Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.     

Nonlinear Hall Effect in Antiferromagnetic Half-Heusler Materials

It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triplepoint semimetal phases, can emerge in antiferromagnetic(AFM) half-Heusler compounds. However, how to determine the AFM structure and to distinguish different topological phases from transport behaviors remains unknown. We show that, due to the presence of combined time-reversal and fractional translation symmetry, the recently proposed second-order nonlinear Hall effect can be used to characterize different topological phases with various AFM configurations. Guided by the symmetry analysis, we obtain expressions of the Berry curvature dipole for different AFM configurations. Based on the effective model, we explicitly calculate the Berry curvature dipole, which is found to be vanishingly small for the triple-point semimetal phase, and large in the Weyl semimetal phase. Our results not only put forward an effective method for the identification of magnetic orders and topological phases in AFM half-Heusler materials, but also suggest these materials as a versatile platform for engineering the nonlinear Hall effect.     

Low-energy electronic properties of a Weyl semimetal quantum dot

We investigate the low-energy electronic structure of a Weyl semimetal quantum dot(QD) with a simple model Hamiltonian with only two Weyl points. Distinguished from the semiconductor and topological insulator QDs, there exist both surface and bulk states near the Fermi level in Weyl semimetal QDs. The surface state, distributed near the side surface of the QD, contributes a circular persistent current, an orbital magnetic moment, and a chiral spin polarization with spin-current locking. There are always surface states even for a strong magnetic field, even though a given surface state gradually evolves into a Landau level with increasing magnetic field. It indicates that these unique properties can be tuned via the QD size. In addition, we show the correspondence to the electronic structures of a three-dimensional Weyl semimetal, such as Weyl point and Fermi arc. Because a QD has the largest surface-to-volume ratio, it provides a new platform to verify Weyl semimetal by separating and detecting the signals of surface states. Besides, the study of Weyl QDs is also necessary for potential applications in nanoelectronics.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

外尔半金属及其输运特性

外尔半金属是继石墨烯以及拓扑绝缘体之后的又一个研究热点。相比于后两者,外尔半金 属独特的三维无能隙线性色散能带结构使得它有很多奇特的性质,如：手性反常、手性磁效应、 反弱局域化、手性朗道能级和负磁阻效应等。实际样品中无序总是不可避免的,所以考虑无序对 体系的影响是很有必要的。我们回顾了无序下第一类以及第二类外尔半金属的相变特性,并获得 了完整的相图,这些无序诱导的相变丰富了拓扑安德森绝缘体和安德森金属绝缘体相变的物理内 涵。我们同样回顾了长程短程无序影响下的第一类外尔半金属体系的输运,发现了一种不能采用 玻尔兹曼输运方程来描述的输运过程。我们介绍Imbert-Fedorov 位移这一光学中的效应在外尔 半金属中的实现,这为更好地应用外尔半金属提供了更多的可能性,随后采用波包散射,我们解 释了外尔半金属中的超高载流子迁移率问题的原因,最后我们给出一个简要的总结。     

Magneto-optical conductivity study in three-dimensional Dirac semimetals of ZrTe<Subscript>5</Subscript>

The three-dimensional (3D) Dirac semimetal material of ZrTe₅ provides a possible platform for studying 3D Dirac fermions. It can realize both the point-node semimetal phase and line-node semimetal phase when the intrinsic Zeeman interaction acts along different crystalline directions. In this work we present a study of magneto-optical conductivity in ZrTe₅. We calculate the optical conductivities in different phases, which exhibit a series of resonant peaks lying on a growing background whose origins are explored. For the Weyl semimetal phase, two striking signatures are found, one is the existence of an additional n = 0 LL transition and another is the double-strong peak structure related to the LL transition in one dispersion branch. While in the line-node semimetal phase, the weak peak appear and the strong peaks have higher degeneracy. We discuss the implications of these results in experiment.     

Quantum interference phenomena between impurity states in d-wave superconductors

We investigate the mutual influence of impurities in two-dimensional d-wave superconductors involving self-consistent solutions of the Bogoliubov-de Gennes equations. The local order parameter suppression, the local density of states as well as the interference of impurity-induced structures are analyzed. We employ an impurity position averaging scheme for the density of states that does not neglect these interference effects, as the commonly used T-matrix approaches do.     

Intrinsic anomalous Hall effect in type-II Weyl semimetals

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.     

Dispersion of the nonlinear optical susceptibility of n-type germanium

We observe a strong impurity-induced resonance in the third-order nonlinear optical susceptibility of n-type germanium. Our observations are used to obtain the cross-sections for electronic Raman scattering between the valley-orbit split 1s states of phosphorus and arsenic donors near 10 μm. Good agreement is found between measurements and calculations. The possibility of obtaining tunable impurity Raman laser action in n-type germanium is discussed.     

Impurity-induced core-valence lumionescence: A new possibility for fast scintillators creation

The impurity-induced core-valence lumionescence (CVL) originating from the radioactive recombination os valence electrons with the uppermost core holes of the impurity is studied in a number of chlorides doped with cesium. A correlation is established between the spectra shape and the local symmetry of the nearest-neighbor anion environment of the CVL-active impurity cation. This proves the cluster nature of the emission mechanism. Cluster calcualtions of the impurity-induced CVL spectra are in good agreement with the experimental results thus supporting the validity of cluster approach to the CVL. Peculiarities of the impurity-induced CVL excitation mechanism are considered. The effect of energy transfer from hist matrix cations to CVL-active ones due to core excitation migration is discussed. Prospects of searching for efficient fast scintillators based on the impurity-induced CVL are examined.     

Impurity effects in the optical absorption of quantum rings

We study the interplay between impurity scattering and Coulomb interaction effects in the absorption spectrum of neutral bound magnetoexcitons confined in quantum-ring structures. Impurity scattering breaks the rotational symmetry of the ring system, introducing characteristic features in the optical emission. Signatures of the optical Aharonov–Bohm effect are still present for weak scattering and strong Coulomb screening. Furthermore, an impurity-induced modulation of the absorption strength is present even for a strong impurity potential and low screening. This behavior is likely responsible of recent experimental observations in quantum-ring structures.     

Recent observations of negative longitudinal magnetoresistance in semimetal

The discovery of Dirac semimetal and Weyl semimetal has motivated a growing passion for investigating the unique magneto-transport properties in the topological materials.A Weyl semimetal can host Weyl fermions as its low-energy quasi-particle excitations,and therefore perform exotic features analogous to those in high-energy physics,such as the violation of the chiral charge conservation known as the chiral anomaly.One of the electrical transport signatures of the chiral anomaly is the Adler-Bell-Jackiw(ABJ) anomaly which presents as a negative magnetoresistance when the magnetic field and the current are parallel.Very recently,numerous experiments reported negative longitudinal magnetoresistance(NLMR) in topological materials,but the details of the measurement results are various.Here the materials and the corresponding experiment results are briefly reviewed.Besides the plausible explanation of the ABJ anomaly,some other origins of the NLMR are also discussed.     

Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.     

Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.This work was supported by the National Science Foundation through the Materials Research Laboratory at the University of Chicago.     

Electronic and Shallow Impurity States in Semiconductor Heterostructures Under an Applied Electric Field

With the use of variational method to solve the effective mass equation, we have studied the electronic and shallow impurity states in semiconductor heterostructures under an applied electric field. The electron energy levels are calculated exactly and the impurity binding energies are calculated with the variational approach. It is found that the behaviors of electronic and shallow impurity states in heterostructures under an applied electric field are analogous to that of quantum wells. Our results show that with the increasing strength of electric field, the electron confinement energies increase, and the impurity binding energy increases also when the impurity is on the surface, while the impurity binding energy increases at first, to a peak value, then decreases to a value which is related to the impurity position when the impurity is away from the surface. In the absence of electric field, the result tends to the Levine＇s ground state energy （-1/4 effective Rydberg） when the impurity is on the surface, and the ground impurity binding energy tends to that in the bulk when the impurity is far away from the surface. The dependence of the impurity binding energy on the impurity position for different electric field is also discussed.     

Weyl semimetal in a topological insulator multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its band structure. This Weyl semimetal has a finite anomalous Hall conductivity and chiral edge states and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator. We find that the Weyl semimetal has a nonzero dc conductivity at zero temperature, but Drude weight vanishing as T(2), and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically protected edge states.     

Insulator-semimetallic transition in quasi-1D charged impurity-infected armchair boron-nitride nanoribbons

We address control of electronic phase transition in charged impurity-infected armchair-edged boron-nitride nanoribbons (ABNNRs) with the local variation of Fermi energy. In particular, the density of states of disordered ribbons produces the main features in the context of pretty simple tight-binding model and Green's functions approach. To this end, the Born approximation has been implemented to find the effect of π-band electron-impurity interactions. A modulation of the π-band depending on the impurity concentrations and scattering potentials leads to the phase transition from insulator to semimetallic. We present here a detailed physical meaning of this transition by studying the treatment of massive Dirac fermions. From our findings, it is found that the ribbon width plays a crucial role in determining the electronic phase of disordered ABNNRs. The obtained results in controllable gap engineering are useful for future experiments. Also, the observations in this study have also fueled interest in the electronic properties of other 2D materials.     

Dual Topological Features of Weyl Semimetallic Phases in Tetradymite BiSbTe_3

Based on first-principles calculations and symmetry arguments,we reveal that the non-centrosymmetric ternary tetradymite BiSbTe_3 possesses exotic dual topological features of Weyl semimetallic phases with Z_2 index(1:000).The results show that the helical Dirac-type surface states protected by the time-reversal symmetry are present in the vicinity of the Brillouin zone center,which is consistent with the experimental report.Furthermore,we show that four pairs of Weyl points reside exactly at the Fermi level,which are guaranteed to be located on highsymmetry planes due to mirror symmetries.The helical surface states and the projected Weyl nodes are well separated in the momentum space,facilitating their observations in experiments.This work not only uncovers a unique quantum phenomenon with dual topological features in the tetradymite family but also paves a fascinating avenue for exploring the coexistence of multi-topological states with wide applications.     

Impurity induced resonance states at the superconducting interface LaAlO3/SrTiO3

Motivated by the recent discovery of superconductivity on the heterointerface LaAlO₃/SrTiO₃, we theoretically investigate the impurity-induced resonance states with coexisting spin singlet s- and triplet p-wave pairing symmetries by considering the influence of Rashba-type spin-orbit interaction (RSOI). Due to the nodal structure of the mixed gap function, we find single nonmagnetic impurity-induced resonance peaks appearing in the local density of state. We also analyze the evolutions of density of states and local density of states with the weight of triplet pairing component determined by the strength of RSOI, which will be widely observed in thin films of superconductors with surface or interface-induced RSOI, or various noncentrosymmetric superconductors in terms of point contact tunneling and scanning tunneling microscopy, and thus shed light on the admixture of the spin singlet and RSOI-induced triplet superconducting states.