30708364
Topological classification and stability of Fermi surfaces.
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.
117851662
The emergence of Hopf term and the marginality of Dirac model
The subtle relation of the marginality of Dirac model and the emergence of the Hopf term through a Yukawa-type interaction is revealed in this work. We show that the improvement of the marginality of Dirac mode through an infinitesimal non-relativistic term, which is irrelevant for renormalization group, is necessary to emerge the Hopf term. It is found that the appearance of the Hopf term is always accompanied with chiral boundary modes, and the sign of the coupling constant of the infinitesimal non-relativistic term decides their chirality. A lattice Dirac model is also constructed to realize the Hopf term.
197485150
Searching for New Topological Types of Majorana Fermions from Boundary-bulk Correspondence of Topological Insulators/Superconductors
Majorana fermions (MFs) are particles that are their own anti-particles and may satisfy non-Abelian statistics. For the past ten years, a kind of MFs have been theoretically predicted in one-dimensional superconducting models without the time-reversal symmetry (TRS), which has recently intrigued a huge experimental interest to search for this type of exotic particles. Here we report our theoretical discoveries, including (i) a general and quantitative relation between topological stabilities of Fermi surfaces (FSs) and topological insulators(TIs)/superconductors(TSCs) is rigorously established; (ii) based on (i), we find four topologically distinct types of MFs in fermionic systems that have at least the particle-hole symmetry (PHS); (iii) apart from the existing one type, three new types of topologically nontrivial gapless edge-modes (MFs) are revealed for the first time in one dimensional finite systems with both TP and (iv) all kinds of candidate models that potentially have MFs are presented, opening a wider door for searching MFs experimentally.
118521941
Relativistic quantum effects of Dirac particles simulated by ultracold atoms
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.
56250567
Macroscopic Klein tunneling in spin-orbit-coupled Bose-Einstein condensates
We propose an experimental scheme to detect macroscopic Klein tunneling with spin-orbit coupled Bose-Einstein condensates (BECs). We show that a nonlinear Dirac equation with tunable parameters can be realized with such BECs. %in a simple configuration to generate the artificial spin-orbit coupling. Through numerical calculations, we demonstrate that macroscopic Klein tunneling can be clearly detected under realistic conditions. Macroscopic quantum coherence in such relativistic tunneling is clarified and a BEC with a negative energy is shown to be able to transmit transparently through a wide Gaussian potential barrier.
34602223
Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid.
We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
925818
Topological order parameters for interacting topological insulators.
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams.
7625841
Topological Hamiltonian as an exact tool for topological invariants.
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
16797551
Analysis of the $B\to a_1(1260)$ form-factors with light-cone QCD sum rules
In this article, we calculate the $B\to a_1(1260)$ form-factors $V_1(q^2)$, $V_2(q^2)$, $V_3(q^2)$ and $A(q^2)$ with the $B$-meson light-cone QCD sum rules. Those form-factors are basic parameters in studying the exclusive non-leptonic two-body decays $B\to AP$ and semi-leptonic decays $B\to A l \nu_l$, $B\to A \bar{l}l$. Our numerical results are consistent with the values from the (light-cone) QCD sum rules. The main uncertainty comes from the parameter $\omega_0$ (or $\lambda_B$), which determines the shapes of the two-particle and three-particle light-cone distribution amplitudes of the $B$ meson, it is of great importance to refine this parameter.
44185566
(3+1)-TQFTs and topological insulators
Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3 + 1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.
123075504
Analysis of the heavy quarkonium states hc and hb with QCD sum rules
In this article, we take the tensor currents to interpolate the P-wave spin-singlet heavy quarkonium states hQ, and study the masses and decay constants with the Borel sum rules and moments sum rules. The masses and decay constants from the Borel sum rules and moments sum rules are consistent with each other, the masses are also consistent with the experimental data. The heavy quarkonium states hQ couple potentially to the tensor currents , and have the quark structure ϵijkξ†σkζ besides the quark structure .