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Register a new userUniversal Non-equilibrium I-V Curve Near Two-channel Kondo-Luttinger Quantum Critical Point
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The Fermi liquid paradigm for metals has contributed enormously to our understanding of condensed matter systems. However a growing number of quantum critical systems have been shown to exhibit non Fermi liquid behavior. A full understanding of such systems is still lacking and in particular analytical results away from equilibrium are rare. In this work, we provide a distinct example of such kind in a two channel Kondo Luttinger model where a Kondo impurity couples to two voltage biased interacting electron leads, experimentally realizable in a dissipative quantum dot. An exotic quantum phase transition has been known to exist for two decades from the one channel to two channel Kondo ground states by enhancing electron interactions in the leads, but a controlled theoretical approach to this quantum critical point has not yet been established. We present a controlled method to this problem and obtain an analytical form for the universal nonequilibrium differential conductance near the transition. The relevance of our results for recent experiments is discussed.
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The problem of a spin-1/2 magnetic impurity near an antiferromagnetic transition of the host lattice is solved. The problem is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the AFM-critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin-fluctuations remains. Besides its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy-fermions.
In metals near a quantum critical point, the electrical resistance is thought to be determined by the lifetime of the carriers of current, rather than the scattering from defects. The observation of $T$-linear resistivity suggests that the lifetime only depends on temperature, implying the vanishing of an intrinsic energy scale and the presence of a quantum critical point. Our data suggest that this concept extends to the magnetic field dependence of the resistivity in the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ near its quantum critical point. We find that the lifetime depends on magnetic field in the same way as it depends on temperature, scaled by the ratio of two fundamental constants $mu_B/k_B$. These measurements imply that high magnetic fields probe the same quantum dynamics that give rise to the $T$-linear resistivity, revealing a novel kind of magnetoresistance that does not depend on details of the Fermi surface, but rather on the balance of thermal and magnetic energy scales. This opens new opportunities for the investigation of transport near a quantum critical point by using magnetic fields to couple selectively to charge, spin and spatial anisotropies.
We study the impurity entanglement entropy $S_e$ in quantum impurity models that feature a Kondo-destruction quantum critical point (QCP) arising from a pseudogap in the conduction-band density of states or from coupling to a bosonic bath. On the local-moment (Kondo-destroyed) side of the QCP, the entanglement entropy contains a critical component that can be related to the order parameter characterizing the quantum phase transition. In Kondo models describing a spin-$Simp$, $S_e$ assumes its maximal value of $ln(2Simp+1)$ at the QCP and throughout the Kondo phase, independent of features such as particle-hole symmetry and under- or over-screening. In Anderson models, $S_e$ is nonuniversal at the QCP, and at particle-hole symmetry, rises monotonically on passage from the local-moment phase to the Kondo phase; breaking this symmetry can lead to a cusp peak in $S_e$ due to a divergent charge susceptibility at the QCP. Implications of these results for quantum critical systems and quantum dots are discussed.
We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{rm G}$ occupies a sizable part of the phase diagram.
Scaling laws and universality play an important role in our understanding of critical phenomena and the Kondo effect. Here we present measurements of non-equilibrium transport through a single-channel Kondo quantum dot at low temperature and bias. We find that the low-energy Kondo conductance is consistent with universality between temperature and bias and characterized by a quadratic scaling exponent, as expected for the spin-1/2 Kondo effect. The non-equilibrium Kondo transport measurements are well-described by a universal scaling function with two scaling parameters.
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