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Physical review. B./Physical review. B

Pseudogap behavior in the local spinon spectrum of the power-law diverging multichannel Kondo model

Zuodong Yu, Danqing Hu, Jiangfan Wang, Xinloong Han

Published Feb 27, 2024• 0 citations
Publisher

Abstract

Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) $({\ensuremath{\rho}}_{c}(\ensuremath{\omega})={\ensuremath{\rho}}_{0}/{|\ensuremath{\omega}|}^{r}, 0<r<1)$ in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling, termed power-law diverging multichannel Kondo model. This model considers $M$ channel and $N$ spin degrees of freedom. Employing a renormalization group analysis and dynamical large-$N$ approach, our results reveal the emergence of a pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. We precisely determine the conditions under which the pseudogap behavior occurs, either by tuning the exponent $r$ or the ratio $\ensuremath{\kappa}=M/N$ to values such as ${r}^{*}$ or ${\ensuremath{\kappa}}^{*}$. This pseudogap phase of spinon exhibits distinct physical properties that could have an impact on the properties of real systems. The results of this study provide novel insights into the pseudogap behaviors in strongly correlated systems and offer a playground to study the interplay between higher-order van Hove singularities and multichannel Kondo physics.

DOI
10.1103/physrevb.109.075161

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Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) (\ensuremathρc(\ensuremathω)=\ensuremathρ0/∣\ensuremathω∣r,0<r<1)({\ensuremath{\rho}}_{c}(\ensuremath{\omega})={\ensuremath{\rho}}_{0}/{|\ensuremath{\omega}|}^{r}, 0<r<1)(\ensuremathρc​(\ensuremathω)=\ensuremathρ0​/∣\ensuremathω∣r,0<r<1) in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling, termed power-law diverging multichannel Kondo model. This model considers MMM channel and NNN spin degrees of freedom. Employing a renormalization group analysis and dynamical large-NNN approach, our results reveal the emergence of a pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. We precisely determine the conditions under which the pseudogap behavior occurs, either by tuning the exponent rrr or the ratio \ensuremathκ=M/N\ensuremath{\kappa}=M/N\ensuremathκ=M/N to values such as r∗{r}^{*}r∗ or \ensuremathκ∗{\ensuremath{\kappa}}^{*}\ensuremathκ∗. This pseudogap phase of spinon exhibits distinct physical properties that could have an impact on the properties of real systems. The results of this study provide novel insights into the pseudogap behaviors in strongly correlated systems and offer a playground to study the interplay between higher-order van Hove singularities and multichannel Kondo physics.
Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) (ρc(ω)=ρ0/∣ω∣rρ_c(ω)=ρ_0/|ω|^{r}ρc​(ω)=ρ0​/∣ω∣r, $0
We discuss a multichannel SU(N) Kondo model which displays nontrivial zero-temperature phase transitions due to a conduction electron density of states vanishing with a power law at the Fermi level. In a particular large- N limit, the system is described by coupled integral equations corresponding to a dynamic saddle point. We exactly determine the universal low-energy behavior of spectral densities at the scale-invariant fixed points, obtain anomalous exponents, and compute scaling functions describing the crossover near the quantum-critical points. We argue that our findings are relevant to recent experiments on impurity-doped d-wave superconductors.
We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap $\mathrm{\ensuremath{\Delta}}$. We find that the low-energy spectrum in the limit $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ actually does not correspond to the spectrum strictly at $\mathrm{\ensuremath{\Delta}}=0$. In particular, in the two-channel Kondo model, the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at $\mathrm{\ensuremath{\Delta}}=0$. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of $\mathrm{\ensuremath{\Delta}}$ tends toward a finite and universal value when $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by $\mathrm{\ensuremath{\Delta}}\ensuremath{\ne}0$. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite $\mathrm{\ensuremath{\Delta}}$: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.
The traditional multichannel Kondo effect takes place when several gapless metallic electronic channels interact with a localized spin-SSS impurity, with the number of channels nnn exceeding the size of the impurity spin, n>2Sn>2Sn>2S, leading to the emergence of non-Fermi liquid impurity behavior at low temperatures. Here, we show that the effect can be realized even when the electronic degrees of freedom are strongly correlated and gapped. The system under consideration consists of a single spin-12\frac{1}{2}21​ impurity coupled isotropically to nnn spin singlet superconducting channels realized by one-dimensional leads with quasi-long-range superconducting order. The competition between the Kondo and superconducting fluctuations induces multiple distinct ground states and boundary phases depending on the relative strengths of the bulk and boundary interactions. Using the Bethe Ansatz technique, we identify four regimes: an overscreened Kondo phase, a zero-mode phase, a Yu-Shiba-Rusinov (YSR) phase, and a local-moment phase with an unscreened impurity, each with its own experimental characteristic. We describe the renormalization-group flow, the excitation spectrum, and the full impurity thermodynamics in each phase. Remarkably, even in the presence of a bulk mass gap, the boundary critical behavior in the Kondo phase is governed by the same exponents as in the gapless theory with the low-energy impurity sector flowing to the SU(2)nSU(2)_nSU(2)n​ Wess-Zumino-Witten (WZW) fixed point, and the impurity entropy monotonically decreasing as a function of temperature. In both the overscreened Kondo and zero-mode phases, the residual impurity entropy is Simp(T→0)=ln⁡[2cos⁡(π/(n+2))]S_{\mathrm{imp}}(T \to 0) = \ln[2\cos(π/(n+2))]Simp​(T→0)=ln[2cos(π/(n+2))]. In the YSR and unscreened phases on the other hand the impurity entropy exhibits non-monotonic temperature dependence and is effectively free at low temperatures with Simp(T→0)=ln⁡2S_{\mathrm{imp}}(T \to 0) = \ln 2Simp​(T→0)=ln2.
Quantum phase transitions out of equilibrium are outstanding emergent subjects in condensed matter physics with great fundamental importance and challenges. We theoretically investigate here the nonequilibrium quantum phase transition in a generic nano-setup: the pseudogap Kondo model where a Kondo quantum dot couples to two---left (L) and right (R)---voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels ${\ensuremath{\mu}}_{L/R}$, ${\ensuremath{\rho}}_{c,L(R)}(\ensuremath{\omega})\ensuremath{\propto}{|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\mu}}_{L(R)}|}^{r}$ with 0<r<10<r<10<r<1. In equilibrium (${\ensuremath{\mu}}_{L}\ensuremath{-}{\ensuremath{\mu}}_{R}=0$) and for 0<r<1/20<r<1/20<r<1/2, with increasing Kondo correlations this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo screened phase. At finite bias voltages and near criticality, we discover new nonequilibrium universal scaling behaviors in conductance, conduction electron TTT matrix, and local spin susceptibility via a controlled frequency-dependent renormalization group (RG) approach. The current-induced decoherence is key to understanding these distinct universal nonequilibrium quantum critical regimes. The relevance of our results to experiment is discussed.
Numerical renormalization group simulations have shown that the underscreened spin-1 Kondo impurity model with power-law bath density of states (DOS) $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{r}$ possesses various intermediate-coupling fixed points, including a stable non-Fermi-liquid phase. In this paper we discuss the corresponding universal low-energy theories, obtain thermodynamic quantities and critical exponents by renormalization group analysis together with suitable ϵϵϵ expansions, and compare our results with numerical data. Whereas the particle-hole symmetric critical point can be controlled at weak coupling using a simple generalization of the spin-1∕21∕21∕2 model, we show that the stable non-Fermi-liquid fixed point must be accessed near strong coupling via a mapping onto an effective ferromagnetic Seff=1∕2{S}_{\mathrm{eff}}=1∕2Seff​=1∕2 model with singular bath DOS with exponent ${r}_{\mathrm{eff}}=\ensuremath{-}r<0$. In addition, we consider the particle-hole asymmetric critical fixed point, for which we propose a universal field theory involving the crossing between doublet and triplet levels.