Final Report Summary - NANOSPIN (Nanoscale spin interactions and dynamics on superconducting surfaces)
Highly promising concepts for quantum computing make use of individual spins and their superposition states. The requirements for device implementations are stringent as the quantum states need to be addressed and manipulated while being sufficiently decoupled from the environment as to preserve them from fast decoherence. Subgap states in superconductors constitute one of the promising platforms. Within this project we investigated Yu-Shiba-Rusinov (YSR) states arising from the exchange coupling of individual magnetic adatoms with a superconducting substrate. The energy of these states is mainly determined by the exchange coupling strength. In case of strong coupling, the spin is “screened”, while it remains “free” at weak coupling. The transition between these states occurs at a critical coupling strength and is known as a quantum phase transition. We detect the YSR states by scanning tunneling spectroscopy as a pair of resonances inside the superconducting energy gap. Our goal was to establish techniques to measure and tune these states in isolated atoms as well as nanostructures.
The measurement process of YSR states by tunneling spectroscopy inherently requires an electronic excitation. As the YSR states are located within the superconducting energy gap, the current would be blocked after a first excitation if the excitation was not sufficiently quickly relaxed to the continuum. By tracking the evolution of the YSR states with increasing tunneling conductance, we determined the relaxation rates of the excited state. Furthermore, we showed that resonant Andreev reflections start to dominate the tunneling current once the excitation rates become similar in magnitude as the relaxation rates (Phys. Rev. Lett. 115, 087001 (2015)). Photon-assisted tunneling provides direct evidence of the tunneling processes. We observed intriguing asymmetric patterns of photon-assisted sidebands in resonant Andreev tunneling through YSR states. We explained these signatures by the threshold requirements on photon absorption and emission and the rate-limiting processes. The distinct fingerprints allow for a determination of the excited states’ lifetimes and reveal perspectives for an unambiguous identification of Majorana states.
We observed that individual atoms and molecules exhibit a characteristic number of YSR states within the superconducting energy gap. We showed that these are a result of the atomic-scale surrounding. The substrate effectively acts as a crystal field, which splits the d levels, where each singly-occupied d state induces a YSR state. The symmetry of the d states is imprinted on the YSR patterns (Phys. Rev. Lett. 117, 186801 (2016)). In case of molecular ligand fields, we found signatures of magnetic anisotropy splitting in the YSR state. A detailed lineshape analysis of the anisotropy-split YSR states including considerations of thermal occupations allowed us to conclude on the many-body ground state of the system (Nat. Commun. 6, 8988 (2015)). Moreover, we used additional molecular ligands to manipulate the coupling strength with the substrate, thereby providing access to the full range of the quantum phase diagram (Nat. Commun. 8, 2016 (2017)). We further showed that the STM tip can be used to continuously tune through the phase diagram and even induce a quantum phase transition between the screened spin state and the free spin state (Phys. Rev. Lett. 121, 196803 (2018)).
When two magnetic adsorbates are brought into sufficiently close distance, their YSR states overlap and hybridize. By mapping the hybrid states, we immediately revealed the nature of symmetric and antisymmetric linear combinations of the YSR states (Phys. Rev. Lett. 120, 156803 (2018)). These insights help for the understanding of the formation of hybrid states in larger structures and eventually of bands in longer atom chains.
Magnetic adatom chains have attracted particular interest in the last years after the Yazdani group revealed signatures of Majorana zero modes (Nadj-Perge et al., Science, 346, 602 (2014)). We have confirmed these signatures and provided further evidence of the topological gap size as well as for a correlation between the d states and the YSR bands (Phys. Rev. Lett. 115, 197204 (2015)). We have further elaborated on alternative Majorana platforms, although these did not show signatures of localized zero-energy modes (Nano Lett. 17, 4473 (2017)).
In summary, we have shown how to address and manipulate YSR states in single atoms and magnetic nanostructures on s-wave superconductors.
The measurement process of YSR states by tunneling spectroscopy inherently requires an electronic excitation. As the YSR states are located within the superconducting energy gap, the current would be blocked after a first excitation if the excitation was not sufficiently quickly relaxed to the continuum. By tracking the evolution of the YSR states with increasing tunneling conductance, we determined the relaxation rates of the excited state. Furthermore, we showed that resonant Andreev reflections start to dominate the tunneling current once the excitation rates become similar in magnitude as the relaxation rates (Phys. Rev. Lett. 115, 087001 (2015)). Photon-assisted tunneling provides direct evidence of the tunneling processes. We observed intriguing asymmetric patterns of photon-assisted sidebands in resonant Andreev tunneling through YSR states. We explained these signatures by the threshold requirements on photon absorption and emission and the rate-limiting processes. The distinct fingerprints allow for a determination of the excited states’ lifetimes and reveal perspectives for an unambiguous identification of Majorana states.
We observed that individual atoms and molecules exhibit a characteristic number of YSR states within the superconducting energy gap. We showed that these are a result of the atomic-scale surrounding. The substrate effectively acts as a crystal field, which splits the d levels, where each singly-occupied d state induces a YSR state. The symmetry of the d states is imprinted on the YSR patterns (Phys. Rev. Lett. 117, 186801 (2016)). In case of molecular ligand fields, we found signatures of magnetic anisotropy splitting in the YSR state. A detailed lineshape analysis of the anisotropy-split YSR states including considerations of thermal occupations allowed us to conclude on the many-body ground state of the system (Nat. Commun. 6, 8988 (2015)). Moreover, we used additional molecular ligands to manipulate the coupling strength with the substrate, thereby providing access to the full range of the quantum phase diagram (Nat. Commun. 8, 2016 (2017)). We further showed that the STM tip can be used to continuously tune through the phase diagram and even induce a quantum phase transition between the screened spin state and the free spin state (Phys. Rev. Lett. 121, 196803 (2018)).
When two magnetic adsorbates are brought into sufficiently close distance, their YSR states overlap and hybridize. By mapping the hybrid states, we immediately revealed the nature of symmetric and antisymmetric linear combinations of the YSR states (Phys. Rev. Lett. 120, 156803 (2018)). These insights help for the understanding of the formation of hybrid states in larger structures and eventually of bands in longer atom chains.
Magnetic adatom chains have attracted particular interest in the last years after the Yazdani group revealed signatures of Majorana zero modes (Nadj-Perge et al., Science, 346, 602 (2014)). We have confirmed these signatures and provided further evidence of the topological gap size as well as for a correlation between the d states and the YSR bands (Phys. Rev. Lett. 115, 197204 (2015)). We have further elaborated on alternative Majorana platforms, although these did not show signatures of localized zero-energy modes (Nano Lett. 17, 4473 (2017)).
In summary, we have shown how to address and manipulate YSR states in single atoms and magnetic nanostructures on s-wave superconductors.