Dartmouth physics professor Rufus Boyack and postdoctoral research associate Nikolay Gnezdilov recently published a groundbreaking paper in condensed matter physics, Upper bound on Tc in a strongly coupled electron boson superconductor, in the journal Physical Review B. The authors solved a long-standing problem about the nature of superconductivity in electron-boson superconductors.
Boyack and Gnezdilov obtained their results by considering an electron-boson model known as the Yukawa-Sachdev-Ye-Kitaev model, which can be solved exactly without any perturbative treatment in the strength of the coupling between electrons and bosons. Their important result provides a pathway to understand strongly correlated matter.
Superconductivity is an incredible phenomenon in which a metal conducts electricity without dissipating any power. This property is extremely desirable for efficient energy transportation and many other applications. The superconducting phase of a metal occurs only below a certain critical temperature, Tc , which is extremely low for most conventional metals. It is highly desirable to have materials where Tc is large enough so that the superconducting phase can be reached more easily.
The conventional theory of superconductivity in metals is based on an electron-phonon pairing mechanism; a metal has a lattice of positively charged ions, which provides the attractive mechanism to pair electrons together. This pairing mechanism is governed by a dimensionless coupling constant λ, which is of the order of one for most common metals.
The critical temperature of an electron-phonon superconductor strongly depends on λ. An interesting idea has been to investigate the maximum possible value of Tc in a metal by considering the limit that λ→∞. A seminal result obtained in the 1970s by Allen and Dynes was that, for λ ≫ 1, Tc/ωD ∼ 0.183√λ , where ωD is a bosonic energy scale known as the Debye frequency. No material in nature has an infinite critical temperature, and so for the past several decades there has been a challenge as to how to obtain a finite critical temperature, even when the coupling λ is infinite. In their recent publication, Gnezdilov and Boyack provided the resolution to this long-standing problem.
Gnezdilov and Boyack showed that in the limit of infinite coupling strength, the dynamics of the boson that mediates the electron-pairing is significantly modified by interactions with electrons. In particular, they provided a general argument that pairing in the asymptotically strong coupling limit is enhanced by large λ, but it is also suppressed by λ due to the boson dynamics being modified in this regime. Their key insight was to account for the boson dynamics, which had generally not been considered before.
The amazing result obtained by Gnezdilov and Boyack is that the critical temperature saturates to a constant in the limit of infinite coupling. In fact, the Allen-Dynes growth of Tc eventually crosses-over to a small fraction of the Fermi energy at asymptotically strong coupling, as shown in the figures below. The latter provides an upper bound on Tc in the system. Moreover, the upper bound for Tc was only slightly higher than the experimentally measured values in exotic two-dimensional superconductors.
rufus_table_1.png
Left: Critical temperature as a function of the electron-boson coupling in units of the Fermi energy. Right: The same in units of the Debye frequency.
The implications of their work are far reaching. Gnezdilov and Boyack showed that the model they considered describes multiple classes of quantum critical electronic systems, opening a new avenue within pairing phenomena in quantum critical metals and introducing techniques significantly impacting the field of strongly correlated materials.
You can read Gnezdilov and Boyack's full publication here.