Magnetic impurity in hybrid and type-Ⅱ nodal line semimetals

We study the Kondo screening of a spin-1/2 magnetic impurity in the hybrid nodal line semimetals(NLSMs) and the type-Ⅱ NLSMs by using the variational method. We mainly study the binding energy and the spin–spin correlation between magnetic impurity and conduction electrons. We find that in both the hybrid and type-Ⅱ cases, the density of states(DOS) is always finite, so the impurity and the conduction electrons always form bound states, and the bound state is more easily formed when the DOS is large. Meanwhile, due to the unique dispersion relation and the spin–orbit couplings in the NLSMs, the spatial spin–spin correlation components show very interesting features. Most saliently, various components of the spatial spin–spin correlation function decay with 1/r^(2) in the hybrid NLSMs, while they follow 1/r^(3) decay in the type-Ⅱ NLSMs. This property is mainly caused by the special band structures in the NLSMs, and it can work as a fingerprint to distinguish the two types of NLSMs.

Magnetotransport Properties of a Nodal Line Semimetal TiSi

We report the magnetoresistance（MR）, de Haas-van Alphen（dHvA） effect and Hall effect measurements on a single crystal of TiSi, which is predicted to be a nodal line semimetal. With application of a magnetic field, a metal-to-insulator-like transition in ρ（T） and a nonsaturating MR are observed at low temperatures. The dHvA oscillations reveal a small Fermi-surface pocket with a nontrivial Berry phase. The analysis of the nonlinear Hall resistivity shows that TiSi is a multiband system with low carrier densities and high mobilities. All these results unambiguously prove the existence of Dirac fermions in TiSi.

Topological Nodal Line Semimetal in Non-Centrosymmetric PbTaS2

Topological semimetals are a new type of matter with one-dimensional Fermi lines or zero-dimensional Weyl or Dirac points in momentum space. Here using first-principles calculations, we find that the non-centrosymmetric PbTaS2 is a topological nodal line semimetal. In the absence of spin-orbit coupling （SOC）, one band inversion happens around a high symmetrical H point, which leads to forming a nodal line. The nodal line is robust and protected against gap opening by mirror reflection symmetry even with the inclusion of strong SOC. In addition, it also hosts exotic drumhead surface states either inside or outside the projected nodal ring depending on surface termination. The robust bulk nodal lines and drumhead-like surface states with SOC in PbTaS2 make it a potential candidate material for exploring the freakish properties of the topological nodal line fermions in condensed matter systems.

Topological nodal line semimetals predicted from first-principles calculations

Topological semimetals are newly discovered states of quantum matter, which have extended the con- cept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimet- als, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin-orbit coupling （SOC） or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay-Terrones crystal （MTC）, anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.

Double drumheadlike surface states in elemental group Ⅴ nodal line semimetals

Drumheadlike surface states are typical characteristics in nodal line semimetals and bring varieties of unusual attractive properties.Here we demonstrate the double drumheadlike surface states in group V elemental semimetals As,Sb,Bi,which family materials behave a nodal line topology with a 3D flowerlike nodal line,using first-principles calculations.On(001)surface of group V elemental semimetals,the projection pattern of the nodal line overlaps and a complicated double drumheadlike surface state appears inside the overlapped region.This double surface state is widely distributed on the surface region up to a penetration depth of 3.5 nm,which is much deeper than the depth of single surface state on(111)surface.Given that the simplicity of the elemental structure and the small gap induced by the spin orbit coupling,this family materials are promising candidates for the experimental observation of the novel double drumheadlike surface state.

Symmetry-enforced two-dimensional Dirac node-line semimetals

Based on symmetry analysis and lattice model calculations,we demonstrate that Dirac nodal line(DNL)can stably exist in two-dimensional(2D)nonmagnetic as well as antiferromagnetic systems.We focus on the situations where the DNLs are enforced by certain symmetries and the degeneracies on the DNLs are inevitable even if spin–orbit coupling is strong.After thorough analysis,we find that five space groups,namely 51,54,55,57 and 127,can enforce the DNLs in 2D nonmagnetic semimetals,and four type-III magnetic space groups(51.293,54.341,55.355,57.380)plus eight type-IV magnetic space groups(51.299,51.300,51.302,54.348,55.360,55.361,57.387 and 127.396)can enforce the DNLs in 2D antiferromagnetic semimetals.By breaking these symmetries,the different 2D topological phases can be obtained.Furthermore,by the first-principles electronic structure calculations,we predict that monolayer YB4C4 is a good material platform for studying the exotic properties of 2D symmetry-enforced Dirac node-line semimetals.

Anomalous Andreev reflection on a torus-shaped Fermi surface

Andreev reflection(AR)refers to the electron-hole conversion at the normal metal-superconductor interface.In a threedimensional metal with a spherical Fermi surface,retro(specular)AR can occur with the sign reversal of all three(a single)components of particle velocity.Here,we predict a novel type of AR with the inversion of two velocity components,dubbed"anomalous Andreev reflection"(AAR),which can be realized in a class of materials with a torus-shaped Fermi surface,such as doped nodal line semimetals.For its toroidal circle perpendicular to the interface,the Fermi torus doubles the AR channels and generates multiple AR processes.In particular,the AAR and retro AR are found to dominate electron transport in the light and heavy doping regimes,respectively.We show that the AAR visibly manifests itself as a ridge structure in the spatially resolved nonlocal conductance,in contrast to the peak structure for the retro AR.Our work opens a new avenue for the AR spectroscopy and offers a clear transport signature of the torus-shaped Fermi surface.