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Domes of $T_c$ in superconductors with finite-range attractive interactions

Nazim Boudjada, Finn Lasse Buessen, Arun Paramekanti

Published Jun 8, 2020• 0 citations
OpenAlex

Abstract

The rise and fall of the superconducting transition temperature $T_c$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of $T_c$, we go beyond the prototypical Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. Using mean-field theory and functional renormalization group (FRG) methods, we find that for a characteristic interaction range $\ell$, there exists a dome in $T_c$ around $k_F \ell \sim \mathcal{O}(1)$. This result can intuitively be understood from the geometric relation between the Fermi surface and the interaction range. We show that our results generally hold for single-band as well as multi-band superconductors, in both two and three dimensions. Our model may be relevant for domes of $T_c$ in dilute weakly coupled superconductors or in engineered cold atom systems.

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The rise and fall of the superconducting transition temperature ${T}_{c}$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of ${T}_{c}$, we go beyond the prototypical attractive Hubbard model and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. By numerically solving the mean-field equations, as well as going beyond mean field theory using a functional renormalization group approach, we find that for a characteristic interaction range $\ensuremath{\ell}$, there exists a dome in ${T}_{c}$ around ${k}_{F}\ensuremath{\ell}\ensuremath{\sim}\mathcal{O}(1)$. For multiband systems, our mean field theory shows the presence of additional domes in the vicinity of Lifshitz transitions. Our results hold in both two and three dimensions and can be intuitively understood from the geometric relation between the Fermi surface and the interaction range. Our model may be relevant for domes of ${T}_{c}$ in dilute weakly coupled superconductors or in engineered cold atom systems.

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High-Temperature Superconductivity from Finite-Range Attractive Interaction

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High-Temperature Superconductivity from Finite-Range Attractive Interaction

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In this Letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range R_{s} that is much greater than the Fermi wavelength λ_{F} breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature T_{c} versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal T_{c}^{*}∼0.1E_{F} on the interaction range at R_{s}≫λ_{F}, E_{F} is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.

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Domes of TcT_cTc​ in superconductors with finite-range attractive interactions
The rise and fall of the superconducting transition temperature TcT_cTc​ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of TcT_cTc​, we go beyond the prototypical Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. Using mean-field theory and functional renormalization group (FRG) methods, we find that for a characteristic interaction range ℓ\ellℓ, there exists a dome in TcT_cTc​ around kFℓ∼O(1)k_F \ell \sim \mathcal{O}(1)kF​ℓ∼O(1). This result can intuitively be understood from the geometric relation between the Fermi surface and the interaction range. We show that our results generally hold for single-band as well as multi-band superconductors, in both two and three dimensions. Our model may be relevant for domes of TcT_cTc​ in dilute weakly coupled superconductors or in engineered cold atom systems.
The rise and fall of the superconducting transition temperature Tc{T}_{c}Tc​ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of Tc{T}_{c}Tc​, we go beyond the prototypical attractive Hubbard model and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. By numerically solving the mean-field equations, as well as going beyond mean field theory using a functional renormalization group approach, we find that for a characteristic interaction range $\ensuremath{\ell}$, there exists a dome in Tc{T}_{c}Tc​ around ${k}_{F}\ensuremath{\ell}\ensuremath{\sim}\mathcal{O}(1)$. For multiband systems, our mean field theory shows the presence of additional domes in the vicinity of Lifshitz transitions. Our results hold in both two and three dimensions and can be intuitively understood from the geometric relation between the Fermi surface and the interaction range. Our model may be relevant for domes of Tc{T}_{c}Tc​ in dilute weakly coupled superconductors or in engineered cold atom systems.
In this letter we consider DDD-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range RsR_sRs​ that is much greater than the Fermi wavelength λFλ_FλF​ breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature TcT_cTc​ versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal Tc∗∼0.1EFT_c^* \sim 0.1 E_FTc∗​∼0.1EF​ on the interaction range at Rs≫λFR_s \gg λ_FRs​≫λF​, EFE_FEF​ is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
In this Letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range R_{s} that is much greater than the Fermi wavelength λ_{F} breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature T_{c} versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal T_{c}^{*}∼0.1E_{F} on the interaction range at R_{s}≫λ_{F}, E_{F} is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
Abstract This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii–Kosterlitz–Thouless (BKT) temperature T BKT as a function of attractive pairing strength by associating it with the onset of ‘quasi-condensation’ in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS–BEC crossover theory for fermions, leads to non-monotonic behavior for T BKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that T BKT has an absolute maximum of the order of 0.1E F. We discuss how our results compare with those derived from the Nelson–Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in T BKT followed by an often dramatic decrease before the system enters the BEC regime.
Inspired by recent advances in the fabrication of surface superlattices, and in particular the triangular lattice made of tin (Sn) atoms on silicon, we study an extended Hubbard model on a triangular lattice. The observations of magnetism in these systems justify the inclusion of a strong on-site repulsion, and the observation of superconductivity suggests including an effective, nearest-neighbor attractive interaction. The attractive interaction mimics the effect of strong on-site repulsion near half filling, which can be seen in strong-coupling vertex calculations such as the Eliashberg method. With this extended Hubbard model on a triangular lattice with its geometrical frustration, we find a rich phase diagram of various magnetic orders and pairing functions, within the framework of self-consistent mean field theory. We uncover the competition between magnetism and unconventional superconductivity, and their coexistence for triplet pairings. We follow the Fermi surface of the system as the system is doped away from half filling and find nesting vectors and a Lifshitz transition, which provide an intuitive understanding of the phase transitions between the many orders we consider.
The phase diagram of the attractive Hubbard model with spatially inhomogeneous interactions is obtained using a single-site dynamical mean-field theory-like approach. The model is characterized by three parameters: the interaction strength, the active fraction (fraction of sites with the attractive interaction), and electron filling. The calculations indicate that in a parameter regime with intermediate values of interaction strength (compared to the bare bandwidth of the electrons), and intermediate values of the active fraction, unconventional superconductivity is obtained. The results of this work are likely to be relevant to many systems with spatially inhomogeneous superconductivity such as strongly correlated oxides, systems with negative UUU centers, and, in future, cold atom optical lattices.