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Register a new userNumerical Renormalization Group Study of Kondo Effect in Unconventional Superconductors
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Masashige Matsumoto
Publication date
2000
fields
Physics
and research's language is
English
Authors
Masashige Matsumoto
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Orbital degrees of freedom of a Cooper pair play an important role in the unconventional superconductivity. To elucidate the orbital effect in the Kondo problem, we investigated a single magnetic impurity coupled to Cooper pairs with a $p_x +i p_y$ ($d_{x^2-y^2}+id_{xy}$) symmetry using the numerical renormalization group method. It is found that the ground state is always a spin doublet. The analytical solution for the strong coupling limit explicitly shows that the orbital dynamics of the Cooper pair generates the spin 1/2 of the ground state.
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A new type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using the Wilsons numerical renormalization group method. In this case, an angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a $p_x +i p_y$-wave state which is a full gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong coupling region ($T_{rm K}/Delta to infty$), while the ground state is always a spin doublet over all the $T_{rm K}/Delta$ region. Here $T_{rm K}$ and $Delta$ are the Kondo temperature and the superconducting energy gap, respectively. This is different from the s-wave pairing case where the Kondo singlet is realized for large $T_{rm K}/Delta$ values. The strong coupling analysis shows that the $p_x +i p_y$-wave Cooper pair is connected to the Kondo singlet via the orbital dynamics of the paired electrons, generating the spin of the ground state. This type of Kondo effect reflects the symmetry of the conduction electron system.
In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we show that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations cause repulsive pair scattering. The latter effect is however weakened by the hybridization splitting of the electron pockets. The resulting $S^{++}_{ee}$-wave pairing symmetry is consistent with experiments. We further propose that the quasiparticle interference pattern in scanning tunneling microscopy and the Andreev reflection in out-of-plane contact tunneling are efficient probes of in-phase versus anti-phase $S$-wave pairing on the electron pockets.
We employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Repulsive interactions usually lead to higher-angular momentum Cooper pairing. By considering not only longer-ranged hoppings, but also non-local electron-electron interactions, we are able to find superconducting solutions for all irreducible representations on the square and hexagonal lattices, including extended regions of chiral topological superconductivity. For the square, triangular and honeycomb lattices, we provide detailed superconducting phase diagrams as well as the coupling strengths which quantify the corresponding critical temperatures depending on the bandstructure parameters, band filling, and interaction parameters. We discuss the sensitivity of the method with respect to the numerical resolution of the integration grid and the patching scheme. Eventually we show how to efficiently reach a high numerical accuracy.
We present a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. We study the evolution of the single-particle spectra throughout the crossover regime. Although the DMFT does not include the interaction of the fermions with the Goldstone mode, we find strong deviations from the mean-field theory in the intermediate and strong coupling (BEC) regimes. In particular, we show that low-energy charge fluctuations induce a transfer of spectral weight from the Bogoliubov quasiparticles to a higher-energy incoherent hump.
The tunneling conductance is calculated as a function of the gate voltage in wide temperature range for the single quantum dot systems with Coulomb interaction. We assume that two orbitals are active for the tunneling process. We show that the Kondo temperature for each orbital channel can be largely different. The tunneling through the Kondo resonance almost fully develops in the region $T lsim 0.1 T_{K}^{*} sim 0.2 T_{K}^{*}$, where $T_{K}^{*}$ is the lowest Kondo temperature when the gate voltage is varied. At high temperatures the conductance changes to the usual Coulomb oscillations type. In the intermediate temperature region, the degree of the coherency of each orbital channel is different, so strange behaviors of the conductance can appear. For example, the conductance once increases and then decreases with temperature decreasing when it is suppressed at T=0 by the interference cancellation between different channels. The interaction effects in the quantum dot systems lead the sensitivities of the conductance to the temperature and to the gate voltage.
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