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arXiv:2008.03223 · Physical review. B./Physical review. B

Quantum thermoelectric and heat transport in the overscreened Kondo regime: Exact conformal field theory results

D. B. Karki, Mikhail N. Kiselev

Published Dec 3, 2020• 15 citations
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Abstract

We develop a conformal field theory approach for investigation of the quantum charge, heat, and thermoelectric transport through a quantum impurity fine-tuned to a non-Fermi liquid regime. The non-Fermi-liquid operational mode is associated with the overscreened spin Kondo effect and controlled by the number of orbital channels. The universal low-temperature scaling and critical exponents for Seebeck and Peltier coefficients are investigated for the multichannel geometry. We discuss the universality of Lorenz ratio and power factor beyond the Fermi-liquid paradigm. Different methods of verifying our findings based on the recent experiments are proposed.

DOI
10.1103/physrevb.102.241402

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We develop a conformal field theory approach for investigation of the quantum charge, heat, and thermoelectric transport through a quantum impurity fine-tuned to a non-Fermi liquid regime. The non-Fermi-liquid operational mode is associated with the overscreened spin Kondo effect and controlled by the number of orbital channels. The universal low-temperature scaling and critical exponents for Seebeck and Peltier coefficients are investigated for the multichannel geometry. We discuss the universality of Lorenz ratio and power factor beyond the Fermi-liquid paradigm. Different methods of verifying our findings based on the recent experiments are proposed.
We theoretically investigate the thermoelectric transport through a circuit implementation of the three-channel charge Kondo model quantum simulator [Z. Iftikhar et al., Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592]. The universal temperature scaling law of the Seebeck coefficient is computed perturbatively approaching the non-Fermi liquid strong coupling fixed point using the Abelian bosonization technique. The predicted T^{1/3}logT scaling behavior of the thermoelectric power sheds light on the properties of Z_{3} emerging parafermions and gives access to exploring prefractionalized zero modes in the quantum transport experiments. We discuss a generalization of approach for investigating a multichannel Kondo problem with emergent Z_{N}→Z_{M} crossovers between "weak" non-Fermi liquid regimes corresponding to different low-temperature fixed points.
The multichannel Kondo model with SU(N)\mathrm{SU}(N)SU(N) spin symmetry and SU(K)\mathrm{SU}(K)SU(K) channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of SU(N),\mathrm{SU}(N),SU(N), corresponding to a fixed number of Abrikosov fermions ${\ensuremath{\sum}}_{\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{\ensuremath{\alpha}}=Q.$ For more than one channel (K>1),(K>1),(K>1), and all values of NNN and Q,Q,Q, the model displays non-Fermi behavior associated with the overscreening of the impurity spin. Universal low-temperature thermodynamic and transport properties of this non-Fermi-liquid state are computed using conformal field theory methods. A large-NNN limit of the model is then considered, in which $K/N\ensuremath{\equiv}\ensuremath{\gamma}$ and $Q/N\ensuremath{\equiv}{q}_{0}$ are held fixed. Spectral densities satisfy coupled integral equations in this limit, corresponding to a (time-dependent) saddle point. A low-frequency, low-temperature analysis of these equations reveals universal scaling properties in the variable $\ensuremath{\omega}/T,$ in agreement with conformal invariance. The universal scaling form is obtained analytically and used to compute the low-temperature universal properties of the model in the large-NNN limit, such as the T=0T=0T=0 residual entropy and residual resistivity, and the critical exponents associated with the specific heat and susceptibility. The connections with the ``noncrossing approximation'' and the previous work of Cox and Ruckenstein are discussed.
We investigate quantum transport through the Kondo impurity assuming both a large number of orbital channels $\mathcal{K}\ensuremath{\gg}1$ for the itinerant electrons and a semiclassical spin $\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$ for the impurity. The non-Fermi-liquid regime of the Kondo problem is achieved in the overscreened sector K>2S\mathcal{K}>2\mathcal{S}K>2S. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: (i) $\mathcal{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$, differential conductance vanishes, and (ii) S/K=C\mathcal{S}/\mathcal{K}=\mathcal{C}S/K=C with 0<C<1/20<\mathcal{C}<1/20<C<1/2, differential conductance reaches some nonvanishing fraction of its unitary value. Using the conformal field theory approach we analyze the behavior of the quantum transport observables and residual entropy in both semiclassical regimes. We show that the semiclassical limit (ii) preserves the key features of resonance scattering and the most essential fingerprints of the non-Fermi-liquid behavior. We discuss possible realization of two semiclassical regimes in semiconductor quantum transport experiments.
We study the coherent properties of fully screened and overscreened Kondo effects based on the Nozieres local Fermi-liquid theory and Affleck-Ludwig boundary conformal-field-theory approach, respectively. Coherent transports through an SU(N)\mathrm{SU}(N)SU(N) generalization of fully screened and the multi-K\mathcal{K}K-channel overscreened Kondo impurities at and beyond the particle-hole (PH) symmetric point are thoroughly investigated. We report distinctive Fermi-liquid coefficients characterizing the finite temperature correction to the transmission phase shift and normalized visibility in fully screened Kondo regime, which can be measured with the existing experimental setups. Our work equally uncovers the significance of temperature correction to the transmission phase shift and visibility in non-Fermi-liquid regime associated with the PH asymmetric overscreened Kondo effects with an arbitrary number of conduction channels K\mathcal{K}K. We propose viable roots of verifying our predictions in connection to the recent experiments, in particular with the experiments studying highly symmetric forms of fully screened Kondo effects and two-channel overscreened Kondo effects realized in quantum dot nanostructures.
The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.
The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its crossover to the one-channel counterpart, a Fermi liquid. Scaling up such a platform, we find a hierarchy of non-Fermi Liquids and their tunable crossovers based on a renormalization group analysis. Utilizing results from a conformal field theory, we further examine the universal conductances of this strongly correlated system and their finite temperature scaling, which elucidate the sharp distinctions between charge and spin Kondo physics.