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Unconventional s-Wave Superconductivity in Fe(Se,Te)

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Science  23 Apr 2010:
Vol. 328, Issue 5977, pp. 474-476
DOI: 10.1126/science.1187399

Breaking Convention

The defining characteristics of a superconductor are symmetry of gap function, which tells us something about how pairs of electrons move through the sample, and the strength of that pairing. Together, this information gives us the highest temperature to which the superconductor can remain superconducting. In conventional superconductors the gap function is symmetric, or s-wave, and tends to have low transition temperatures. The newly discovered iron-based superconductors also have s-wave symmetry, but the rather high transition temperatures, in addition to other properties, indicate that they are not conventional. Hanaguri et al. (p. 474; see the Perspective by Hoffman) use scanning tunneling microscopy to provide direct experimental confirmation of the unconventional s-wave pairing of the superconducting carriers in these materials.

Abstract

The superconducting state is characterized by a pairing of electrons with a superconducting gap on the Fermi surface. In iron-based superconductors, an unconventional pairing state has been argued for theoretically. We used scanning tunneling microscopy on Fe(Se,Te) single crystals to image the quasi-particle scattering interference patterns in the superconducting state. By applying a magnetic field to break the time-reversal symmetry, the relative sign of the superconducting gap can be determined from the magnetic-field dependence of quasi-particle scattering amplitudes. Our results indicate that the sign is reversed between the hole and the electron Fermi-surface pockets (s±-wave), favoring the unconventional pairing mechanism associated with spin fluctuations.

The discovery of iron-based superconductors (1) triggered efforts to elucidate the mechanism of electron pairing responsible for a superconducting (SC) transition temperature of 55 K (2). Superconductivity in iron-based compounds occurs in close proximity to a magnetic order (3), invoking a pairing mechanism associated with spin fluctuations (47). The most fundamental information to identify the mechanism of pairing is the structure of SC-gap function, a measure of the strength and the quantum mechanical phase of electron pairs in momentum (k) space. Although the SC-gap function of conventional phonon-mediated superconductors has the same sign all over k space (s-wave symmetry), that of spin fluctuation–mediated superconductors is expected to exhibit a sign reversal between the Fermi momenta connected by the characteristic wave vector Q for spin fluctuations (8). As a consequence of the sign reversal, nodal planes in which the SC gap vanishes should exist in k space. If such nodal planes intersect the Fermi surface, low-energy quasi-particle (QP) states will emerge near the nodes.

In the case of iron-based superconductors, however, the presence of multiple bands at the Fermi level makes the situation much more complicated and exotic because the Fermi surface consists of disconnected two-dimensional hole and electron pockets centered at Γ and M points, respectively (Fig. 1A) (9). Because the hole and the electron pockets are similar in both shape and volume, the inter-band nesting between these pockets may generate spin fluctuations at Q = (π, 0) (in a Brillouin zone defined by the unit cell containing one iron). If such a spin fluctuation is responsible for the electron pairing, a sign reversal of the SC-gap function occurs between the hole and the electron pockets, resulting in s±-wave symmetry (47).

Fig. 1

Schematic of reciprocal-space electronic states of an iron-based superconductor. (A) Fermi surface and inter-Fermi-pocket scatterings in k space. According to a band calculation (9), there are two hole cylinders and two electron cylinders around Γ and M points, respectively. For simplicity, two Fermi cylinders are represented by one circle. The black dotted diamond denotes the crystallographic Brillouin zone, and the red square indicates the “unfolded” Brillouin zone defined by the unit cell containing one iron atom. Signs of the SC gap expected for s±-wave symmetry are shown by different colors. The arrows denote inter-Fermi-pocket scatterings. q2 and q3 connect different pockets, whereas q1 is an umklapp process. (B) Expected QPI spots in q space associated with inter-Fermi-pocket scatterings. Blue filled circles and red filled diamonds represent sign-preserving and sign-reversing scatterings, respectively, for the s±-wave SC gap. The former will be enhanced by a magnetic field, whereas the latter may be suppressed (16).

The low-energy QP excitation spectrum of s±-wave superconductor, however, is indistinguishable from those of conventional s-wave superconductors because the nodal planes do not exist on the Fermi pockets. Indeed, penetration depth measurement (10) and angle-resolved photoemission spectroscopy (11, 12) suggest that the amplitude of the SC gap is finite all over the Fermi surfaces. In order to distinguish an unconventional s±-wave from a conventional s-wave, the relative sign of the SC gap between the hole and the electron pockets must be determined by means of a phase-sensitive experiment (13).

We used a spectroscopic-imaging scanning tunneling microscopy (SI-STM) technique to measure the tunneling conductance as a function of energy at every pixel of the STM image. If the experiments are performed at low enough temperatures, each tunneling spectrum reflects QP density of states from which one can infer whether or not the nodal planes intersect the Fermi surface. By analyzing the data by use of Fourier transformation, k-resolved information on QP states can be obtained (1416). Also, the data under the magnetic field contain information on the relative sign of the SC-gap function (16). By combining these, the structure of the SC gap can then be determined unambiguously.

We performed SI-STM experiments on single crystals of Fe(Se,Te) with transition temperatures of Tc = 13 to ~14.5 K (13). Fe(Se,Te) has the simplest crystal structure among the various iron-based superconductors, consisting of only Fe(Se,Te) layers (17). The single crystals were cleaved so as to expose clean and flat surfaces, which were expected to be electronically neutral, minimizing the surface reconstruction. In a typical topographic image of a cleaved surface (Fig. 2A, inset), we imaged a square lattice with defects. The lattice constant was estimated to be ~3.8 Å, which is in good agreement with the inter-chalcogen distance. There are several bright spots in the image that probably represent excess iron atoms, which is in agreement with previous reports (18, 19).

Fig. 2

STM characterization of Fe(Se, Te). (A) Topographic image of the sample with Tc ~ 13 K taken at 1.5 K. The setup conditions for imaging were a sample-bias voltage of –20 mV and a tunneling current of 0.1 nA. Red arrows denote directions of the nearest iron-iron bond. The excess iron atoms are imaged as bright spots. (Inset) Magnified image showing an atomic lattice of chalcogens. (B) Temperature dependence of the tunneling spectrum examined at the same location 7 nm apart from the nearest iron atom. Data were collected for the sample with Tc ~ 14.5 K. The residual spectral weight at the Fermi energy is negligibly small, indicating that the SC gap is finite everywhere on the Fermi surface. Data were taken with a sample-bias voltage of –20 mV and a tunneling current of 0.1 nA. Bias-modulation amplitude was set to 0.1 mVrms.

The SC gap was identified in the tunneling spectra (Fig. 2B). At 0.4 K, the spectral weight is completely removed over a finite energy range near the Fermi energy, and instead very sharp gap-edge peaks grow at ~±1.7 meV. These features—characteristics of full-gap superconductivity—strongly suggest that there is no node in the SC-gap function on the Fermi surface. At elevated temperatures, the SC gap is smeared out and eventually disappears at about 11 K, which is somewhat lower than a bulk Tc ~ 14.5 K, presumably because of a spatial distribution of Tc inside the sample. Below Tc, additional structures can be seen outside the gap-edge peaks (around ~±4 meV), which are not symmetric about the Fermi level. The origin of these structures is unclear at present.

To explore QP states in k space by using SI-STM, we needed to detect QP interference (QPI) effect by means of Fourier analyses of spectroscopic images (1416). In the presence of defects in the sample, QPs are scattered and interfere with each other, generating electronic standing waves modulated with QP scattering vector q in real space. If the excitation energy E is low enough as compared with the Fermi energy, q connects different k points on the Fermi surface. Because of the presence of disconnected Fermi-surface pockets around the Γ and M points, the dominant QP scattering vectors may include the inter-Fermi-pocket scatterings q1, q2, and q3 (Fig. 1A), which can be observable in q space (Fig. 1B) by performing Fourier analyses of QPI patterns. Here, q1 connects the same pocket, representing the umklapp scattering. The remaining vectors q2 and q3, which bridge different Fermi-surface pockets, are important to discussion of the phase relationship between the hole and the electron pockets.

In order to image the standing waves associated with QPI, we collected the tunneling conductance g(r, E), where r is the position at the surface. We then mapped a ratio Z(r, E) ≡ g(r, +E)/g(r, –E). This ratio-taking process has a twofold purpose (15, 20). First, any extrinsic effects associated with the feedback loop so as to stabilize the tip-sample separation are removed (20). Second, QPI of Bogoliubov QPs should be particle-hole symmetric, namely q(+E) = q(–E), and the modulations at +E should be out of phase spatially with the modulations at –E (15, 21). The ratio-taking process naturally extracts particular modulations fitting these constraints.

The QPI experiments were performed at 1.5 K in the same field of view shown in Fig. 2A. As seen in Fig. 3A, Z(r, E) shows patchy domains of a length scale of a few nanometers, within which horizontal and vertical periodical streaks can be recognized. The streaks were rotated by 45° with respect to the atomic rows in Fig. 2A. These modulations with periodicity of twice the nearest iron-iron distance give rise to the broad peaks at q2 in the Fourier map Z(q, E) (Fig. 3B). Weak but clear peaks appear at q3 as well. Thus, the two scattering processes connecting different Fermi pockets were observed. The pronounced contrast of intensities between q2 and q3 (Fig. 3B) might suggest that the two processes are different in character.

Fig. 3

Magnetic field–dependent QPI patterns of Fe(Se, Te). (A) Real-space QPI pattern imaged by mapping the conductance ratio Z(r, E = 1 meV). Setup conditions were a sample-bias voltage of –20 mV and a tunneling current of 0.1 nA. Bias-modulation amplitude was set to 0.5 mVrms. (B) Z(q, E = 1 meV) obtained by taking a Fourier transformation. In order to enhance the signal-to-noise ratio, the original Z(q, E = 1 meV) map is averaged by folding it so as to superimpose the equivalent q positions. QPI signals are observed at two qs corresponding to the inter-Fermi-pocket scatterings q2 and q3. (C and D) Z(r, E = 1 meV) and Z(q, E = 1 meV) under a magnetic field of 10 T, respectively. QPI signals in q space exhibit prominent magnetic-field dependence. These experiments were carried out in the same field of view as Fig. 2A.

The intensity of the QPI is influenced strongly by the relative sign of the SC gap between the two Fermi pockets involved in the respective scattering, through the coherence factor C(q) representing the pairing of electrons. This gives rise to a phase-sensitive q selectivity for the QPI (16, 22, 23), which depends on the time-reversal symmetry of scattering potential. For scalar potential scattering that is even under time reversal, C(q) ~ 0 if q connects the states with the same sign of the SC gap. As a result, the QPI intensity, which is proportional to C(q), will appear only at sign-reversing momenta. For magnetic scattering that is odd under time reversal, the situations are opposite to scalar potential; C(q) ~ 0 if q connects the states with the opposite sign of the SC gap. If the SC gap is spatially inhomogeneous, Andreev scattering would also contribute to QPI. Similarly to magnetic scattering, C(q) of this process diminishes for sign-reversing momenta (16, 22, 23).

Once we know the nature of the QP scatterers, the phase-sensitive q selectivity for QPI provides an opportunity to highlight the relative sign of SC gaps in the Fourier-transformed QPI patterns (16, 22, 23). Similar ideas have also been proposed theoretically (2426). In practice, however, various QP scatterers inevitably coexist in the same sample. To use the phase-sensitive q selectivity for QPI, we needed to intentionally introduce scatterers that activate only either sign-reversing or sign-preserving scatterings.

As a source of extra scattering with well-defined q selectivity, we used magnetic-field effects (16, 2224). The magnetic field breaks the time-reversal symmetry and gives rise to vortices. Therefore, extra time reversal–odd scaterings may be generated, and also the suppression of a SC gap at the center of vortices may induce Andreev scattering (16, 22, 23). In both cases, scatterings with sign-preserving momenta should be selectively enhanced, as discussed above. In addition to such q-selective enhancement of QP scatterings, there may be a q-independent overall reduction of QPI intensity under magnetic fields; a Doppler shift of QP energies induced by supercurrent around vortices has been argued to suppress QPI amplitude irrespective of the nature of the scatterings (16, 22, 23). In total, sign-preserving and sign-reversing scatterings will be enhanced and suppressed, respectively, by a magnetic field. This technique was successfully applied in the detection of the d-wave SC-gap function in a cuprate superconductor (16).

In the case of s±-wave symmetry, q2 connects Fermi pockets with the opposite sign of the SC gap (sign-reversing scattering), whereas q3 does Fermi pockets with the same sign (sign-preserving scattering) (Fig. 1A). Therefore, intensities of QPI at q2 and q3 should be suppressed and enhanced, respectively, with application of the magnetic field. If the gap symmetry were of a d-wave or conventional s-wave, the magnetic-field dependence of intensities of QPI at q2 and q3 would be qualitatively different from that expected for s±-wave symmetry (13).

Shown in Fig. 3, C and D, are Z(r, E) and Z(q, E), respectively, under a magnetic field of 10 T applied perpendicular to the surface. Both scatterings at q2 and q3 show field dependence. In the field-induced change in Z(q, E) (Fig. 4), an opposite-field dependence is clearly observed between the two scatterings; the intensity at q2 is suppressed by a field, whereas that at q3 is enhanced, which was observed at all E studied (< 5 meV) and pronounced at 1 to ~3 meV near the edge of the SC gap (13). These observations are exactly what are expected for s±-wave symmetry, implying that the sign of the SC gap is reversed between the Fermi pockets around Γ and M points, whereas adjacent M-point Fermi pockets have the same sign. With the support of the fully gapped behavior of QP density of states demonstrated in Fig. 2B, we conclude that only s±-wave symmetry is consistent with the SI-STM data.

Fig. 4

Magnetic field–induced change in QPI intensities indicates the s±-wave symmetry. Difference between Z(q, E = 1 meV) maps with and without a magnetic field is shown by subtracting Fig. 3B from Fig. 3D. It is clear that signals at q2 and q3 exhibit totally opposite behavior, indicating that these two scatterings have different characters. This pattern can only be explained if the SC gap possesses s±-wave symmetry (13).

The sign reversal in the SC-gap function implies that the electron pairing is mediated by repulsive interaction in k space (8), which is most likely spin fluctuations associated with the nesting between the Fermi pockets (47). It was theoretically pointed out in models based on spin fluctuations that s±-wave is not the only possible symmetry in iron-based superconductors; d-wave and nodal s±-wave symmetries may be stabilized within the same theoretical framework, depending on the details of the band structure (27, 28). Experimentally, nodal superconductivity has indeed been suggested for LaFePO and BaFe2(As1-xPx)2 (29, 30). It should therefore be meaningful to establish the phase structure of the SC-gap function in these materials by using the k-resolved phase-sensitive QPI technique to step further toward understanding the pairing mechanism of iron-based superconductors.

Supporting Online Material

www.sciencemag.org/cgi/content/full/328/5977/474/DC1

Materials and Methods

SOM Text

Figs. S1 to S3

Tables S1 and S2

References

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. Position-dependent tip-sample separation generates an extra modulation in g(r, E) which predominantly has a periodicity of the underlying lattice (31). Unless wave function drastically changes its character in passing through the Fermi energy, such a modulation diminishes in Z(r, E).
  3. The authors thank H. Aoki, R. Arita, P. Coleman, Y. Kato, Y. Kohsaka, Y. Matsuda, I. I. Mazin, Y. Nagai, M. Ogata, T. Shibauchi, T. Shimojima, and S. Shin for valuable discussions and comments. This work has been supported by an Incentive Research Grant from RIKEN and Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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