Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter.Comment: Main Text (6 pages, 2 figures) + Supplemental Material (7 pages, 1 figure

Superconductivity from incoherent Cooper pairs in strong-coupling regime

We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the situation when the increase of interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially phase incoherent Cooper pair order parameter. We show that this state can be characterized by a pseudogap and a scattering rate, which are determined by the self-energy due to electron scattering on phase fluctuations. At low temperatures, however, long-range correlations between the regions with different phases become important and establish global phase coherence hence superconductivity in the system. We develop a mean-field theory to describe a phase transition between the preformed Cooper pair and superconducting states. This scenario of superconductivity applies not only to conductors with parabolic bands but also to the flat-band systems in which flat and dispersive bands coexist and responsible for the Cooper pair formation as well as their phase synchronization.Comment: 9 pages, 1 figur

Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter

Preformed Cooper pairs in flat-band semimetals

Funding Information: The authors are thankful to Vladimir Zyuzin for critical discussions and to Pirinem School of Theoretical Physics for warm hospitality. This research was supported by the Academy of Finland (Project No. 308339) and in parts by the Academy of Finland Centre of Excellence program (Project No. 336810). Publisher Copyright: © 2022 American Physical Society.We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider a semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave intervalley pairing channel. The nearly dispersionless nature of the flat band at strong attraction between electrons promotes local Cooper pair formation so that the system may be modeled as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent superconductivity at low temperatures. We develop a mean-field theory to calculate transition temperature between the preformed Cooper pair state and the phase-coherent state for different interaction strengths in the Cooper channel. The transition temperature between semimetal and preformed Cooper pair phases is proportional to the interaction constant, the dependence of the transition temperature to the phase-coherent state on the interaction constant is weaker.Peer reviewe