In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.

As PT and CP symmetries are fundamental in physics, we establish a unified topological theory of PT and CP invariant metals and nodal superconductors, based on the mathematically rigorous KO theory. Representative models are constructed for all nontrivial topological cases in dimensions d=1, 2, and 3, with their exotic physical meanings being elucidated in detail. Intriguingly, it is found that the topological charges of Fermi surfaces in the bulk determine an exotic direction-dependent distribution of topological subgap modes on the boundaries. Furthermore, by constructing an exact bulk-boundary correspondence, we show that the topological Fermi points of the PT and CP invariant classes can appear as gapless modes on the boundary of topological insulators with a certain type of anisotropic crystalline symmetry.

Manipulating physical properties using the spin degree of freedom constitutes a major part of modern condensed matter physics and is a key aspect for spintronics devices. Using the newly discovered two-dimensional van der Waals ferromagnetic CrI as a prototype material, we theoretically demonstrated a giant magneto band-structure (GMB) effect whereby a change of magnetization direction significantly modifies the electronic band structure. Our density functional theory calculations and model analysis reveal that rotating the magnetic moment of CrI from out-of-plane to in-plane causes a direct-to-indirect bandgap transition, inducing a magnetic field controlled photoluminescence. Moreover, our results show a significant change of Fermi surface with different magnetization directions, giving rise to giant anisotropic magnetoresistance. Additionally, the spin reorientation is found to modify the topological states. Given that a variety of properties are determined by band structures, our predicted GMB effect in CrI opens a new paradigm for spintronics applications.

A second-order topological insulator (SOTI) in d spatial dimensions features topologically protected gapless states at its (d − 2)-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state, it has been attracting great interest, but it remains a challenge to identify a realistic SOTI material in two dimensions (2D). Here, based on combined first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized 2D material graphdiyne as the first realistic example of a 2D SOTI, with topologically protected 0D corner states. The role of crystalline symmetry, the robustness against symmetry-breaking, and the possible experimental characterization are discussed. Our results uncover a hidden topological character of graphdiyne and promote it as a concrete material platform for exploring the intriguing physics of higher-order topological phases.Lattice structure.-GDY is a carbon allotrope with a 2D planar network structure [ Fig. 1(a)], which may be viewed as formed by inserting the diacetylenic linkage between two neighboring benzene rings in a graphene structure. The lattice is completely flat, with a single-atom arXiv:1904.09985v2 [cond-mat.mes-hall] 3 Jan 2020

Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the P T symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya nogo theorem, 2D sub topological insulators and Fermi arcs, are studied in the P T symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about P T symmetric Dirac nodal line semimetals.

In the pursuit of broadband photodetection materials from visible to mid-IR region, the fresh three-dimensional topological insulators (3D TIs) are theoretically predicted to be a promising candidate due to its Dirac-like stable surface state and high absorption rate. In this work, a self-powered inorganic/organic heterojunction photodetector based on n-type 3D TIs Bi 2 Te 3 combined with p-type pentacene thin film was designed and fabricated. Surprisingly, it was found that the Bi 2 Te 3 /pentacene heterojunction photodetector exhibited a fast and wideband response from 450 to 3500 nm. The optimized responsivity of photodetector reached 14.89 A/W, along with the fast response time of 1.89 ms and the ultrahigh external quantum efficiency of 2840%. Moreover, at the mid-IR 3500 nm, our devices demonstrated a responsivity of 1.55 AW −1 , which was several orders of magnitude higher than that of previous 3D TIs photodetector. These excellent properties indicate that the inorganic/organic heterojunction, that is, the combination of 3D TIs with organic materials, is an exciting structure for high performance photodetectors in the wideband detection region. On account of the fact that the device is constructed on mica substrate, this work also represents a potential scenario for flexible optoelectronic devices. KEYWORDS: inorganic/organic heterojunction, wideband photodetector, Bi 2 Te 3 thin films, self-powered, fast response, flexible

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that the 4D spinless topological insulator, due to its symmetry properties, is particularly well suited to be implemented in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulate the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibit pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.

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