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arXiv:2308.16009

Coherent exchange-coupled nonlocal Kondo impurities

Lidia Stocker, Oded Zilberberg

Published Aug 30, 2023• 0 citations
arXivHTMLPDF

Abstract

Quantum dots exhibit a variety of strongly correlated effects, e.g., when tuned to emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dots setups, the magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic whispering gallery modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the coherent RKKY-like interaction that the cavity facilitates. Specifically, we find that (i) Kondo can win and form on each dot individually, or (ii) the cavity can win and mediate between the two dots either a singlet or a novel nonlocal Kondo-like effect phase, which we call "cat Kondo". We systematically study the quantum phase transitions between the different many-body states. Our discoveries lay the foundation for the experimental observation of unconventional nonlocal magnetic impurities.

DOI
10.3929/ethz-b-000679176

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Coherent exchange-coupled nonlocal Kondo impurities

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Quantum dots exhibit a variety of strongly correlated effects, e.g., they can emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dot setups, such magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the combined coherent orbital hybridization and RKKY-like interaction that the cavity facilitates. Specifically, we find that Kondo can form on each dot individually whereby the cavity can either (i) destroy the Kondo via the RKKY that mediates a singlet state on the two dots, or (ii) lead to an exotic orbital macrsoscopic superposition of the Kondo forming on each of the dots. We dub the latter “Kondo cat”. En route to this key finding, we rigorously study the many-body phase diagram of the system, as well as compare it with the case of coupling the dots via an incoherent RKKY channel. The realization of a Kondo cat can facilitate applications in metrology, and reveal the spin coherence length in mesoscopic devices. Published by the American Physical Society 2024

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In this thesis we study the physical properties of quantum magnetic impurities in con- densed matter systems. More precisely, we are interested in the quantum many-body phenomena emerging in metallic quantum wires with spin-orbit coupling (SOC) in the presence of magnetic impurities. In particular, we investigate Kondo effect in topological superconducting quantum wires sustaining Majorana zero modes (MZMs) bound to their edges. The first part of this work is dedicated to a general digression on the formation of localized magnetic moments in solid state materials and the emergence of the Kondo effect in single-impurity systems. We further study a system composed by a single level quantum dot coupled to a metallic reservoir and to two MZMs with opposite polarizations. The system is described by a version of single impurity Anderson model (SIAM) adapted to account for the MZMs. To access the Kondo physics we used the projection approach to derive an effective Kondo-like Hamiltonian from the SIAM. We show the coexistence of the many-body Kondo singlet and a local Majorana singlet which results from the robustness of the Kondo fixed points even in the presence local Majorana operators. Moreover, we show that the free MZMs of the system are responsible for the impurity residual entropy S res = N/ 2 k B ln(2), where N is the number of free MZMs. This result reveals a fractional residual entropy for an odd number of free MZMs associated with a local non-Fermi liquid behavior. Both results were confirmed by the perturbative Anderson’s Poor Man’s scaling (PMS), and the nonperturbative Wilson’s numerical renormalization group (NRG). The second part of the thesis is dedicated to the low-temperature physics of two-impurity systems. We revisit the well known Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two spatially separated magnetic impurities in a quantum wire with SOC. To compute the RKKY coupling we use the original Ruderman-Kittel approach, based on the traditional second-order perturbation theory. This allows us find also the Dzaloshinskii-Moriya and Ising interactions between the impurities, both originated from the SOC. Our results show that due to momentum-spin-lock, provided by the SOC, the RKKY coupling does not decay with the inverse of the inter-impurities distance, as in the usual case. Instead, the coupling survives even at large distances oscillating with a characteristic wave-vector 2k R, where k R is proportional to the Rashba SOC.

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arXiv:2406.05029•Physical review. B./Physical review. B•Aug 9, 2024•1 citation
Quantum dots exhibit a variety of strongly correlated effects, e.g., when tuned to emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dots setups, the magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic whispering gallery modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the coherent RKKY-like interaction that the cavity facilitates. Specifically, we find that (i) Kondo can win and form on each dot individually, or (ii) the cavity can win and mediate between the two dots either a singlet or a novel nonlocal Kondo-like effect phase, which we call "cat Kondo". We systematically study the quantum phase transitions between the different many-body states. Our discoveries lay the foundation for the experimental observation of unconventional nonlocal magnetic impurities.
Quantum dots exhibit a variety of strongly correlated effects, e.g., they can emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dot setups, such magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the combined coherent orbital hybridization and RKKY-like interaction that the cavity facilitates. Specifically, we find that Kondo can form on each dot individually whereby the cavity can either (i) destroy the Kondo via the RKKY that mediates a singlet state on the two dots, or (ii) lead to an exotic orbital macrsoscopic superposition of the Kondo forming on each of the dots. We dub the latter “Kondo cat”. En route to this key finding, we rigorously study the many-body phase diagram of the system, as well as compare it with the case of coupling the dots via an incoherent RKKY channel. The realization of a Kondo cat can facilitate applications in metrology, and reveal the spin coherence length in mesoscopic devices. Published by the American Physical Society 2024
We study the two-impurity Kondo model (TIKM) in two dimensions with spin-orbit coupled conduction electrons. In the first part of the paper we analyze how spin-orbit interactions of Rashba as well as Dresselhaus type influence the Kondo and Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions in the TIKM, generalizing results obtained by H. Imamura et al. [Phys. Rev. B 69, 121303(R) (2004)] and J. Malecki [J. Stat. Phys. 129, 741 (2007)]. Using our findings we then explore the effect from spin-orbit interactions on the non-Fermi-liquid quantum critical transition between the RKKY-singlet and Kondo-screened RKKY-triplet states. We argue that spin-orbit interactions under certain conditions produce a line of critical points exhibiting the same leading scaling behavior as that of the ordinary TIKM. In the second part of the paper we shift focus and turn to the question of how spin-orbit interactions affect the entanglement between two localized RKKY-coupled spins in the parameter regime where the competition from the direct Kondo interaction can be neglected. Using data for a device with two spinful quantum dots patterned in a gated InAs heterostructure we show that a gate-controlled spin-orbit interaction may drive a maximally entangled state to one with vanishing entanglement or vice versa (as measured by the concurrence). This has important implications for proposals using RKKY interactions for nonlocal control of qubit entanglement in semiconductor heterostructures.
We study the ground-state entanglement properties of nanostructured Kondo systems consisting of a pair of impurity spins coupled to a background of confined electrons. The competition between the Ruderman-Kittel-Kasuya-Yosida-like coupling and the Kondo effect determines the development of quantum correlations between the different parts of the system. A key element is the electronic filling due to confinement. An even electronic filling leads to results similar to those found previously for extended systems, where the properties of the reduced impurity spin subsystem are uniquely determined by the spin-correlation function defining a one-dimensional phase space. An odd filling, instead, breaks spin rotation symmetry unfolding a two-dimensional phase space showing rich entanglement characteristics as, e.g., the requirement of a larger amount of entanglement for the development of nonlocal correlations between impurity spins. We illustrate these results by numerical simulations of elliptic quantum corrals with magnetic impurities at the foci as a case study.
In this thesis we study the physical properties of quantum magnetic impurities in con- densed matter systems. More precisely, we are interested in the quantum many-body phenomena emerging in metallic quantum wires with spin-orbit coupling (SOC) in the presence of magnetic impurities. In particular, we investigate Kondo effect in topological superconducting quantum wires sustaining Majorana zero modes (MZMs) bound to their edges. The first part of this work is dedicated to a general digression on the formation of localized magnetic moments in solid state materials and the emergence of the Kondo effect in single-impurity systems. We further study a system composed by a single level quantum dot coupled to a metallic reservoir and to two MZMs with opposite polarizations. The system is described by a version of single impurity Anderson model (SIAM) adapted to account for the MZMs. To access the Kondo physics we used the projection approach to derive an effective Kondo-like Hamiltonian from the SIAM. We show the coexistence of the many-body Kondo singlet and a local Majorana singlet which results from the robustness of the Kondo fixed points even in the presence local Majorana operators. Moreover, we show that the free MZMs of the system are responsible for the impurity residual entropy S res = N/ 2 k B ln(2), where N is the number of free MZMs. This result reveals a fractional residual entropy for an odd number of free MZMs associated with a local non-Fermi liquid behavior. Both results were confirmed by the perturbative Anderson’s Poor Man’s scaling (PMS), and the nonperturbative Wilson’s numerical renormalization group (NRG). The second part of the thesis is dedicated to the low-temperature physics of two-impurity systems. We revisit the well known Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two spatially separated magnetic impurities in a quantum wire with SOC. To compute the RKKY coupling we use the original Ruderman-Kittel approach, based on the traditional second-order perturbation theory. This allows us find also the Dzaloshinskii-Moriya and Ising interactions between the impurities, both originated from the SOC. Our results show that due to momentum-spin-lock, provided by the SOC, the RKKY coupling does not decay with the inverse of the inter-impurities distance, as in the usual case. Instead, the coupling survives even at large distances oscillating with a characteristic wave-vector 2k R, where k R is proportional to the Rashba SOC.
The goal of this book is the investigation of physical effects at low energies caused by magnetic impurity adatoms, coupled to a small non-magnetic metallic substrate surface. Such systems can be understood with help of multi-impurity Kondo models, describing the substrate as a tight-binding model of finite-size and the impurities as quantum spins, which are antiferromagnetically coupled locally to their respective substrate sites. Focusing on one-dimensional finite-size systems with open boundary conditions at half-filling numerical exact diagonalisation and the variation of matrix product states (VMPS) method are used for the investigation. It is the aim to study finite-size effects in different regimes of the magnetic exchange interaction. For example due to the finite size of the system, the interplay of the Kondo effect and the indirect magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between impurity spins is site dependent and non-trivial for at least three impurity Kondo systems. Furthermore evidence for an unconventional and novel magnetic coupling mechanism, causing magnetic order in the actually non-magnetic substrate, due to inverse indirect magnetic exchange, will be given.
The competition between the Kondo screening and indirect magnetic exchange in systems with two magnetic impurities coupled to a conventional sss-wave superconductor gives rise to a nontrivial ground-state phase diagram. Here, we utilize the density matrix renormalization group (DMRG) method and exploit the non-Abelian spin-SU(2) symmetry to study the phase diagram for two quantum spin-12\frac{1}{2}21​ impurities locally exchange coupled to large one-dimensional chains. The nonlocal interimpurity exchange is treated as an emergent Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling. We find qualitatively different phase diagrams for impurity spins coupled to sites with odd or even distances ddd on the chain and a partial Kondo-screened spin-doublet phase that extends over the whole range of local exchange couplings JJJ in the limit of weak superconducting pairing strength $\mathrm{\ensuremath{\Delta}}$. Our numerical DMRG studies are complemented by exact diagonalization of small (quantum-box) systems and by perturbative-in-JJJ computations of the ddd- and $\mathrm{\ensuremath{\Delta}}$-dependent RKKY interaction. It is thereby demonstrated that the specific system geometry is essential for our understanding of magnetic impurity interactions in superconducting hosts, and thus for insights into the control of quantum-state properties in nanoparticle systems and topological superconductivity.