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A particle beam may undergo an anomalous spatial shift when it is reflected at an interface. The shift forms a vector field defined in the two-dimensional interface momentum space. We show that, although the shift vector at individual momentum is typically sensitive to the system details, its integral along a close loop, i.e., its circulation, could yield a robust quantized number under certain conditions of interest. Particularly, this is the case when the beam is incident from a trivial medium, then the quantized circulation of anomalous shift (CAS) directly manifests the topological character of the other medium. We demonstrate that the topological charge of a Weyl medium as well as the unconventional pair potentials of a superconductor can be captured and distinguished by CAS. Our work unveils a hidden quantized feature in a ubiquitous physical process, which may also offer a new approach for probing topological media. [ABSTRACT FROM AUTHOR]

The current valleytronics research is based on the paradigm of time-reversal-connected valleys in two-dimensional (2D) hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. Here, we go beyond the existing paradigm to explore 2D systems with a novel valley-layer coupling (VLC) mechanism, where the electronic states in the emergent valleys have a valley-contrasted layer polarization. The VLC enables a direct coupling between a valley and a gate electric field. We analyze the symmetry requirements for a system to host VLC, demonstrate our idea via first-principles calculations and model analysis of a concrete 2D material example, and show that an electric, continuous, wide-range, and switchable control of valley polarization can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. Our finding opens a new direction for valleytronics and 2D materials research. [ABSTRACT FROM AUTHOR]

Superconductors with unconventional pairings have been a fascinating subject of research, for which a central issue is to explore effects that can be used to characterize the pairing. The process of Andreev reflection--the reflection of an electron as a hole at a normal-metal-superconductor interface--offers a basic mechanism to probe the pairing. Here we predict that in Andreev reflection from unconventional superconductors, the reflected hole acquires an anomalous spatial shift normal to the plane of incidence, arising from the unconventional pairing. The transverse shift is sensitive to the superconducting gap structure, exhibiting characteristic features for each pairing type, and can be detected as voltage signals. Our work not only unveils a fundamentally new effect with a novel underlying mechanism, but also suggests a possible new technique capable of probing the structure of unconventional pairings. [ABSTRACT FROM AUTHOR]

We study the transport properties at the surface state of a topological insulator (TI) with a potential barrier. Due to the hexagonal warping effect, the number of reflected propagating states for an incident electron beam can change from one to two, corresponding to a change from normal reflection to double reflection, by controlling the Fermi energy. Associated with the change, the corresponding reflection probability shows a significant jump in its derivative. In addition, for a junction with potential barrier, the reflection probability should oscillate as the potential energy varies due to the tunneling resonance. The oscillation period in the TI junction is closely related to the warping strength. Thus, these two proposals both can be used to identify the hexagonal warping strength of the TI surface state and especially, are robust against the influence of lateral surfaces, as they depend on the relative variation of transport. Remarkably, the latter proposal is compatible with the recent experiment in graphene [Chen et al., Science 353, 1522 (2016)], which achieves a direct measurement of the angle-resolved scattering probability. [ABSTRACT FROM AUTHOR]

An incoming electron is reflected back as a hole at a normal-metal-superconductor interface, a process known as Andreev reflection. We predict that there exists a universal transverse shift in this process due to the effect of spin-orbit coupling in the normal metal. Particularly, using both the scattering approach and the argument of angular momentum conservation, we demonstrate that the shifts are pronounced for lightly doped Weyl semimetals, and are opposite for incoming electrons with different chirality, generating a chirality-dependent Hall effect for the reflected holes. The predicted shift is not limited to Weyl systems, but exists for a general three-dimensional spin-orbit-coupled metal interfaced with a superconductor. [ABSTRACT FROM AUTHOR]

A nodal loop appears when two bands, typically one electronlike and one holelike, are crossing each other linearly along a one-dimensional manifold in reciprocal space. Here, we propose a type of nodal loop which emerges from the crossing between two bands which are both electronlike (or holelike) along a certain direction. Close to any point on such a loop (dubbed as a type-II nodal loop), the linear spectrum is strongly tilted and tipped over along one transverse direction, leading to marked differences in magnetic, optical, and transport responses compared with conventional (type-I) nodal loops. We show that the compound K4P3 is an example that hosts a pair of type-II nodal loops close to the Fermi level. Each loop traverses the whole Brillouin zone, and hence can only be annihilated in a pair when symmetry is preserved. The symmetry and topological protections of the loops as well as the associated surface states are discussed. [ABSTRACT FROM AUTHOR]

Topological metals with protected band-crossing points have been attracting great interest. Here we report topological band features in a family of metal diboride materials. Using first-principles calculations, we show that these materials are metallic, and close to Fermi level, there appears coexistence of one pair of nodal rings and one pair of triply degenerate nodal points (TNPs). The nodal ring here is distinct from the previously studied ones in that its formation requires four entangled bands, not just two as in previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably, we show that FNR features Dirac-cone-like surface states, in contrast to the usual drumhead surface states for two-band nodal rings. Due to the presence of inversion symmetry, the TNP here is also different from those discussed previously in inversion-asymmetric systems. Especially, when spin-orbit coupling is included, the TNP here transforms into a novel Dirac point that is close to the borderline between the type-I and type-II Dirac point categories. We discuss their respective symmetry protections, and construct effective models for their characterization. The large linear energy range (>2 eV) in these materials should facilitate the experimental detection of the signatures of these nontrivial band crossings. [ABSTRACT FROM AUTHOR]

We propose a realization of pure spin currents and perfect valley filters based on a quantum anomalous Hall insulator, around which edge states with up spin and down spin circulate. By applying staggered sublattice potential on the strips along the edges of sample, the edge states with down spin can be pushed into the inner boundaries of the strips while the other edge states with up spin remain on the outer boundaries, resulting in spatially separated chiral states with perfect spin polarization. Moreover, a valley filter, which is immune to both long-range and short-range scatterers, can be engineered by additionally applying boundary potentials on the outmost lattices of the sample. We also find that the boundary potential can be used to control the size effect induced oscillation of the inner chiral states. The connection of the boundary potential to size effect is revealed. [ABSTRACT FROM AUTHOR]

We show several distinct signatures in the magnetoresponse of type-II Weyl semimetals. The energy tilt tends to squeeze the Landau levels (LLs), and, for a type-II Weyl node, there always exists a critical angle between the B field and the tilt, at which the LL spectrum collapses, regardless of the field strength. Before the collapse, signatures also appear in the magneto-optical spectrum, including the invariable presence of intraband peaks, the absence of absorption tails, and the special anisotropic field dependence. [ABSTRACT FROM AUTHOR]

We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventional (first-order) topological insulators. The approach works for both three dimensions (3D) and two dimensions (2D), and is particularly suitable for 2D, where it can be achieved by coupling a quantum spin Hall insulator with a magnetic substrate. Using first-principles calculations, we predict bismuthene on EuO(111) surface as the first realistic system for a two-dimensional magnetic SOTI. We explicitly demonstrate the existence of the protected corner states. Benefitting from the large spin-orbit coupling and sizable magnetic proximity effect, these corner states are located in a boundary gap ∼83 meV, and hence can be readily probed in experiment. By controlling the magnetic phase transition, a topological phase transition between a first-order TI and a SOTI can be simultaneously achieved in the system. The effect of symmetry breaking, the connection with filling anomaly, and the experimental detection are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nonsymmorphic space group symmetries can generate exotic band crossings in topological metals and semimetals. Here, based on symmetry analysis and first-principles calculations, we reveal rich band-crossing features in the existing layered compounds Ta3 SiTe6 and Nb3 SiTe6, enabled by nonsymmorphic symmetries. We show that in the absence of spin-orbit coupling (SOC), these three-dimensional (3D) bulk materials possess accidental Dirac loops and essential fourfold nodal lines. In the presence of SOC, there emerges an hourglass Dirac loop--a fourfold degenerate nodal loop, on which each point is a neck point of an hourglass-type dispersion. We show that this interesting type of band crossing is protected and dictated by the nonsymmorphic space group symmetries and it gives rise to drumheadlike surface states. Furthermore, we also investigate these materials in the monolayer form. We show that these two-dimensional (2D) monolayers host nodal lines in the absence of SOC and the nodal lines transform to essential spin-orbit Dirac points when SOC is included. Our work suggests a realistic material platform for exploring the fascinating physics associated with nonsymmorphic band crossings in both 3D and 2D systems. [ABSTRACT FROM AUTHOR]

The recent proposal of the type-II Weyl semimetal state has attracted significant interest. In this Letter, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node can be split into four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict that the Landau level spectrum arising from the type-II Dirac fermions in VAl3 is distinct from that of known Dirac or Weyl semimetals. We also demonstrate a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. [ABSTRACT FROM AUTHOR]