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Unconventional superconductivity from crystal field fluctuations

M. A. Zeb

TL;DR

The paper proposes a novel mechanism for unconventional superconductivity driven by crystal field fluctuations associated with localized charge dynamics in strongly correlated systems. By deriving a fully quantum crystal-field interaction within an Anderson lattice and performing a Schrieffer–Wolff transformation, it shows how an attractive $V_{ ext{eff}}$ can mediate pairing, yielding a $d$-wave gap in cuprates when projected onto heavy-fermion bands formed by Kondo hybridization. The authors develop a three-band CuO$_2$ model, demonstrating that the gap takes the form $oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{k}}}}}}}} o oldsymbol{ ext{Delta}}_{f k} propto ( ext{cos}oldsymbol{k}_x a- ext{cos}oldsymbol{k}_y a)$, consistent with experiments, and connect Tc to the charge-transfer energy via $g \nsim 1/oldsymbol{ riangle}_{ ext{CT}}^2$. The work further conjectures how the experimental phase diagram, including the superconducting dome and pseudogap phenomena, can arise from doping-dependent localization of correlated orbitals and competition with Kondo screening.

Abstract

We present a novel pairing mechanism for superconductivity in strongly correlated electron systems, which often have both localised and itinerant charge carriers. An effective anisotropic interaction between the itinerant particles originates from the fluctuations in the crystal field associated with virtual hopping of the localised particles, a process that is also responsible for the Kondo exchange. Interestingly, this interaction is \emph{attractive} for charge transfer insulators such as cuprates. Considering a simple toy model for cuprates, without the antiferromagnetic exchange, this interaction leads to the correct d-wave superconducting gap, thus demonstrating its relevance.

Unconventional superconductivity from crystal field fluctuations

TL;DR

The paper proposes a novel mechanism for unconventional superconductivity driven by crystal field fluctuations associated with localized charge dynamics in strongly correlated systems. By deriving a fully quantum crystal-field interaction within an Anderson lattice and performing a Schrieffer–Wolff transformation, it shows how an attractive can mediate pairing, yielding a -wave gap in cuprates when projected onto heavy-fermion bands formed by Kondo hybridization. The authors develop a three-band CuO model, demonstrating that the gap takes the form , consistent with experiments, and connect Tc to the charge-transfer energy via . The work further conjectures how the experimental phase diagram, including the superconducting dome and pseudogap phenomena, can arise from doping-dependent localization of correlated orbitals and competition with Kondo screening.

Abstract

We present a novel pairing mechanism for superconductivity in strongly correlated electron systems, which often have both localised and itinerant charge carriers. An effective anisotropic interaction between the itinerant particles originates from the fluctuations in the crystal field associated with virtual hopping of the localised particles, a process that is also responsible for the Kondo exchange. Interestingly, this interaction is \emph{attractive} for charge transfer insulators such as cuprates. Considering a simple toy model for cuprates, without the antiferromagnetic exchange, this interaction leads to the correct d-wave superconducting gap, thus demonstrating its relevance.

Paper Structure

This paper contains 7 sections, 11 equations, 2 figures.

Table of Contents

  1. Effective interaction from crystal field fluctuations
  2. Superconductivity
  3. $d$-wave pairing in cuprates
  4. Some conjectures about the experimental phase diagram
  5. Methods
  6. Fully quantum crystal field interaction
  7. Effective interaction in the Anderson lattice model

Figures (2)

  • Figure 1: Three band model for CuO$_2$ and its d-wave superconducting gap function. (a) Orbitals considered in the model and the hopping amplitudes between them. (b) Fermi surface (white dotted lines) and superconducting gap function $\Delta_{{\bf k}} \propto (\cos k_xa-\cos k_ya)$ for the model with pairing mediated by the crystal field fluctuations. Red and blue show the sign while the curve thickness represents the size. The energy bands are calculated at $J=0.6$ and a high doping concentration of $0.7$. These fixed bands are used with the pairing interaction to obtain the superconductivity.
  • Figure 2: Temperature dependance of the gap (a) at $g=0.5$ alongwith zero temperature gap $\Delta(0)$ and critical temperature $T_c$ as a function of the coupling strength $g$ (b) for the fermi surface shown in Fig. \ref{['fig:model']}.