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arXiv:1905.03425 · Chinese Physics B

Resistivity minimum emerges in Anderson impurity model modified with Sachdev–Ye–Kitaev interaction*

Lan Zhang, Yin Zhong, Hong‐Gang Luo

Published Mar 18, 2021• 0 citations
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Abstract

We investigate a modified Anderson model at the large-N limit, where the Coulomb interaction is replaced by the Sachdev–Ye–Kitaev random interaction. The resistivity of conduction electron ρ c has a minimum value around temperature T*, which is similar to the Kondo system, but the impurity electron’s density of state A d(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface. This provides a counterintuitive example where resistivity minimum exists without Kondo resonance. The impurity electron’s entropy S d and specific heat capacity C v show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature. The system is a Fermi liquid at T < T*, and becomes a non-Fermi liquid at T > T*, and then becomes a Fermi gas at sufficiently high temperatures T ≫ T*. The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model. We also make a renormalization group analysis, which confirms the crossover from Fermi liquid to the non-Fermi behavior. It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid, which provides an alternative example showing resistivity minimum in condensed matter physics.

DOI
10.1088/1674-1056/abefcb

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We investigate a modified Anderson model at the large-N limit, where the Coulomb interaction is replaced by the Sachdev–Ye–Kitaev random interaction. The resistivity of conduction electron ρ c has a minimum value around temperature T*, which is similar to the Kondo system, but the impurity electron’s density of state A d(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface. This provides a counterintuitive example where resistivity minimum exists without Kondo resonance. The impurity electron’s entropy S d and specific heat capacity C v show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature. The system is a Fermi liquid at T < T*, and becomes a non-Fermi liquid at T > T*, and then becomes a Fermi gas at sufficiently high temperatures T ≫ T*. The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model. We also make a renormalization group analysis, which confirms the crossover from Fermi liquid to the non-Fermi behavior. It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid, which provides an alternative example showing resistivity minimum in condensed matter physics.
The periodic Anderson model is a classic theoretical model for understanding novel physics in heavy fermion systems. Here, we modify it with the Sachdev-Ye-Kitaev interaction, (random all-to-all interaction) thus the resultant model admits an exact solution at large- N (e.g. spin flavor) limit. By analytical field theory arguments and numerical calculations, we establish that the system supports a low-temperature (heavy) Fermi liquid and more interestingly a non-Fermi liquid solution at elevated temperature/energy. For physical observable, the latter one contributes a sharp peak at Fermi energy for spectral function, a non-Fermi liquid-like resistivity and shows a robust Fano lineshape in tunneling spectrum. This system may be simulated by ultracold atom gases and can serve as a good playground for studying ubiquitous symmetry-breaking instabilities like unconventional superconductivity or topological orders in generic heavy fermion systems.
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We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-MMM [where spin symmetry is enlarged to SU(M)]\mathrm{SU}(M)]SU(M)] study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of Tc{T}_{c}Tc​ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in Tc{T}_{c}Tc​ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.
A variety of exotic non-Fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The ``standard'' approach to studying these NFLs is by coupling a Fermi liquid to quantum critical fluctuations, which potentially can drive the system into a NFL. In this work we seek for an alternative understanding of these various NFLs in a unified framework. We first construct two ``elementary'' randomness-free models with four-fermion interactions only, whose many properties can be analyzed exactly in certain limit just like the Sachdev-Ye-Kitaev model. The most important new feature of our models is that, the fermion scaling dimension in the conformal invariant solution in the infrared limit is tunable by charge density. Then based on these elementary models, we propose two versions of lattice models with four-fermion interactions which give us non-Fermi liquid behaviors with dc resistivity scaling $\ensuremath{\varrho}\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ in a finite-temperature window, and $\ensuremath{\alpha}\ensuremath{\in}[1,2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.