Unconventional Superconductivity from Fermi Surface Fluctuations in Strongly Correlated Metals

Abstract

In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics 1,2 . When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of R ln 2 per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivity 3-5 is both pressing and challenging. Here we do so in the exemplary setting of heavy-fermion metals, where the amplified quantum fluctuations manifest in the form of Kondo destruction and large-tosmall Fermi-surface fluctuations. These fluctuations lead to unconventional superconductivity whose transition temperature is exceptionally high relative to the effective Fermi temperature, reaching several percent of the Kondo temperature scale. Our results provide a natural understanding of the enigmatic superconductivity in a host of heavy-fermion metals. Moreover, the qualitative physics underlying our findings and their implications for the formation of unconventional superconductivity apply to a variety of highly correlated metals with strong Fermi surface fluctuations 6,7 .

Nuclear-order-induced quantum criticality and heavy-fermion superconductivity at ultra-low temperatures in YbRh$_2$Si$_2$

“…The ultra-low temperature work on YbRh 2 Si 2 strongly supports the notion that superconductivity robustly develops in the vicinity of such a 'partial-Mott' QCP, as has been theoretically derived in Kondo-lattice models for a Kondo-destroying QCP [69] and experimentally evidenced from de Haas-van Alphen studies in high magnetic fields [24] and transport measurements [25] on pressurized CeRhIn 5 . Therefore, the results on these two compounds provide the long-sought [70] link between unconventional superconductivity in heavyfermion metals [71] and that occurring near a true Mott metal-insulator transition, e.g., in the cuprates [72] and organic charge-transfer salts [73].…”

Multiple superconducting phases in heavy-fermion metals

“…Moreover, because of the involvement of the Kondo effect, the spectral weight of the quantum critical fluctuations is large. The resulting superconducting transition temperature T c is found to be high, reaching several percent of the effective Fermi energy (Hu et al, 2021a).…”

“…For the AFM case, it has been recognized that, even in the order-parameter fluctuation description i.e. nominally the first class, the quantum criticality is actually distinct from the original Hertz-Millis picture and is accordingly labeled SDW r quantum criticality instead (Hu et al, 2021a). Here, the subscript "r" marks the fact that the underlying quasiparticles are highly renormalized by the Kondo effect, which makes the Landau description valid only below a very small energy scale k B T cr *.…”

“…Characteristic features of the KD quantum criticality include dynamical Planckian ( Zω kBT ) scaling and a sudden jump of "large" to "small" Fermi surface (FS) across the QCP. The amplified quantum fluctuations of the KD quantum criticality in the normal state have been shown to drive HF superconductivity (Hu et al, 2021a). Moreover, because of the involvement of the Kondo effect, the spectral weight of the quantum critical fluctuations is large.…”

Dynamical Planckian scaling of charge response at a particle-hole-asymmetric quantum critical point with Kondo destruction

“…Such a charge-channel singularity is indeed found theoretically near Kondo-destruction transitions in Kondo-limit models with SU(2) symmetry [20] or very large spin degeneracy [21,22]. It has been argued that the singular charge response is important both for strange-metal behavior [19] and emergent high-T c superconductivity [23], making it important to establish the generality of the phenomenon. In the Kondo limit, which involves local moments that are necessarily particle-hole-symmetric, the charge-channel singularity is ultimately traced to the fate of the local moments, and thus develops in the same energy range as the singular spin response [17,[24][25][26][27].…”