Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Trivial Fixed Points and Truncated SU(4) Kondo Models in a Quasi-Quartet Multipolar Quantum Impurity Problem
109
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focussed on impurities that have two degenerate internal states. In this work, inspired by recent experiments on the tetragonal material YbRu$_{2}$Ge$_{2}$, which has been shown to exhibit a local moment with a quasi-fourfold degenerate ground state, we consider the Kondo effect for such a quasi-quartet multipolar impurity. In the tetragonal crystal field environment, the local moment supports dipolar, quadrupolar, and octupolar moments, which interact with conduction electrons in entangled spin and orbital states. Using renormalization group analysis, we uncover a number of emergent quantum ground states characterized by non-trivial fixed points. It is shown that these previously unidentified fixed points are described by truncated SU(4) Kondo models, where only some of the SU(4) generators (representing the impurity degrees of freedom) are coupled to conduction electrons. Such novel non-trivial fixed points are unique to the quasi-quartet multipolar impurity, reinforcing the idea that an unexplored rich diversity of phenomena may be produced by multipolar quantum impurity systems.
rate research
Read More
Recently it was shown that the multipolar Kondo problem, wherein a quantum impurity carrying higher-rank multipolar moments interacts with conduction electrons, leads to novel non-Fermi liquid states. Because of the multipolar character of the local moments, the form of the interaction with conduction electrons is strongly dependent on the orbital-symmetry of the conduction electrons via crystalline symmetry constraints. This suggests that there may exist a variety of different non-Fermi liquid states in generic multipolar Kondo problems depending on the character of conduction electrons. In this work, using renormalization group analysis, we investigate a model where the multipolar local moment is coupled to conduction electrons with two different orbital-symmetry components, namely $p$-wave and $f$-wave symmetries. When each orbital-symmetry component is present alone, non-Fermi liquid states with exactly the same thermodynamic singularities appear. When both orbital-symmetry components are allowed, however, a completely different non-Fermi liquid state arises via the quantum fluctuations in the mixed scattering channels. This remarkable result suggests that the multipolar Kondo problem presents novel opportunities for the discovery of unexpected non-Fermi liquid states.
We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.
We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $propto 1/ [ | omega | ln ^{2}( Lambda /| omega | ) ] $ near the Dirac point $omega rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.
We examine the low energy behavior of a double quantum dot in a regime where spin and pseudospin excitations are degenerate. The individual quantum dots are described by Anderson impurity models with an on-site interaction $U$ which are capacitively coupled by an interdot interaction $U_{12}<U$. The low energy response functions are expressed in terms of renormalized parameters, which can be deduced from an analysis of the fixed point in a numerical renormalization group calculation. At the point where the spin and pseudospin degrees of freedom become degenerate, the free quasiparticle excitations have a phase shift of $pi/4$ and a 4-fold degeneracy. We find, however, when the quasiparticle interactions are included, that the low energy effective model has SU(4) symmetry only in the special case $U_{12}=U$ unless both $U$ and $U_{12}$ are greater than $D$, the half-bandwidth of the conduction electron bath. We show that the gate voltage dependence of the temperature dependent differential conductance observed in recent experiments can be described by a quasiparticle density of states with temperature dependent renormalized parameters.
Realization of semimetals with non-trivial topologies such as Dirac and Weyl semimetals, have provided a boost in the study of these quantum materials. Presence of electron correlation makes the system even more exotic due to enhanced scattering of charge carriers, Kondo screening etc. Here, we studied the electronic properties of single crystalline, SmBi employing varied state of the art bulk measurements. Magnetization data reveals two magnetic transitions; an antiferromagnetic order with a Neel temperature of ~ 9 K and a second magnetic transition at a lower temperature (= 7 K). The electrical resistivity data shows an upturn typical of a Kondo system and the estimated Kondo temperature is found to be close to the Neel temperature. High quality of the crystal enabled us to discover signature of quantum oscillation in the magnetization data even at low magnetic field. Using a Landau level fan diagram analysis, a non-trivial Berry phase is identified for a Fermi pocket revealing the topological character in this material. These results demonstrate an unique example of the Fermiology in the antiferromagnetic state and opens up a new paradigm to explore the Dirac fermion physics in correlated topological metal via interplay of Kondo interaction, topological order and magnetism.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
