Bootstrapping solutions of scattering equations

The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations based on the numerical algebraic geometry. The cornerstone of our method is the concept of the physical homotopy between different points in the kinematic space, which naturally induces a homotopy of the scattering equations. As a result, the solutions of the scattering equations with different points in the kinematic space can be tracked from each other. Finally, with the help of soft limits, all solutions can be bootstrapped from the known solution for the four-particle scattering.Comment: v2: published version. The code is available at https://github.com/zxrlha/sehom

Artificial Quantum Many-Body States in Complex Oxide Heterostructures at Two-Dimensional Limit

As the representative family of complex oxides, transition metal oxides, where the lattice, charge, orbital and spin degrees of freedom are tightly coupled, have been at the forefront of condensed matter physics for decades. With the advancement of state-of-the-art heteroepitaxial deposition techniques, it has been recognized that combining these oxides on the atomic scale, the interfacial region offers great opportunities to discover emergent phenomena and tune materials\u27 functionality. However, there still lacks general guiding principles for experimentalists, following which one can design and fabricate artificial systems on demand. The main theme of this dissertation is to devise and propose some basic rules for heterostructure engineering. Towards this goal, I first report the growth of high quality YTiO3/CaTiO3 superlattices by pulsed laser deposition. Electrical transport measurements reveal that a novel, non- SrTiO3 based two-dimensional electron gas system has formed at the interface. What is more, these studies add solid evidences that interface engineering via charge modulation is an effective approach to realizing exotic many-body phenomena. Secondly, a new concept, denoted as \geometrical lattice engineering is proposed with pioneering experimental efforts. Aiming at designing magnetically frustrated systems, (111)- oriented CoCr2O4 thin films and CoCr2O4/Al2O3 heterostructures have been fabricated for the first time. Comprehensive structural and electronic characterizations reveal that no disorder in the cation distribution or multivalency issue is present. As a result, unique quasi-two dimensional geometrically frustrated lattices composed of alternating kagome and triangular lattices, are naturally established via this topological approach. These CoCr2O4/Al2O3 heterostructures have been found to exhibit remarkably different behaviors from the bulk compounds. Towards the two dimensional limit, the ground state of the ultrathin superlattices transforms from the bulk-like nonlinear ferrimagnetic phase, into an emergent collinear ferrimagnetic phase, and finally into an exotic magnetically disordered phase with an extensively large frustration parameter, which is a hallmark of quantum spin liquid. These findings corroborate geometrical lattice engineering has excellent potential in achieving novel electronic, magnetic, and topological phases

Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formula ABO3 and A2B2O7, where the B sites are occupied by an open-shell transition metal ion with a local moment, and the A sites are typically a rare earth. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin-orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude the Perspective by articulating open challenges and opportunities in this actively developing field

A space for reconciliation

The environment where I grew up retains some characteristics from The Chinese Cultural Revolution, and still influences my thinking and behavior close to the mainstream and following the rules unconsciously. Contemporary jewelry has affected me to be more critical in a positive way. I want to share this transformative experience with people who have never had contact with contemporary art, which is an alien concept for most Chinese people. I use jewelry as the medium to express my ideas. But the typical response to my work is “I appreciate your concepts, but I can’t accept your pieces.” So, how can I find a jewelry form that is both conceptual and acceptable? I will explore this in my thesi

Chemically Ordered Pt–Co–Cu/C as Excellent Electrochemical Catalyst for Oxygen Reduction Reaction

This paper reveals the ordered structure and composition effect to electrochemical catalytic activity towards oxygen reduction reaction (ORR) of ternary metallic Pt–Co–Cu/C catalysts. Bimetallic Pt-Co alloy nanoparticles (NPs) represent an emerging class of electrocatalysts for ORR, but practical applications, e.g. in fuel cells, have been hindered by low catalytic performances owning to crystal phase and atomic composition. Cu is introduced into Pt-Co/C lattices to form PtCoxCu1−x/C (x = 0.25, 0.5 and 0.75) ternary-face-centered tetragonal (fct) ordered ternary metallic NPs. The chemically ordered Pt–Co–Cu/C catalysts exhibit excellent performance of 1.31 A mg−1 Pt in mass activity and 0.59 A cm−2 Pt in specific activity which are significantly higher than Pt-Co/C and commercial Johnson Matthey (JM) Pt/C catalysts, because of the ordered crystal phase and composition control modified the Pt-Pt atoms distance and the surface electronic properties. The presence of Cu improves the surface electronic structure, as well as enhances the stability of catalysts