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Register a new userYu-Shiba-Rusinov screening of spins in double quantum dots
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Added by
Kasper Grove-Rasmussen
Publication date
2017
fields
Physics
and research's language is
English
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A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model.
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Theoretical descriptions of Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities inside the gap of a superconductor typically rely on a classical spin model or are restricted to spin-1/2 quantum spins. These models fail to account for important aspects of YSR states induced by transition-metal impurities, including the effects of higher quantum spins coupled to several conduction-electron channels, crystal or ligand-field effects, and magnetic anisotropy. We introduce and explore a zero-bandwidth model, which incorporates these aspects, is readily solved numerically, and analytically tractable in several limiting cases. The principal simplification of the model is to neglect Kondo renormalizations of the exchange couplings between impurity spin and conduction electrons. Nevertheless, we find excellent correspondence in those cases, in which we can compare our results to existing numerical-renormalization-group calculations. We apply the model to obtain and understand phase diagrams as a function of pairing strength and magnetic anisotropy as well as subgap excitation spectra. The single-channel case is most relevant for transition-metal impurities embedded into metallic coordination complexes on superconducting substrates, while the multi-channel case models transition-metal adatoms.
When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity1. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap2-4. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes5 suitable for topological quantum computing6. Here we report the first realization of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms. We induce superconductivity in graphene by proximity effect7-9 brought by adsorbing nanometer scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy we measure the superconducting proximity gap in graphene and we visualize Yu-Shiba-Rusinov states in graphene grain boundaries. Our results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long sought experimental confirmation that graphene grain boundaries host local magnetic moments10-14 and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.
Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.
NbSe$_2$ is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wavefunctions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make NbSe$_2$ a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.
Photon-assisted tunneling frequently provides detailed information on the underlying charge-transfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a systematic Keldysh calculation of the subgap conductance and provides a detailed analytical understanding of photon-assisted tunneling into subgap states, in excellent agreement with a recent experiment. We focus on tunneling from superconducting electrodes and into Yu-Shiba-Rusinov states associated with magnetic impurities or adatoms, but we also explicitly extend our results to include normal-metal electrodes or other types of subgap states in superconductors. In particular, we argue that photon-assisted Andreev reflections provide a high-accuracy method to measure small, but nonzero energies of subgap states which can be important for distinguishing conventional subgap states from Majorana bound states.
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