity-induced Zeeman effect. As a demonstration, our first principles calculations of monolayer MoTe$_2$ on a EuO substrate show that valley splitting over 300 meV can be generated. The proximity coupling also makes interband transition energies valley dependent, enabling valley selection by optical frequency tuning in addition to circular polarization. The valley splitting in the heterostructure is also continuously tunable by rotating substrate magnetization. The giant and tunable valley splitting adds a readily accessible dimension to the valley-spin physics with rich and interesting experimental consequences, and offers a practical avenue for exploring device paradigms based on the intrinsic degrees of freedom of electrons.Comment: 8 pages, 5 figures, 1 tabl

Dissipative State and Output Estimation of Systems with General Delays

Dissipative state and output estimation for continuous time-delay systems pose a significant challenge when an unlimited number of pointwise and general distributed delays (DDs) are concerned. We propose an effective solution to this open problem using the Krasovski\u{\i} functional (KF) framework in conjunction with a quadratic supply rate function, where both the plant and the estimator can accommodate an unlimited number of pointwise and general DDs. All DDs can contain an unlimited number of square-integrable kernel functions, which are treated by an equivalent decomposition-approximation scheme. This novel approach allows for the factorization or approximation of any kernel function without introducing conservatism, and facilitates the construction of a complete-type KF with integral kernels that can encompass any number of differentiable (weak derivatives) and linearly independent functions. Our proposed solution is expressed as convex semidefinite programs presented in two theorems along with an iterative algorithm, which eliminates the need of nonlinear solvers. We demonstrate the effectiveness of our method using two challenging numerical experiments, including a system stabilized by a non-smooth controller.Comment: submitting to TA

Entanglement Polygon Inequality in Qubit Systems

We prove a set of tight entanglement inequalities for arbitrary $N$-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.Comment: 8 pages, 4 figure