Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.12435

Eliashberg Theory and Superfluid Stiffness of Band-Off-Diagonal Pairing in Twisted Graphene

Bernhard Putzer·Mathias S. Scheurer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Recently, band-off-diagonal superconductivity has been proposed [Nat. Commun. 14, 7134 (2023)] as a candidate pairing state for twisted graphene systems. Based on mean-field theory, it was shown that it not only naturally emerges from both intervalley electron-phonon coupling and fluctuations of the nearby correlated insulator, but also exhibits nodal and gapped regimes as indicated by scanning tunneling microscopy experiments. Here we study band-off-diagonal pairing within Eliashberg theory. We show that despite the additional frequency dependence, the leading-order description of both intervalley coherent fluctuations or intervalley phonons exhibits a symmetry prohibiting admixture of an intraband component to the interband pairing state. It is found that even- and odd-frequency pairing mix, which originates from the reduced number of flavor degrees of freedom in the normal state. From analytic continuation, we obtain the electronic spectral function showing that, also within Eliashberg theory, the interband nature leads to an enhanced spectral weight below the order-parameter energy compared to band-diagonal pairing. Finally, we also study the superfluid stiffness of band-off-diagonal pairing, taking into account multi-band and quantum geometry effects. It is shown that for $s$-wave and chiral momentum dependencies, conventionally leading to fully gapped phases, an interband structure reduces the temperature scale below which the stiffness saturates. Depending on parameters, for the chiral state, this scale can even be suppressed all the way to zero temperature leading to a complex competition of multiple dispersive and geometrical contributions. Our results show that interband pairing might also be able to explain more recent stiffness measurements in the superconducting state of twisted multilayer graphene.

Explore related subjects

cond-mat.supr-concond-mat.str-el

Keep this discovery

BibTeXRIS

Bernhard Putzer, Mathias S. Scheurer. 2025-01-21. Eliashberg Theory and Superfluid Stiffness of Band-Off-Diagonal Pairing in Twisted Graphene. https://doi.org/10.1103/physrevb.111.144513

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Out-of-equilibrium relaxation dynamics of the superconducting order parameter in CsV$_3$Sb$_5$

The application of a time-varying strain field drives a superconducting order parameter out of equilibrium. How the order parameter relaxes back to equilibrium depends both on the structure of the superconducting gap and on the nature of quasiparticle scattering. We report the discovery of an ultrasonic attenuation peak inside the superconducting state of the kagome superconductor CsV$_3$Sb$_5$. This peak is the natural consequence of the order parameter relaxation time matching the ultrasonic drive frequency near $T_{\rm c}$. From the measured frequency dependence of the peak, we extract a microscopic scattering time of $\tau_N = 25$ ps. This timescale is two orders of magnitude longer than the elastic scattering time as determined by resistivity measurements, but is comparable to the inelastic scattering time determined by thermal transport. Within the conventional framework of order-parameter relaxation, this implies that elastic scattering is ineffective at relaxing the superconducting condensate, consistent with a sign-preserving $s$-wave state obeying Anderson's theorem.

cond-mat.supr-con↗
arXiv2026

Eight-unit-cell electronic modulations in cuprates originating from local molecular orbitals

The pair density wave (PDW) state with eight-unit-cell (8a0) periodicity has been widely regarded as the primary order in cuprates, yet its existence and origin remain subjects of intense debate. Using spectroscopic imaging scanning tunneling microscopy, we observe spatial modulations of the electronic states with approximately 8a0 periodicity in both the superconducting and insulating regimes of hole-doped Ca2CuO2Cl2 cuprate. We find that the 8a0 spatial patterns are generated by the formation of molecular orbitals by doped holes, which organize into 4a0*4a0 plaquettes as the basic unit. Our results identify the 4a0 molecular orbital as the fundamental electronic building block in cuprates, while the 8a0 PDW represents a spatial subharmonic that emerges at sufficiently high doping.

cond-mat.supr-con↗
arXiv2026

Record-Breaking Elemental Superconductivity in Tetralayer Kagome Borophene

Superconductivity above the liquid-nitrogen temperature remains rare in two-dimensional elemental crystals, where strong covalent bonding often yields high phonon frequencies but insufficient electron-phonon coupling. Here, using first-principles calculations and fully anisotropic Migdal-Eliashberg theory, we predict tetralayer kagome borophene (TKB) stabilized by ABAB covalent stacking, as a liquid-nitrogen-temperature elemental superconductor. With a predicted critical temperature of 102 K, TKB sets a record-high value among previously reported elemental superconductors. Unlike known high-Tc boron-based superconductors dominated by in-plane sigma-bonding states and high-frequency in-plane B-B stretching modes, TKB realizes an out-of-plane s-pz-bonding-mediated pairing mechanism, in which interlayer s-pz bonding states at the Fermi level are strongly coupled to low-frequency out-of-plane vibrations of boron atoms. These results reveal a distinct out-of-plane pairing channel in multilayer borophene and establish covalent stacking engineering as a potential route for high-Tc superconductivity in two-dimensional materials.

cond-mat.supr-con↗