Direct Observation of Nodes and Twofold Symmetry in FeSe Superconductor

See allHide authors and affiliations

Science  17 Jun 2011:
Vol. 332, Issue 6036, pp. 1410-1413
DOI: 10.1126/science.1202226


We investigated the electron-pairing mechanism in an iron-based superconductor, iron selenide (FeSe), using scanning tunneling microscopy and spectroscopy. Tunneling conductance spectra of stoichiometric FeSe crystalline films in their superconducting state revealed evidence for a gap function with nodal lines. Electron pairing with twofold symmetry was demonstrated by direct imaging of quasiparticle excitations in the vicinity of magnetic vortex cores, Fe adatoms, and Se vacancies. The twofold pairing symmetry was further supported by the observation of striped electronic nanostructures in the slightly Se-doped samples. The anisotropy can be explained in terms of the orbital-dependent reconstruction of electronic structure in FeSe.

Despite intense experimental investigation, the pairing symmetry in the recently discovered iron (Fe)–based superconductors remains elusive (13). Phonon-mediated pairing in conventional superconductors is typically isotropic, leading to s-wave symmetry. Unconventional pairing mechanisms, such as spin fluctuations, may give rise to an order parameter with its sign change over the Fermi surfaces and a pairing symmetry such as s± (4, 5). The s± scenario is supported by the phase-sensitive “Josephson tunneling” (6, 7) and angle-resolved photoemission spectroscopy (8) experiments. If the sign change occurs on a single electron or hole pocket, then nodes should show up in the superconducting gap function (5). The presence of nodes in the Fe-based superconductors is still very controversial (912). Here, we report the observation of nodal superconductivity in iron selenide (FeSe) by use of a low-temperature scanning tunneling microscope (STM). We find that the symmetry of the order parameter is twofold instead of fourfold.

FeSe is the simplest Fe-based superconductor with an ambient-pressure transition temperature of Tc ~ 8 K that can increase to 37 K at a pressure of 8.9 GPa (1, 2). However, the uncertainty in the stoichiometry of Fe(Se,Te) samples (13) has made it challenging to understand the superconducting and normal states in the materials. To avoid this complexity, we grew the stoichiometric FeSe single-crystalline films on the SiC(0001) substrate with molecular beam epitaxy (MBE) in ultra-high vacuum (UHV) (13) and performed the STM experiment on the films in the same UHV system. The MBE growth of the FeSe films is characterized by a typical layer-by-layer mode, as demonstrated in fig. S1. The STM topographic images (Fig. 1, A and B, and fig. S1) revealed atomically flat and defect-free Se-terminated (001) surfaces with large terraces. The selenium atom spacing of the (1 × 1)–Se lattice (Fig. 1B) in the topmost layer was 3.8 Å, which is in good agreement with a previous report (1). The synchrotron x-ray power diffraction exhibited a structural transition from tetragonal to orthorhombic symmetry at 90 K for FeSe (14). In the low-temperature orthorhombic phase, the Fe-Fe lattice’s constant difference between the two close-packed directions was 0.012 Å at 20 K. This difference is too small to be resolved with STM, so Fig. 1B appears as a square lattice.

Fig. 1

STM characterization of the as-grown FeSe films. (A) Topographic image (2.5 V, 0.1 nA, 200 by 200 nm2) of a FeSe film (~30 unit cells thick). The step height is 5.5 Å. (Inset) The crystal structure. (B) Atomic-resolution STM topography (10 mV, 0.1 nA, 5 by 5 nm2) of FeSe film. The bright spots correspond to the Se atoms in the top layer. a and b correspond to either of Fe-Fe bond directions. The same convention is used for a and b axes throughout. (C) Temperature dependence of differential conductance spectra (setpoint, 10 mV, 0.1 nA). (D) Schematic of the unfolded Brillouin zone and the Fermi surface (green ellipses). The nodal lines for coskxcosky and (coskx + cosky ) gap functions are indicated by black and red dashed lines, respectively. The sizes of all pockets are exaggerated for clarity. The black arrow indicates the direction of nesting.

The scanning tunneling spectroscopy (STS) probes the quasiparticle density of states and measures the superconducting gap at the Fermi energy (EF) (15). In Fig. 1C, we show the tunneling spectra on the sample in Fig. 1A at various temperatures. The spatial homogeneity of the STS spectra (fig. S2) further demonstrates the high quality of the MBE samples. At a temperature below Tc, the spectra exhibit two conductance peaks and a gap centered at the Fermi energy. The maximum of the superconducting gap ∆0 = 2.2 meV is half of the energy between the two conductance peaks. The most striking feature of the spectra at 0.4 K, analogous to the cuprate high-Tc superconductors (15), is the V-shaped dI/dV and the linear dependence of the quasiparticle density of states on energy near EF. This feature explicitly reveals the existence of line nodes in the superconducting gap function. At elevated temperatures, the V-shaped spectra in Fig. 1C smear out as the superconducting gap disappears above Tc.

We suggest that the nodal superconductivity exists only in FeSe with a composition close to stoichiometry. By introducing Te into the compound, the ternary Fe(Se,Te) becomes a nodeless s±-wave superconductor, which is characterized by a fully gapped tunneling spectrum in the low-temperature limit (16). The nodes are intrinsic to the superconducting gap function of the stoichiometric FeSe. The scattering-induced extrinsic origin of the V-shaped spectrum in FeSe is quite unlikely. If the scattering strength is too weak, the gap is not closed; if it is too strong, there is a finite residual density of states at the Fermi level. In this extrinsic scenario, the V-shaped spectrum without residual density of states at the Fermi level is only possible in an accidental case in which scattering strength exactly matches a specific value (17).

Examination of the electronic structure in the Brillouin zone (BZ) reveals the origin of the nodes as well as the symmetry of the order parameter. In the unfolded BZ of FeSe (Fig. 1D), the hole and electron pockets are centered at the Γ [k = (0, 0)] and M [k = (0, ±π) and (±π, 0)] points, respectively (18). The five-band model (19) suggests that the electron pockets at (0, ±π) are mainly derived from the dxz and dxy orbitals of Fe and those at (±π, 0) from the dyz and dxy orbitals. The hole pockets at (0, 0) are derived from the dxz and dyz orbitals. In real space, the nodeless and nodal s±-wave gap correspond to the pairing between electrons on the next-nearest-neighbor (NNN) and nearest-neighbor (NN) Fe atoms, respectively. For the nodeless s± pairing, the Se-mediated exchange interaction J2 between the NNN Fe sites dominates, giving rise to the formation of spin-density wave (SDW) and the full sign reversal between the superconducting gap functions on the hole and electron pockets. However, if the exchange interaction J1 between the NN Fe sites is comparable with J2 then nodes may develop on the electron pockets (the nodal s±-wave) to minimize the total energy of the system (5).

In the extended s±-wave model, the gap function is given byΔs± = Δ1coskxcosky + Δ2(coskx + cosky) (1)The nodal lines of both coskxcosky and (coskx + cosky) are shown in Fig. 1D. According to the local density approximation calculation (18), the radius of the pockets at M points is not large enough to intercept with the nodal lines of coskxcosky, whereas (coskx + cosky ) can naturally lead to the nodes of superconducting gap on the electron pockets in the two orthogonal Fe-Fe directions. The gap function of FeSe is expected to contain the main features of (coskx + cosky), implying a stronger exchange interaction between NN than NNN. This scenario is also consistent with the absence of (π, 0) nesting-driven SDW order in FeSe (2). Both coskxcosky and (coskx + cosky ) belong to the same representation of the lattice point group; thus, they naturally coexist. Although the d-wave–like pairing cannot be ruled out on the basis of our current experimental results, the extended s±-wave pairing is much more natural, considering other evidence for the materials in the same family (16).

The reason why the Cooper pairing is nodal in FeSe but nodeless in Fe(Se,Te) remains a theoretical challenge. A possible mechanism involves the different chalcogen-height hch measured from the Fe plane in FeSe and Fe(Se, Te). Previous studies have shown that in pnictide superconductors, the pnictogen height hpn can act as a switch from the high-Tc nodeless pairing with large hpn (for example, LaFeAsO) to the low-Tc nodal pairing with small hpn (for example, LaFePO) (20). FeSe has the smallest hch (1.55 Å) among the FeSexTe1-x compounds. We expect that the small chalcogen-height in FeSe enhances the exchange interaction between the nearest-neighbor Fe atoms and results in a dominant (coskx + cosky) pairing symmetry with nodes on the electron pockets.

We generated inhomogeneity in the superconducting state using magnetic field and impurities to gain further insight into the pairing symmetry. When a magnetic field was applied (perpendicularly) to the FeSe sample surface, the field could enter the superconductor in the form of vortices (fig. S3). The superconducting order parameter is zero at the center of a vortex and approaches the zero field value at a distance in the order of coherence length ξ. Low-energy-bound states exist in the vortex because of the constructive interference of repeated Andreev scatterings at the boundary between the normal and superconducting states (21, 22). In the case of a superconductor with nodes, the quasiparticles form resonance states instead.

The dI/dV curve at center of a vortex in FeSe showed a pronounced zero-bias peak (Fig. 2A), in contrast to that in BaFe1.8Co0.2As2 (23). The appearance of such a peak demonstrates the high quality of the MBE-grown FeSe films (13). The spatial distribution of the peak reflected the quasiparticle wave function and was mapped out by measuring dI/dV at zero bias in the vicinity of a single vortex (Fig. 2B). This resonance state elongates along the a axis (presumably a direction with nodes). Intuitively, anisotropic distribution of the core state can be understood by the difference between coherence lengths ξ along the a and b directions, which mainly stems from the twofold symmetry of the gap function. Away from the center of a vortex core, the resonance peak splits into two symmetric branches in energy (Fig. 2, C and D). Although the peaks along the b axis eventually merge into the gap edges at a distance of 20 nm from the center (Fig. 2D), the energy of the peaks along the a axis approaches to ±0.6 meV instead of ∆0 = 2.2 meV (Fig. 2C).

Fig. 2

The vortex core states. (A) STS (setpoint, 10 mV, 0.1 nA) on the center of a vortex core. (B) Zero-bias conductance map (40 × 40 nm2; setpoint, 10 mV, 0.1 nA) for a single vortex at 0.4 K and 1 T magnetic field. (C and D) Tunneling conductance curves measured at equally spaced (2 nm) distances along a and b axes.

The above features are rather similar to the conventional s-wave superconductor NbSe2 (22), in which the observed sixfold star-shaped local density of states of a single vortex and the direction-dependent spectra are attributed to the anisotropic s-wave pairing with hexagonal symmetry (24). Further theoretical analysis is needed to fully understand the direction-dependent behavior of the resonance peaks in a nodal superconductor.

Not all of the vortex cores orientate along the same direction. Twin boundaries occurred in the crystalline films, and the magnetic vortices were easily pinned at these boundaries. As shown in fig. S4, two sides of a twin boundary exhibited different orientations of the vortex cores. Across the boundary (fig. S4, red arrows), the elongation direction of the core states was rotated by 90°. If a sample is composed of twinned domains, the twofold pairing symmetry cannot be revealed by macroscopic probes.

The response of a superconductor to impurities provides another method for uncovering the nature of superconducting pairing symmetry (15). The twofold symmetry of the FeSe gap function is further supported by the impurity-induced resonance states inside the superconducting gap. We deposited Fe atoms (Fig. 3A) on FeSe surface at low temperature (50 K). Single Fe adatoms formed and occupied hollow sites of the surface Se lattice. On a Fe adatom, two resonance states (at –1.4 meV and –0.4 meV) were clearly observed in STS in Fig. 3B. The density of states map in Fig. 3C again shows the twofold symmetry, but the state is more visible in the direction perpendicular to the long axis of a vortex core. Similar spectra and density of states maps were also observed on Se vacancies (Fig. 3, D to F) (13).

Fig. 3

Impurity-induced bound states in superconducting gap. (A to C) STM topography (10 mV, 0.1 nA, 3 by 3 nm2), dI/dV spectrum (0.4 K; setpoint, 10 mV, 0.1 nA), and density of states map (–0.4 mV, 0.1 nA, 1.5 by 1.5 nm2) of a single Fe adatom. (D to F) STM topography (10 mV, 0.1 nA, 3 by 3 nm2), dI/dV spectrum (0.4 K; setpoint, 10 mV, 0.1 nA), and density of states map (–1.0 mV, 0.1 nA, 3 by 3 nm2) of a single Se vacancy. The white dots indicate the topmost Se atoms. For each impurity type, at least five impurities were measured, and the energies of the bound states were found to be reproducible within an error of 0.1 meV.

The symmetry breaking from C4 to C2 is further supported by the quantum interference pattern of quasiparticles on samples with extra Se atoms deposited on the surface (Fig. 4A and fig. S5B). A typical topographic image at a sample bias of 10 mV is shown in Fig. 4A. The unidirectional stripes with the wave vectors exclusively along the a axis were observed. The measured period is 4.4 nm, which is approximately 16 times the Fe-Fe atom spacing according to autocorrelation analysis (Fig. 4B). Similarly striped nanostructure was recently demonstrated in the lightly doped Ca(Fe1-xCox)2As2 (25). In FeSe, we suggest that the C2 symmetric hole pockets (implying nesting, as shown in Fig. 1D) is responsible for the observed unidirectional stripes (26) and the twofold symmetry in electron pairing (fig. S6).

Fig. 4

Unidirectional electronic nanostructure induced by extra Se doping. (A) STM topography (10 mV, 0.1 nA, 40 by 40 nm2) of a Se-rich sample. The unidirectional stripes are along the b axis. The bright features, which are elongated along the diagonal directions of a and b axes, are due to the extra Se atoms. (B) Autocorrelation analysis of the STM image in (A).

The twofold symmetry could arise from the structural transition from tetragonal to orthorhombic phase at 90 K (14). However, the orthorhombic lattice distortion of 0.012 Å (half a percent of the lattice constant) can only lead to a very small anisotropy (~3%) in electronic structure according to the tight binding model, which is not large enough to account for the anisotropy of the vortex core. The relation between the symmetry breaking and antiferromagnetism is not clear either because long-range–ordered antiferromagnetism is not observed in FeSe under ambient pressure (2). As one of the many possible mechanisms, the recently proposed orbital-dependent reconstruction (2629) lifts the degeneracy between dxz and dyz orbitals of Fe and may explain the symmetry breaking from C4 to C2 as well as the nested Fermi surface geometry. Nevertheless, our experimental data are still not sufficient enough to support such a scenario, and the origin of C2 symmetry remains an open question.

Supporting Online Material

Materials and Methods

Figs. S1 to S6


References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. Acknowledgments: We thank J. P. Hu, T. Xiang, and X. Dai for helpful discussions. The work was financially supported by National Science Foundation and Ministry of Science and Technology of China. C.J.W. and H.-H.H. are supported by U.S. Army Research Office under award W911NF0810291.
View Abstract

Stay Connected to Science

Navigate This Article