Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

Let $L$ be a nonnegative, self-adjoint operator on $L^2(\mathbb{R}^n)$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\mathcal{L}^{2,\lambda}_{-\Delta}(\mathbb R^n)$, in \cite{DXY} the quadratic Campanato space $\mathcal{L}_L^{2,\lambda}(\mathbb{R}^n)$ is defined by a variant of the maximal function associated with the semigroup $\{e^{-tL}\}_{t\geq 0}$. On the basis of \cite{DX} and \cite{YY} this paper addresses the preduality of $\mathcal{L}_L^{2,\lambda}(\mathbb{R}^n)$ through an induced atom (or molecular) decomposition. Even in the case $L=-\Delta$ the discovered predual result is new and natural.Comment: 19 page

Topological superconductivity at the edge of transition metal dichalcogenides

Time-reversal breaking topological superconductors are new states of matter which can support Majorana zero modes at the edge. In this paper, we propose a new realization of one-dimensional topological superconductivity and Majorana zero modes. The proposed system consists of a monolayer of transition metal dichalcogenides MX2 (M=Mo, W; X=S, Se) on top of a superconducting substrate. Based on first-principles calculations, we show that a zigzag edge of the monolayer MX2 terminated by metal atom M has edge states with strong spin-orbit coupling and spontaneous magnetization. By proximity coupling with a superconducting substrate, topological superconductivity can be induced at such an edge. We propose NbS2 as a natural choice of substrate, and estimate the proximity induced superconducting gap based on first-principles calculation and low energy effective model. As an experimental consequence of our theory, we predict that Majorana zero modes can be detected at the 120 degree corner of a MX2 flake in proximity with a superconducting substrate

Self-Learning Determinantal Quantum Monte Carlo Method

Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal quantum Monte Carlo simulation of interacting fermion systems. Guided by a self-learned bosonic effective action, our method uses a cumulative update [arXiv:1611.09364] algorithm to sample auxiliary field configurations quickly and efficiently. We demonstrate that self-learning determinantal Monte Carlo method can reduce the auto-correlation time to as short as one near a critical point, leading to $\mathcal{O}(N)$-fold speedup. This enables to simulate interacting fermion system on a $100\times 100$ lattice for the first time, and obtain critical exponents with high accuracy.Comment: 5 pages, 4 figure

One-way cloak based on nonreciprocal photonic crystal

We propose a physical concept of non-reciprocal transformation optics, by which a one-way invisible cloak is designed. The one-way invisible cloak is made of a coordinate-transformed nonreciprocal photonic crystal, showing a perfect cloaking for wave incident from one direction but acting as a perfect reflector for wave from the counter direction. The proposed design shows a high promise of applications in military, as protecting the own information to be detected but efficiently grabbing the information from the “enemy” side

Topological insulators in filled skutterudites

We propose new topological insulators in cerium filled skutterudite (FS) compounds based on ab initio calculations. We find that two compounds CeOs4As12 and CeOs4Sb12 are zero gap materials with band inversion between Os-d and Ce-f orbitals, which are thus parent compounds of two and three-dimensional topological insulators just like bulk HgTe. At low temperature, both compounds become topological Kondo insulators, which are Kondo insulators in the bulk, but have robust Dirac surface states on the boundary. This new family of topological insulators has two advantages compared to previous ones. First, they can have good proximity effect with other superconducting FS compounds to realize Majarona fermions. Second, the antiferromagnetism of CeOs4Sb12 at low temperature provides a way to realize the massive Dirac fermion with novel topological phenomena.Comment: 4 page, 3 figure