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arXiv:0906.1838 · Physical Review B

Quantum criticality near the Stoner transition in a system of two tunnel-coupled quantum dots with spin-orbit coupling

Oleksandr Zelyak, Ganpathy N. Murthy

Published Nov 12, 2009• 7 citations
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Abstract

We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large-$N$ approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.

DOI
10.1103/physrevb.80.205310

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We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large-NNN approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.
Interacting electrons in quantum dots with large Thouless number ggg in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.
Quantum dots with a large Thouless number ggg embody a regime where both disorder and interactions can be treated nonperturbatively using large-NNN techniques (with N=gN=gN=g) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large-NNN approach, as we illustrate with two experimentally relevant examples.
Quantum criticality plays a central role in understanding non-Fermi liquid behavior and unconventional superconductivity in strongly correlated systems. In this review, we explore the quantum critical Eliashberg theory, which extends conventional Eliashberg approaches to non-Fermi liquid regimes governed by critical fluctuations. We discuss the theoretical foundations and recent developments in the field, focusing on the interplay between electronic interactions and bosonic modes near quantum phase transitions as described in the Yukawa-coupled version of the Sachdev-Ye-Kitaev model. Special emphasis is placed on the breakdown of quasiparticle coherence, anomalous scaling behaviour, Cooper pairing without quasiparticles, and emergent universality in different physical settings. Starting from a zero-dimensional "quantum-dot" model, we discuss the generalization to higher spatial dimensions and demonstrate the connection between quantum-critical Eliashberg theory and holographic superconductivity. Our analysis provides a perspective on how quantum criticality shapes the dynamics of strongly correlated metals and superconductors.
Quantum criticality plays a central role in understanding non-Fermi liquid behavior and unconventional superconductivity in strongly correlated systems. In this review, we explore the quantum critical Eliashberg theory, which extends conventional Eliashberg approaches to non-Fermi liquid regimes governed by critical fluctuations. We discuss the theoretical foundations and recent developments in the field, focusing on the interplay between electronic interactions and bosonic modes near quantum phase transitions as described in the Yukawa-coupled version of the Sachdev–Ye–Kitaev model. Special emphasis is placed on the breakdown of quasiparticle coherence, anomalous scaling behavior, Cooper pairing without quasiparticles, and emergent universality in different physical settings. Starting from a zero-dimensional quantum dot model, we discuss the generalization to higher spatial dimensions and demonstrate the connection between quantum critical Eliashberg theory and holographic superconductivity. Our analysis provides a perspective on how quantum criticality shapes the dynamics of strongly correlated metals and superconductors.
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We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP1^{1}1 representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velocity of spinons becomes zero, approaching the ferromagnetic quantum critical point, which implies emergence of local quantum criticality. Based on this scenario, we predict the ω/Tω/Tω/T scaling behavior near ferromagnetic quantum criticality beyond the conventional scenario of the weak-coupling approach.