In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is found that there appear various types of Majorana fermions such as surface flat band, Majorana quartet and Möbius twisted surface state. Our theoretical results show that iron-based superconductors are promising platforms to realize rich topological crystalline phases.
The field and temperature dependencies of the longitudinal and Hall resistivity have been studied for high-quality FeSe${}_{1-x}$S${}_{x}$ (x up to 0.14) single crystals. Quasiclassical analysis of the obtained data indicates a strong variation of the electron and hole concentrations under the studied isovalent substitution and proximity of FeSe to the point of the majority carrier-type inversion. On this basis, we propose a `doped semimetal' scheme for the superconducting phase diagram of the FeSe family, which can be applied to other iron-based superconductors. In this scheme, the two local …
Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy "Fermi arcs" at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all …
One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to …
We have studied the newly found superconductor compound LaO$_{1-x}$F$_x$FeAs through the first-principles density functional theory calculations. We find that the parent compound LaOFeAs is a quasi-2-dimensional antiferromgnetic semimetal with most carriers being electrons and with a magnetic moment of $2.3μ_B$ located around each Fe atom on the Fe-Fe square lattice. Furthermore this is a commensurate antiferromagnetic spin density wave due to the Fermi surface nesting, which is robust against the F-doping. The observed superconduction happens on the Fe-Fe antiferromagnetic layer, suggesting a…
We predicted that AMgBi (A=K,Rb Cs), which have the same lattice structures as the 111 family of iron-based superconductors (Na/LiFeAs), are symmetry-protected Dirac semimetals located near the boundary of type-I and type-II Dirac semimetal phases. Doping Rb or Cs into KMgBi can drive the transition between the two phases. The materials can also be turned into Weyl semimetals and topological insulators by explicitly or spontaneously breaking time-reversal symmetry and C$_4$ lattice symmetry respectively.
While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superco…
Topological Dirac semimetals (TDSs) exhibit bulk Dirac cones protected by time reversal and crystal symmetry, as well as surface states originating from non-trivial topology. While there is a manifold possible onset of superconducting order in such systems, few observations of intrinsic superconductivity have so far been reported for TDSs. We observe evidence for a TDS phase in FeTe$_{1-x}$Se$_x$ ($x$ = 0.45), one of the high transition temperature ($T_c$) iron-based superconductors. In angle-resolved photoelectron spectroscopy (ARPES) and transport experiments, we find spin-polarized states o…
We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably Li(Fe$_{1-x}$Co$_x$)As. A key ingredient of this proposal are the 3D Dirac cones recently observed in ARPES experiments [P. Zhang et al., Nat. Phys. $\textbf{15}$, 41 (2019)]. Using an effective Hamiltonian around the $Γ-Z$ line we demonstrate the development of gapless one-dimensional helical Majorana modes, protected by $C_4$ symmetry. A topological index is derived which links the helical Majorana modes to the presence of monopoles in the Berry c…
We report the effect of hydrostatic pressure on the magnetotransport properties of the Weyl semimetal NbAs. Subtle changes can be seen in the $ρ_{xx}(T)$ profiles with pressure up to 2.31 GPa. The Fermi surfaces undergo an anisotropic evolution under pressure: the extremal areas slightly increase in the $\mathbf{k_x}$-$\mathbf{k_y}$ plane, but decrease in the $\mathbf{k_z}$-$\mathbf{k_y}$($\mathbf{k_x}$) plane. The topological features of the two pockets observed at atmospheric pressure, however, remain unchanged at 2.31 GPa. No superconductivity can be seen down to 0.3 K for all the pressures…
Lately, the three-dimensional (3D) Dirac semimetal, which possesses 3D linear dispersion in electronic structure as a bulk analogue of graphene, has generated widespread interests in both material science and condensed matter physics. Very recently, crystalline Cd3As2 has been proposed and proved to be one of 3D Dirac semimetals which can survive in atmosphere. Here, by controlled point contact (PC) measurement, we observe the exotic superconductivity around point contact region on the surface of Cd3As2 crystal. The observation of zero bias conductance peak (ZBCP) and double conductance peaks …
Measurements of the London penetration depth and tunneling conductance in single crystals of the recently discovered stoicheometric, iron - based superconductor, CaKFe$_4$As$_4$ (CaK1144) show nodeless, two effective gap superconductivity with a larger gap of about 6-9 meV and a smaller gap of about 1-4 meV. Having a critical temperature, $T_{c,onset}\approx$35.8 K, this material behaves similar to slightly overdoped Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (e.g. $x=$0.54, $T_c \approx$ 34 K)---a known multigap $s_{\pm}$ superconductor. We conclude that the superconducting behavior of stoichiometric CaK11…
We report the electronic properties of superconductivity in the topological nodal-line semimetal PbTaSe$_2$. Angle-resolved photoemission measurements accompanied by band calculations confirmed the nodal-line band structure in the normal state of single crystalline PbTaSe$_2$. Resistivity, magnetic-susceptibility and specific heat measurements have also been performed on high-quality single crystals. We observed upward features and large anisotropy in upper critical field ($H_{c2}$) measured in-plane (H//\textbf{ab}) and out-plane (H//\textbf{c}), respectively. Especially, $H_{c2}$ measured in…
Iron-chalcogenide single crystals with the nominal composition FeSe$_{0.5}$Te$_{0.5}$ and a transition temperature of $T_{c}\simeq14.6$ K were synthesized by the Bridgman method. The structural and anisotropic superconducting properties of those crystals were investigated by means of single crystal X-ray and neutron powder diffraction, SQUID and torque magnetometry, and muon-spin rotation. Room temperature neutron powder diffraction reveals that 95% of the crystal volume is of the same tetragonal structure as PbO. The structure refinement yields a stoichiometry of Fe_1.045Se_0.406Te_0.594. Add…
We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an appl…
The electronic structure, magnetic and structural properties of the superconductor ThFeAsN are discussed in relation to the Fe-pnictide and Fe-chalcogenide superconductors based on results of first principles calculations. The electronic structure is that of a high density of states semimetal. It shows approximately nested hole and electron Fermi surfaces of Fe $d$ character involving the $xz,yz$ and $xy$ orbitals. There is a strong tendency towards magnetism at the GGA level, and this magnetism is important for describing the Fe-As bonding, but greatly overestimates the magnetic ordering. The…
In the presence of certain symmetries, three-dimensional Dirac semimetals can harbor not only surface Fermi arcs, but also surface Dirac cones. Motivated by the experimental observation of rotation-symmetry-protected Dirac semimetal states in iron-based superconductors, we investigate the potential intrinsic topological phases in a $C_{4z}$-rotational invariant superconducting Dirac semimetal with $s_{\pm}$-wave pairing. When the normal state harbors only surface Fermi arcs on the side surfaces, we find that an interesting gapped superconducting state with a quartet of Bogoliubov-Dirac cones o…
Topological insulators/semimetals and unconventional iron-based superconductors have attracted major attentions in condensed matter physics in the past 10 years. However, there is little overlap between these two fields, although the combination of topological states and superconducting states will produce more exotic topologically superconducting states and Majorana bound states (MBS), a promising candidate for realizing topological quantum computations. With the progress in laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) with very high energy- and momentum-res…
We report the complex dielectric function of high-quality $A\textrm{Fe}_2\textrm{As}_2$, ($A$=Ca, Sr, Ba) single crystals with $T_{\mathrm{N}}\approx150\ \textrm{K}$, $200\ \textrm{K}$, and $138\ \textrm{K}$, respectively, determined by broadband spectroscopic ellipsometry at temperatures $10\leq T\leq300\ \textrm{K}$ and wavenumbers from $100\ \textrm{cm}^{-1}$ to $52000\ \textrm{cm}^{-1}$. In $\textrm{CaFe}_2\textrm{As}_2$ we identify the optical spin-density--wave gap $2Δ_{\mathrm{SDW}}\approx1250\ \textrm{cm}^{-1}$. The $2Δ_{\mathrm{SDW}}/(k_{\mathrm{B}}T_{\mathrm{N}})$ ratio, characterizi…
We report a doping study directed to intentionally induce disorder in PdTe$_2$ by the isoelectronic substitution of Pt. Two single-crystalline batches Pd$_{1-x}$Pt$_x$Te$_2$ have been prepared with nominal doping concentrations x = 0.05 and x = 0.10. Sample characterization by energy dispersive x-ray spectroscopy (EDX) revealed Pt did not dissolve homogeneously in the crystals. For the nominal value x = 0.10 small single crystals cut from the batch appeared to have x = 0.09, as well as the non stoichiometric composition Pd$_{0.97}$Pt$_{<0.004}$Te$_{2.03}$. Magnetic and heat capacity measuremen…
Single crystal neutron diffraction study has been performed on new superconductor A2Fe4Se5, where A = Cs, K, (Tl,Rb) and (Tl,K), and the same Fe vacancy ordered crystal structure and the same block checkerboard antiferromagne tic order recently discovered in the K2Fe4Se5 superconductor are observed. Thus, all known alkali metal and/or Tl intercalated iron selenide superconductors share common crystalline and magnetic structure. Investigation on electronic process in these new superconductors, for which a different electronic structure from those in previous Fe-based high-Tc superconductors is …
While bulk bismuth (Bi) is a semimetal, we have found clear evidence of superconductivity in a crystalline 72 nm diameter Bi nanowire below 1.3 K. In a parallel magnetic field (H), the residual resistance of the nanowire below Tc displays periodic oscillations with H, and the period corresponds to the superconducting flux quantum. This result provides evidence that the superconductivity comes from the interface shell between Bi and the surface oxide. In a perpendicular H, the resistance in the superconducting state shows Shubnikov-de Haas (SdH) oscillations, a signature of a normal metal. Thes…
Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even though the principal combination of topological bands and superconductivity promises exotic unprecedented avenues of superconducting states and Majorana bound states (MBSs), the central building block for topological quantum computation. Along with progressing laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) toward…
