Magnetoelectric spectroscopy of Andreev bound states in Josephson quantum dots

Wentzell, Nils; Florens, Serge; Meng, Tobias; Meden, V.; Andergassen, Sabine

doi:10.1103/physrevb.94.085151

Cited by 22 publications

(32 citation statements)

References 105 publications

(44 reference statements)

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“…This cutoff function was also used for quantum dots with BCS leads. [35,72,73,65] (iv) Differentiate the generating functional of one-particle irreducible vertex functions with respect to Λ.…”

Section: The Functional Renormalization Group Approachmentioning

confidence: 99%

The Anderson–Josephson quantum dot—a theory perspective

Meden

2019

J. Phys.: Condens. Matter

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Recent progress in nanoscale manufacturing allowed to experimentally investigate quantum dots coupled to two superconducting leads in controlled and tunable setups. The equilibrium Josephson current was measured in on-chip SQUID devices and subgap states were investigated using weakly coupled metallic leads for spectroscopy. This put back two "classic" problems also on the agenda of theoretical condensed matter physics: the Josephson effect and quantum spins in superconductors. The relevance of the former is obvious as the barrier separating the two superconductors in a standard Josephson junction is merely replaced by the quantum dot with well separated energy levels. For odd filling of the dot it acts as a quantum mechanical spin-1/2 and the relevance of the latter becomes apparent as well. For normal conducting leads and at odd dot filling the Kondo effect strongly modifies the transport properties as can, e.g., be studied within the Anderson model. One can expect that also for superconducting leads and in certain parameter regimes remnants of Kondo physics, i.e. strong electronic correlations, will affect the Josephson current.In this topical review we discuss the status of the theoretical understanding of the Anderson-Josephson quantum dot in equilibrium mainly focusing on the Josephson current. We introduce a minimal model consisting of a dot which can only host one spin-up and one spin-down electron repelling each other by a local Coulomb interaction. The dot is tunnel-coupled to two superconducting leads described by the BCS Hamiltonian. This model was investigated using a variety of methods, some capturing aspects of Kondo physics others failing in this respect. We briefly review this. The model shows a first order level-crossing quantum phase transition when varying any parameter provided the others are within appropriate ranges. At vanishing temperature it leads to a jump of the Josephson current. When being interested in the qualitative behavior of the phase diagram or the Josephson current several of the methods can be used. However, for a quantitative description elaborate quantum many-body methods must be employed.We show that a quantitative agreement between accurate results obtained for the simple model and measurements of the current can be reached. This confirms that the experiments reveal the finite temperature signatures of the zero temperature transition.In addition, we consider two examples of more complex dot geometries which might be experimentally realized in the near future. The first is characterized by the interplay of the above level-crossing physics and the Fano effect, the second by the interplay of superconductivity and almost degenerate singlet and triplet two-body states.

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Section: The Functional Renormalization Group Approachmentioning

confidence: 99%

The Anderson–Josephson quantum dot—a theory perspective

Meden

2019

J. Phys.: Condens. Matter

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“…In-gap states may cross each other (at the Fermi energy) when energies of the singly occupied configurations |↑ , |↓ coincide with one of the BCS-type superpositions [10]. In S-QD-S circuits this singlet-doublet quantum phase transition is responsible for a reversal of the DC Josephson current, so called "0−π transition", studied theoretically [11][12][13] and in the last decade observed experimentally [14,15].…”

Section: Introductionmentioning

confidence: 99%

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

et al. 2017

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We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-π) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact Numerical Renormalization Group and Quantum Monte Carlo calculations along with perturbative treatments in terms of the Coulomb repulsion and the hybridization term. Our results address especially the correlation effects reflected in dependencies of various quantities on the local Coulomb interaction strength as well as on the coupling to the normal lead. We quantitatively establish the phase-dependent Kondo temperature log TK (φ) ∝ cos 2 (φ/2) and show that it can be read off from the half-width of the zero-bias enhancement in the Andreev conductance in the doublet phase, which can be experimentally measured by the tunneling spectroscopy.

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“…where the topological transition and zero-energy modes occurs. Notice also that discontinuities in the Josephson CPR are still present in the interacting case [65] at zero temperature. As shown in Ref.…”

Section: Josephson Current-phase Discontinuitiesmentioning

confidence: 89%

“…In the limit of a large superconducting gap, i.e., when the gap is larger than the characteristic frequencies of the quantum dot, the degrees of freedom of the leads can be effectively integrated out [35,[64][65][66][67][68]. In absence of interactions (U = 0) the system can be described by an effective Hamiltonian which reads [35,64,65,67,68]…”

Section: Effective Modelmentioning

confidence: 99%

A zero-dimensional topologically nontrivial state in a superconducting quantum dot

Marra

Braggio

Citro

2018

Beilstein J. Nanotechnol.

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The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current–phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.

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Magnetoelectric spectroscopy of Andreev bound states in Josephson quantum dots

Cited by 22 publications

References 105 publications

The Anderson–Josephson quantum dot—a theory perspective

The Anderson–Josephson quantum dot—a theory perspective

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

A zero-dimensional topologically nontrivial state in a superconducting quantum dot

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