The effective attractive interaction between electrons, mediated by electron-phonon coupling, is a well-established mechanism of conventional superconductivity. In metals exhibiting a Fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Therefore, such superconductors are found only at temperatures below a few kelvin. Systems with flat energy bands have been suggested to cure the problem and provide a route to room-temperature superconductivity, but previous studies are limited to only BCS models with an effective attractive interaction. Here we generalize Eliashberg's theory of strong-coupling superconductivity to systems with flat bands and relate the mean-field critical temperature to the microscopic parameters describing electron-phonon and electron-electron interaction. We also analyze the strong-coupling corrections to the BCS results and construct the phase diagram exhibiting superconductivity and magnetic phases on an equal footing. Our results are especially relevant for novel quantum materials where electronic dispersion and interaction strength are controllable.

/pdf/competition-of-electron-phonon-mediated-superconductivity-3f7wwbs3bz.pdf

Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Two topologically distinct Dirac-line semimetal phases and topological phase transitions in rhombohedrally stacked honeycomb lattices

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

Recently published structural analysis and galvanomagnetic studies of a large number of different bulk and mesoscopic graphite samples of high quality and purity reveal that the common picture assuming graphite samples as a semimetal with a homogeneous carrier density of conduction electrons is misleading. These new studies indicate that the main electrical conduction path occurs within 2D interfaces embedded in semiconducting Bernal and/or rhombohedral stacking regions. This new knowledge incites us to revise experimentally and theoretically the diamagnetism of graphite samples. We found that the c-axis susceptibility of highly pure oriented graphite samples is not really constant, but can vary several tens of percent for bulk samples with thickness t ≳ 30 μm, whereas by a much larger factor for samples with a smaller thickness. The observed decrease of the susceptibility with sample thickness qualitatively resembles the one reported for the electrical conductivity and indicates that the main part of the c-axis diamagnetic signal is not intrinsic to the ideal graphite structure, but it is due to the highly conducting 2D interfaces. The interpretation of the main diamagnetic signal of graphite agrees with the reported description of its galvanomagnetic properties and provides a hint to understand some magnetic peculiarities of thin graphite samples.

https://www.mdpi.com/2312-7481/4/4/52/pdf

Diamagnetism of Bulk Graphite Revised

Multiple-excitation study of the double-resonance Raman bands in rhombohedral graphite

Measuring with high precision the electrical resistance of highly ordered natural graphite samples from a Brazil mine, we have identified a transition at $\sim$350~K with $\sim$40~K transition width. The step-like change in temperature of the resistance, its magnetic irreversibility and time dependence after a field change, consistent with trapped flux and flux creep, and the partial magnetic flux expulsion obtained by magnetization measurements, suggest the existence of granular superconductivity below 350~K. The zero-field virgin state can only be reached again after zero field cooling the sample from above the transition. Paradoxically, the extraordinarily high transition temperature we found for this and several other graphite samples is the reason why this transition remained undetected so far. The existence of well ordered rhombohedral graphite phase in all measured samples has been proved by x-rays diffraction measurements, suggesting its interfaces with the Bernal phase as a possible origin for the high-temperature superconductivity, as theoretical studies predicted. The localization of granular superconductivity at these two dimensional interfaces prevents the observation of a zero resistance state or of a full Meissner state.

Identification of a possible superconducting transition above room temperature in natural graphite crystals

Measuring with high precision the electrical resistance of highly ordered natural graphite samples from a Brazil mine, we have identified a transition at ~350 K with ~40 K transition width. The step-like change in temperature of the resistance, its magnetic irreversibility and time dependence after a field change, consistent with trapped flux and flux creep, and the partial magnetic flux expulsion obtained by magnetization measurements, suggest the existence of granular superconductivity below 350 K. The zero-field virgin state can only be reached again after zero field cooling the sample from above the transition. Paradoxically, the extraordinarily high transition temperature we found for this and several other graphite samples is the reason why this transition remained undetected so far. The existence of well ordered rhombohedral graphite phase in all measured samples has been proved by x-rays diffraction measurements, suggesting its interfaces with the Bernal phase as a possible origin for the high-temperature superconductivity, as theoretical studies predicted. The localization of the granular superconductivity at these two dimensional interfaces prevents the observation of a zero resistance state or of a full Meissner state.

https://iopscience.iop.org/article/10.1088/1367-2630/18/11/113041/pdf

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Identification of a possible superconducting transition above room temperature in natural graphite crystals

Identification of a possible superconducting transition above room temperature in natural graphite crystals