Flat Surface States Research Articles

Pressure-induced superconductivity and topological phase transitions in the topological nodal-line semimetal SrAs3

Topological nodal-line semimetals (TNLSMs) are materials whose conduction and valence bands cross each other, meeting a topologically protected closed loop rather than discrete points in the Brillouin zone (BZ). The anticipated properties for TNLSMs, include drumhead-like nearly flat surface states, unique Landau energy levels, special collective modes, long-range Coulomb interactions, or the possibility of realizing high-temperature superconductivity. Recently, SrAs3 has been theoretically proposed and then experimentally confirmed to be a TNLSM. Here, we report high-pressure experiments on SrAs3, identifying a Lifshitz transition below 1 GPa and a superconducting transition accompanied by a structural phase transition above 20 GPa. A topological crystalline insulator (TCI) state is revealed by means of density functional theory (DFT) calculations on the emergent high-pressure phase. As the counterpart of topological insulators, TCIs possess metallic boundary states protected by crystal symmetry, rather than time reversal. In consideration of topological surface states (TSSs) and helical spin texture observed in the high-pressure state of SrAs3, the superconducting state may be induced in the surface states, and is most likely topologically nontrivial, making pressurized SrAs3 a strong candidate for topological superconductor.

Nodal Line Spin-Gapless Semimetals and High-Quality Candidate Materials.

Spin-gapless semimetals (SGSMs), which generate 100% spin polarization, are viewed as promising semi-half-metals in spintronics with high speed and low consumption. We propose and characterize a new Z_{2} class of topological nodal line (TNL) in SGSMs. The proposed TNLSGSMs are protected by space-time inversion symmetry or glide mirror symmetry with two-dimensional (2D) fully spin-polarized nearly flat surface states. Based on first-principles calculations and effective model analysis, a series of high-quality materials with R3[over ¯]c and R3c space groups are predicted to realize such TNLSGSMs (chainlike). The 2D fully spin-polarized nearly flat surface states may provide a route to achieving equal spin pairing topological superconductivity as well as topological catalysts.

Impurity-induced resonant states in topological nodal-line semimetals

Nodal-line semimetals are characterized by a kind of topologically nontrivial bulk-band crossing, giving rise to almost flat surface states. Yet, a direct evidence of the surface states is still lacking. Here we study theoretically impurity effects in topological nodal-line semimetals based on the T-matrix method. It is found that for a bulk impurity, some in-gap states may be induced near the impurity site, while the visible resonant impurity state can only exist for certain strength of the impurity potentials. For a surface impurity, robust resonant impurity states exist in a wide range of impurity potentials. Such robust resonant states stem from the topological protected weak dispersive surface states, which can be probed by scanning tunneling microscopy, providing a strong signature of the topological surface states in the nodal-line semimetals.

Emergence of Topological insulator and Nodal line semi-metal states in XX\u2032Bi (X\u2009=\u2009Na, K, Rb, Cs; X\u2032\u2009=\u2009Ca, Sr)

In this article, we predict the emergence of non-trivial band topology in the family of XX′Bi compounds having Poverline{6}2m (# 189) space group. Using first principles calculations within hybrid functional framework, we demonstrate that NaSrBi and NaCaBi are strong topological insulator under controlled band engineering. Here, we propose three different ways to engineer the band topology to get a non-trivial order: (i) hydrostatic pressure, (ii) biaxial strain (due to epitaxial mismatch), and (iii) doping. Non-triviality is confirmed by investigating bulk band inversion, topological Z2 invariant, surface dispersion and spin texture. Interestingly, some of these compounds also show a three dimensional topological nodal line semi-metal (NLS) state in the absence of spin orbit coupling (SOC). In these NLS phases, the closed loop of band degeneracy in the Brillouin zone lie close to the Fermi level. Moreover, a drumhead like flat surface state is observed on projecting the bulk state on the [001] surface. The inclusion of SOC opens up a small band gap making them behave like a topological insulator.

Drumhead surface states and their signatures in quasiparticle scattering interference

We consider a two-orbital tight-binding model defined on a layered three-dimensional hexagonal lattice to investigate the properties of topological nodal lines and their associated drumhead surface states. We examine these surface states in centrosymmetric systems, where the bulk nodal lines are of Dirac type (i.e., four-fold degenerate), as well as in non-centrosymmetric systems with strong Rashba and/or Dresselhaus spin-orbit coupling, where the bulk nodal lines are of Weyl type (i.e., two-fold degenerate). We find that in non-centrosymmetric systems the nodal lines and their corresponding drumhead surface states are fully spin polarized due to spin-orbit coupling. We show that unique signatures of the topologically nontrivial drumhead surface states can be measured by means of quasiparticle scattering interference, which we compute for both Dirac and Weyl nodal line semimetals. At the end, we analyze the possible crystal structures with a symmetry that supports flat surface states which are effectively ringlike.

Selective phonon damping in topological semimetals

Topological semimetals are characterized by their intriguing Fermi surfaces (FSs) such as Weyl and Dirac points, or nodal FS, and their associated surface states. Among them, topological crystalline semimetals, in the presence of strong spin-orbit coupling, possess a nodal FS protected by nonsymmorphic lattice symmetries. In particular, it was theoretically proposed that ${\mathrm{SrIrO}}_{3}$ exhibits a bulk nodal ring due to glide symmetries, as well as flat two-dimensional surface states related to chiral and mirror symmetries. However, due to the semimetallic nature of the bulk, direct observation of these surface states is difficult. Here we study the effect of flat-surface states on phonon modes for ${\mathrm{SrIrO}}_{3}$ side surfaces. We show that mirror odd optical surface phonon modes are damped at the zone center, as a result of coupling to the surface states with different mirror parities, while even modes are unaffected. This observation could be used to infer their existence, and experimental techniques for such measurements are also discussed.

Mott insulator–superfluid phase transition in two-band Bose–Hubbard models with gapless nodal lines

Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose–Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid–Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of single-particle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.

Monoclinic C16: sp2-sp3 hybridized nodal-line semimetal protected by PT-symmetry

Based on first-principles calculations and Wannier tight-binding model, a three-dimensional (3D) carbon structure, named mC16, composed of interpenetrating graphene, is shown to be a topological nodal-line semimetal. The band structure calculations reveal that mC16 exhibits some exceptional properties. These include the Dirac band and band inversion around the Fermi level, and four nodal-lines in the entire Brillouin zone, symmetrically distributed on both sides of the mirror plane, and protected by the PT symmetry. In addition, the topological “drumhead-like” surface states appear on the (001) surface of mC16 and the double “drumhead-like” flat surface state emerges on the type-II (001) surface of the 3D mC16 structure. Moreover, the exotic surface Dirac points are located on the type-I (001) surface, implying that mC16 may process interesting surface transport properties. These new features make mC16 a new member in the topological carbon family, with promising novel applications in electronic device.

Dirac Line Nodes in Inversion-Symmetric Crystals.

We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2 invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu_{3}N near the Fermi energy by doping nonmagnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This Letter includes a brief discussion of the effects of spin-orbit interactions and symmetry breaking as well as comments on experimental implications.

Surface states of perovskite iridatesAIrO3: Signatures of a topological crystalline metal with nontrivialZ2index

There have been increasing efforts in realizing topological metallic phases with nontrivial surface states. It was suggested that orthorhombic perovskite iridates are classified as a topological crystalline metal (TCM) with flat surface states protected by lattice symmetries. Here we perform first-principles electronic structure calculations for epitaxially stabilized orthorhombic perovskite iridates. Remarkably, two different types of topological surface states are found depending on surface directions. On side surfaces, flat surface states protected by lattice symmetries emerge, manifesting the topological crystalline character. On the top surface, on the other hand, an unexpected Dirac cone appears, indicating surface states protected by a time-reversal symmetry, which is confirmed by the presence of a nontrivial topological $\mathbb{Z}_2$ index. These results suggest that the orthorhombic iridates are unique systems exhibiting both lattice- and global-symmetry-protected topological phases and surface states. Transitions to weak and strong topological insulators and implications of surface states in light of angle resolved photoemission spectroscopy are also discussed.

Electronic structures of ZnO(0001)-Zn and (000−1)-O polar surfaces

We investigated the electronic structures of ZnO(0001)-Zn and (000−1)-O surfaces by means of first-principles calculations. According to the results of the relaxation and the electrostatic criterion, the surface geometric relaxations and the charge transfer almost take place on the outer four double layers. For the (0001)-Zn surface, steep surface states appear in the band gap of bulk ZnO and follow the bottom of bulk conduction band. Moreover, Fermi level shifts up into the conduction band, which leads to the n-type conduction behaviour of (0001)-Zn surface. The dispersed partial charge densities derived from the Zn-4s state spread evenly on the surface and apparently lead to difficulty of getting an atom-resolved STM image. For the (000−1)-O surface, flat surface states emerge above the top of the valence band of bulk ZnO as Fermi level shifts down a little into the valence band. Based on that, the (000−1)-O surface can be predicted to have the p-type conductivity. The localized partial charge densities derived from the O-2p state makes it possible to get an atom-resolved STM image within the low bias voltage.

Nonlinear Competition between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.

Surface electronic structure of Tm(0001) and Yb(111).

Occupied d-like surface states were observed for the close-packed surfaces of Tm(0001) and Yb(111) metal films grown epitaxially on W(110) and Mo(110) substrates, respectively. In the case of Tm metal, the surface state exhibits almost no dispersion and is extended over the whole surface Brillouin zone, while in the case of Yb metal, it is restricted to a narrow region around the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} point. The surface shifts of the 4f binding energies on these close-packed surfaces were determined to be 0.47\ifmmode\pm\else\textpm\fi{}0.05 eV for Tm(0001) and 0.45\ifmmode\pm\else\textpm\fi{}0.03 eV for Yb(111). Both values are substantially smaller than reported previously for polycrystalline surfaces of the two metals. State-of-the-art band-structure calculations, based on density-functional theory, predict a flat surface state slightly above the Fermi energy. There is no obvious explanation for this inconsistency at the present time.