Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2204.05654

Impurity scattering in superconductors revisited

F. Yang·M. W. Wu
View original source ↗Read source document ↗Export metadata ↓

Abstract

The diagrammatic formalism and transport equation are conventionally considered as separate but complementary techniques to tackle the impurity scattering effect. To compare with the previous studies from the gauge-invariant kinetic equation approach [F. Yang and M. W. Wu, Phys. Rev. B 98, 094507 (2018); 102, 144508 (2020)], we analytically perform a diagrammatic formulation of the impurity scattering in superconductors, with both transport and collective Higgs mode studied, in order to fill the long missing calculation of the Kubo current-current correlation in superconductors with impurity scattering and resolve the controversy (whether the impurity scattering can lead to the damping of Higgs mode) between gauge-invariant kinetic equation and Eilenberger equation. For transport behavior, through a special unitary transformation that is equivalent to the Wilson-line technique for the diamagnetic response, we derive the Meissner-supercurrent vertex. Then, by formulating the supercurrent-supercurrent correlation with Born and vertex corrections from impurity scattering, we recover the previously revealed microscopic momentum-relaxation rate of superfluid by gauge-invariant kinetic equation. This rate is finite only when the superconducting velocity is larger than a threshold, at which the normal fluid emerges and causes the friction with the superfluid current, similar to the Landau's superfluid theory of liquid helium. This derivation also provides a physical understanding of the relaxation-time approximation in the previous diagrammatic formulation in the literature, which leads to the friction resistance of the Meissner supercurrent. For the collective Higgs mode, we calculate the amplitude-amplitude correlation with Born and vertex corrections from impurity scattering. The vertex correction, which only emerges at nonequilibrium case, leads to a Higgs-mode damping, ......

Explore related subjects

cond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

F. Yang, M. W. Wu. 2022-04-12. Impurity scattering in superconductors revisited. https://doi.org/10.1103/physrevb.106.144509

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↗