Enhancing superconductivity using thermal bosons

Abstract

We investigate how the strong coupling of a superconductor to thermal bosons can enhance its superconducting critical temperature. To tackle this problem, we use a renormalization group approach that allows us to describe the competition between density fluctuations and the build-up of boson-induced attraction between fermions. Capturing the mutual influence of bosonic and fermionic sectors, the self-consistent renormalization group framework predicts a robust increase of the critical temperature across a wide range of interactions. We find a nontrivial dependence of the critical temperature on the boson mass and we establish a phase diagram for enhanced superconductivity driven by bosons being either in the condensed or thermal state. We outline possible experimental realizations in cold atomic systems and discuss implementations using electron-exciton mixtures in van der Waals material heterostructures.

Figures (4)

• Figure 1: Platforms for thermal-boson enhanced superconductivity. a) Ultracold atomic Bose-Fermi mixture in three dimensions. Black (blue) dots depict fermions (bosons), and relevant scales of the model are illustrated. b) 2D material heterostructure where interlayer excitons in a transition metal dichalcogenide (TMD) bilayer interact with electrons in a superconducting layer, allowing the formation of an interlayer trion (exciton-electron) bound state.
• Figure 2: Renormalization group analysis. (a) Diagrammatic representation of the RG equations. Black (blue) lines denote fermionic (bosonic) propagators. (b,c) RG flow with RG scale $k$ of the coupling constants $g_k$ and $\lambda_k$ with $n_B/n_F=0.1$, $(k_Fa_{BF})^{-1}=-0.2$, $T/T_F=0.4$, $m_B/m_F=2.175$. Solid curves represent the self-consistent solution, while dashed curves show the non-selfconsistent flow ($I_1=0$ and $I_2=0$ in (a)).
• Figure 3: Thermal-boson enhanced superconductivity. (a) Critical temperature $T_c/T_F$ as function of $1/(k_Fa_{FF})$ at fixed boson density (solid green and red), compared to the case where bosons are absent (dashed blue). The black line shows the temperature of Bose-Einstein condensation $T_c^{BEC}$. Parameters are $(k_F a_{BF})^{-1}=-0.2$, $n_B/n_F=0.1$, $m_B/m_F=2.175$. Inset: Dependence of $T_c$ on $(k_Fa_{BF})^{-1}$ at $(k_Fa_{FF})^{-1}=-1$. (b) Phase diagram of boson-modified superconductivity for a Bose-Fermi mixture as in (a). The border between the thermally induced and enhanced superconductivity is determined by the condition $T_c=2T_c^0$.
• Figure 4: Mass scaling. Enhancement of $T_c$ relative to its bare value $T_c^0$ as function of the mass ratio $m_B/m_F$ for $n_B/n_F=0.1$, $(k_F a_{BF})^{-1}=-0.2$ and $(k_F a_{FF})^{-1}=-1.5$. Inset: Log-linear plot showing $T_c$ up to large values of $m_B/m_F$.