Can a repulsive electron-electron interaction lead to electron pairing?

Superconductivity is caused by pairing of electrons (formation of Cooper pairs). Usually the required electron-electron interaction is mediated by phonons –vibrations of positive ions in the crystal lattice. In this case Nature finds a smart way of avoiding direct Coulomb repulsion of equally charged electrons in the pair. The large difference in masses of electrons and ions leads to retardation of electron-phonon interaction in time. The second electron is attracted to the position, where the first electron has been in a previous time frame. Therefore, electron-phonon interaction is attractive and naturally leads to formation of Cooper pairs with charge 2e. This explains appearance of the conventional low-temperature superconductivity in elementary metals like Niobium. However, there are reasons to doubt if high-temperature superconductivity is caused by the same electron-phonon mechanism. Theoreticians are speculating about a possibility of e-e pairing due to a much stronger, but repulsive electron-electron interaction. A new work published recently in Physical Review Letters by researchers from Fysikum provides a strong experimental evidence for that in novel type of iron-based high-temperature superconductors.  

Iron-based superconductors are perhaps the most interesting of all unconventional superconductors. Primarily, due to coexistence and competition of magnetism in iron and high-temperature superconductivity, and also because pnictides represent a rare example of multi-band superconductors (see Figure 1), which opens an additional degree of freedom in the electronic system.

Figure 1. A sketch of the Fermi surfaces: blue – hole type, red – electron type sheets. The black square represents a Brillouin zone in momentum space kx,y.

Generally, superconductivity is caused by pairing of electrons, due to their mutual interaction. An ordinary type of electron-electron interaction is phonon-mediated. Such interaction is attractive and naturally leads to formation of Cooper pairs with charge 2e. This explains appearance of conventional low-temperature superconductivity in materials like Niobium at T<Tc~few K. In this case Nature finds a smart way of avoiding direct Coulomb repulsion of equally charged electrons in the pair. Due to a large difference in masses of electrons and ions the electron-phonon interaction is retarded in time. The second electron is attracted to the position, where the first electron has been in a previous time frame. The wave function of the superconducting condensate in this case has the same phase, irrespective of electron momentum. This is called the s-wave order parameter, which has the same sign (no phase shifts) along the Fermi surface.

Iron-pnictide superconductors, like the studied compound Ba1−xNaxFe2As2, are high-temperature superconductors with an order of magnitude higher Tc~ few tens of K. Besides, they have an in-built magnetism in Fe-atoms. In this case the electron-electron interaction can be also mediated by “magnons”, i.e., spin-waves. Since magnons are electronic waves, there are no significant mass differences and consequently no significant retardation of interaction in time. Therefore, magnon-mediated e-e interaction is very strong, but repulsive, like a conventional Coulomb interaction. Yet, it has been predicted, that even a purely repulsive e-e interaction may lead to superconductivity IF there is a sign-change of the superconducting order parameter (shift of the phase of the superconducting condensate by p). Interestingly, in a multi-band superconductor, the sign-change may occur between different bands. For example, if the superconducting wave function at corner Fermi sheets will have a p-phase shift with respect to the bands in the center of the Brillouin zone, as sketched in the right panel of Figure 2. Thus, establishing of the symmetry of the superconducting order parameter within the Brillouin zone would provide an important direct clue about the mechanism of superconductivity. At present there is no confident experimental determination of the corresponding symmetry in iron-based superconductors. Such determination requires phase-sensitive measurements, which would allow direct determination of the eventual sign-change and phase-shifts of the order parameter.

Figure 2. A sketch of Josephson supercurrent flow between a single-band s-wave superconductor (left) and a two-band s± superconductor with a p-phase shift between central (blue) and corner (red) Fermi sheets (right). The p-shift between bands in the s± superconductor leads to a reversal of the current direction, as indicated by the blue and red arrows. This leads to a mutual cancellation of the supercurrent: Despite each of the bands can carry a large supercurrent the net current can be almost zero.

Josephson current between two superconductors provides a phase sensitive tool for probing their pairing symmetries. A Josephson junction occurs at a contact between two superconductors. The Josephson supercurrent is a product of the amplitudes of the order parameters (pair concentrations) and the sinus of the phase difference. The latter is the consequence of interference of the two wave functions within the junction. Thus, the p-phase shift leads to reversal of the current direction. Figure 2 represents a sketch of the Josephson junction between a conventional s-wave, and an s± superconductor. The p-shift between bands in the s± superconductor leads to reversal of the current direction, as indicated by the blue and red arrows. This leads to a mutual cancellation of supercurrent.

 

In the manuscript, published recently in Physical Review Letters, researchers from the Experimental Condensed Matter Physics group at Fysikum has performed such a phase-sensitive test of the pairing symmetry in iron-pnictide Ba1-xNaxFe2As2. They have fabricated and studied experimentally high-quality Josephson junctions between a conventional s-wave superconductor Nb and Ba1-xNaxFe2As2 single crystal. Left panel in Figure 3 shows an image of the studied sample.

Figure 3. Left: Scanning electron microscope impge of the studied sample. Right: Measured Josephson critical current versus magnetic field. Fraunhofer modulation Ic(H) is a clear indication of wave-function interference within the junction.

Right panel shows magnetic field dependence of the Josephson critical current in such Nb/ Ba1-xNaxFe2As2 junctions. Fraunhofer modulation Ic(H) is a clear indication of wave-function interference within the junction – which confirms phase sensitivity of the experiment.

 

“Our main observation is that the amplitude of the supercurrent in Nb/Ba1-xNaxFe2As2 junctions is almost three orders of magnitudes smaller than expected for a conventional s-wave superconductor. This is a clear evidence for the sign-reversal s± symmetry of the order parameter in this iron-pnictide. The p-phase shift between different Fermi-bands leads to an almost complete (to a sub-percent) cancellation of the total supercurrent. This in turn points towards unconventional repulsive magnon-mediated mechanism of superconductivity in iron-pnictides”, says prof. Vladimir Krasnov.

Contact: prof. Vladimir Krasnov (vladimir.krasnov@fysik.su.se)

Reference:Phase-Sensitive Evidence for the Sign-Reversal s± Symmetry of the Order Parameter in an Iron-Pnictide Superconductor Using Nb/Ba1−xNaxFe2As2 Josephson Junctions by A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, A. A. Kordyuk, and V. M. Krasnov
Phys. Rev. Lett. 120, 067001 (2018)– Published 6 February 2018

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