Two‐Channel Kondo Physics: From Engineered Structures to Quantum Materials Realizations

Abstract

The Kondo effect assumes a central role in condensed matter physics. It describes the exchange scattering of electrons with a localized moment and occurs in a wide range of settings from rare earth‐based intermetallics to nanotubes and semiconductor heterostructures. A conceptually simple extension of the model, known as the two‐channel Kondo model, can give rise to singular scattering and the formation of an unconventional metal. Although the observation of the standard Kondo effect has become ubiquitous, its two‐channel counterpart has been proven difficult to realize. This article reviews attempts, challenges, and successes in realizing the two‐channel Kondo effect in artificial structures and real quantum materials.

Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem

“…The constitutive relation δΦ(G) = −T Tr[ΣδG] together with the assumption that G B , G f , g c and g Φ are diagonal in their respective indices, results in Eqs. (15,16). The impurity contribution to the free energy is given by…”

“…In addition to Eqs. (15,16), G f has to respect the constraint G f (τ → 0 − ) = q 0 , which is enforced through the Lagrange multiplier λ. For the relation between the free energy and the saddle point action S one finds f = S/β.…”

“…a magnetic moment, that hy-bridizes with a continuous and gapless bath of fermionic or bosonic modes and thus form an important testing ground for understanding that interplay. A well-known example is the isotropic two-channel Kondo model which possesses a residual entropy √ 2 which is understood in terms of a Majorana zero mode [14][15][16]. Here, this impurity entropy is defined as the difference between the entropies of the full quantum impurity model and that of the gapless host in which the impurity is embedded, i.e., the bath.…”

Qubit based on spin-singlet Yu-Shiba-Rusinov states

“…In the absence of flux bias, to make the two superconductors behave as two independent channels at least one of them needs to have a significant charging energy. It may be noted that this is also the necessary condition for observing the two-channel Kondo effect in normal-state systems 25,[49][50][51][52] . Coupling an impurity spin to two independent SC islands produces two singlet subgap states, as a Bogoliubov quasiparticle from either of the channels can screen the impurity spin 53 .…”

Kondo‐Mania

“…Die Streuung von Leitungselektronen an einem solchen Zwei-Niveau-System kann Übergänge zwischen den beiden lokalen Zuständen induzieren, was in der Pseudospin-Darstellung einem Austauschprozess wie im Kondo-Modell entspricht. Es zeigt sich allerdings, dass für Tunnelsysteme, in denen die Entartung der lokalen Zustände nicht durch eine Symmetrie geschützt ist, der dynamisch erzeugte effektive Zeeman-Term viel größer als die Kondo-Energie ist, sodass kein Kondo-Effekt auftreten kann [8].…”