Tip-induced superconductivity commonly existing in the family of transition-metal dipnictides MPn_2

We report the tip-induced superconductivity on the topological semimetal NbSb₂, similar to the observation on TaAs₂ and NbAs₂. Belonging to the same family of MPn₂, all these materials possess similar band structures, indicating that the tip-induced superconductivity may be closely related to their topological nature and share a common mechanism. Further analysis suggests that a bulk band should play the dominant role in such local superconductivity most likely through interface coupling. In addition, the compatibility between the induced superconductivity and tips’ ferromagnetism gives an evidence for its unconventional nature. These results provide further clues to elucidate the mechanism of the tip-induced superconductivity observed in topological materials.     

On the Mathai-Quillen formalism of topological sigma models

We present a Mathai-Quillen interpretation of topological sigma models. The key to the construction is a natural connection in a suitable infinite-dimensional vector bundle over the space of maps from a Riemann surface (the world sheet) to an almost complex manifold (the target). We show that the covariant derivative of the section defined by the differential that appears in the equation for pseudo-holomorphic curves is precisely the linearization of the operator itself. We also discuss the Mathai-Quillen formalism of gauged topological sigma models.     

压力诱导酌拓扑绝缘体化合物Bi2Te3常压相的超导性

通过高压电阻测量,发现了拓扑绝缘体化合物BizTe3压力诱导的超导性,在3-6GPa的压力范围内,超导临界温度L约为3K．高压下原位同步辐射的结果证明这个超导相来源于常压相结构．通过霍尔效应的测量,发现超导的Bi2Te3样品的载流子为P型．对高压同步辐射结果Reitveld精修得到的晶格参数和原子位置,并以此进行第一性...     

Superconductors with topological order

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivity is concretely realized as global superconductivity in Josephson junction arrays.     

A 1n expandable series of non-linear σ models with instantons

We formulate and discuss in detail the recently discovered $\text{C}\text{P}{}^{\mathrm{n?1}}$ non-linear σ models in two dimensions. We find that the fundamental particles in these theories are confined by a topological Coulomb force.     

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.     

A brief review on Majorana bound states in topological superconductors

Topological superconductivity has drawn much attention recently, and most interests are focused on the Majorana bound states existing at the edges of one-dimensional topological superconductors. These Majorana bound states are ideal platform for studying non-Abelian statistics. Meanwhile, they are proposed to be useful in quantum computation. In this review, we introduce the basic concepts and models in this area. We begin from the Kitaev model, which is the most concise model for one-dimensional topological superconductivity. Then, we discuss how to realize this model with spin-orbit coupling in realistic materials. Finally, we show some simple methods to detect the Majorana bound states and study their novel properties with the help of adjacent quantum dots.     

Dimerization,trimerization and quantum pumping

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the appearance of edge states and the mechanism of dimerization and trimerization is analyzed. Then we show that a quantum pumping process can be constructed based on each one-dimensional topological model. The quantum pumping process is explicitly demonstrated by the instantaneous energy spectrum and local current. The result shows that the pumping is assisted by the gapless states connecting the bands and one charge is pumped during a cycle, which also defines a nonzero Chern number. Our study systematically shows the connection of one-dimensional topological models and quantum pumping, and is useful for the experimental studies on topological phases in optical lattices and photonic quasicrystals.     

Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments

The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunneling process when electrons are injected into such states. Using a nonequilibrium Green function formalism, we find exact analytic expressions for the tunneling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.     

Engineering complex topological memories from simple Abelian models

In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.     

Topological massive sigma models

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.     

Topological matter in four dimensions

Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried out using both the topological algebra and its central extension, which arise from the twisting of N = 2 supersymmetry in four dimensions. The framework on which the construction is based is constituted by the superspace associated to these algebras. The models show new features of topological quantum field theories which could provide either a mechanism for topological symmetry breaking, or the analog of two-dimensional mirror symmetry in four dimensions.     

铁基超导体多轨道模型中的电子关联与轨道选择

大部分铁基超导体的正常态呈现坏金属行为, 这表明体系中存在较强的电子关联效应. 最近的实验与理论研究显示, 铁基超导体中的电子关联具有多轨道的特征. 本文介绍与评论铁基超导体多轨道哈伯德模型中电子关联方面理论研究的最新进展; 着重讨论以隶自旋技术为代表的一系列量子多体计算方法在研究多轨道系统中金属绝缘体相变的应用. 理论计算给出了铁基超导体多轨道哈伯德模型基于电子关联的基态相图. 在对应母体化合物的电子填充数时, 基态存在从金属到绝缘体的莫特转变. 临近莫特转变, 体系呈现坏金属行为; 其电子性质存在较强的轨道选择性. 轨道选择性的强弱与体系中的洪德耦合和轨道的晶体场劈裂密切相关. 对钾铁硒系统, 研究发现其基态相图存在轨道选择莫特相: 其中铁的3d xy轨道已被莫特局域化, 但其他3d轨道电子仍具有巡游性. 这一新相的发现, 对理解以钾铁硒为代表的一大类铁基超导体正常态与超导之间的联系提供了重要线索.     

Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.     

Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials

The critical theory of the onset of antiferromagnetism in metals, with concomitant Fermi surface reconstruction, has recently been shown to be strongly coupled in two spatial dimensions. The onset of unconventional superconductivity near this critical point is reviewed: it involves a subtle interplay between the breakdown of fermionic quasiparticle excitations on the Fermi surface and the strong pairing glue provided by the antiferromagnetic fluctuations. The net result is a logarithm-squared enhancement of the pairing vertex for generic Fermi surfaces, with a universal dimensionless coefficient independent of the strength of interactions, which is expected to lead to superconductivity at the scale of the Fermi energy. We also discuss the possibility that the antiferromagnetic critical point can be replaced by an intermediate 'fractionalized Fermi liquid' phase, in which there is Fermi surface reconstruction but no long-range antiferromagnetic order. We discuss the relevance of this phase to the underdoped cuprates and the heavy fermion materials.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

From entanglement renormalisation to the disentanglement of quantum double models

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models in which the Hamiltonian is gradually simplified along a parallel simplification of the connectivity of the lattice. We consider the case of Kitaev’s quantum double models, both Abelian and non-Abelian, and we obtain a rederivation of the known map of the toric code to two Ising chains; we pay particular attention to the non-Abelian models and discuss their space of states on the torus. Ultimately, the construction is universal for such models and its essential feature, the lattice simplification, may point towards a renormalisation of the metric in continuum theories.