Non-Majorana modes in diluted spin chains proximitized to a superconductor

Abstract

Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes [1][2][3][4][5][6] . The recent use of atomic manipulation techniques raised great expectations for successfully creating and controlling such chains [7][8][9][10] . Here, we craft diluted spin chains atom-by-atom following seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity 3 . We demonstrate that, starting from deep Shiba states, it is possible to cross the quantum phase transition, a necessary condition for the emergence of topological superconductivity, for very short chains. This transition is associated with the emergence of highly localized zero energy end modes. The use of a substrate with highly anisotropic Fermi surface enables to create spin chains characterized by distinct magnetic configurations along

Systematic study of Mn atoms, artificial dimers and chains on superconducting Ta(110)

“…For various experimental platforms, where artificial structures were fabricated by STM tip-induced atom manipulation, studies of the single YSR impurity and dimers have proven useful to understand the properties of chains, e.g. for Fe on Re(0001) [21], Cr on β − Bi 2 Pd [22], Mn on Nb(110) [23][24][25], Cr on Nb(110) [26,27] and Fe on NbSe 2 [28]. Therefore, one can consider the in-depth study of artificial dimers as a prerequisite for tailoring the Shiba bands in chains, which is necessary to determine potentially interesting crystallographic building directions and spacings for a given adatom species and superconducting substrate.…”

Effect of substrate spin-orbit coupling on the topological gap size of Shiba chains

“…One major difference, however, is the strength of SOC effects which is increased by a factor of ∼ 3 for Ta(110) compared to Nb(110) [23,30,32]. This allows us to directly compare new results using the Ta(110) substrate with previous ones using a Nb(110) substrate, which is particularly well-characterized in combination with Cr [34], Mn [22,23,35] and Fe [36] adatom structures. Since the superconducting gap of Ta(110) is sizeable (∆ Ta = 690 µeV) and atom manipulation is easily possible [24], we can determine the effect of a higher SOC in the superconducting substrate on Mn chains with an interatomic spacing of a = 331 pm in [001]direction (referred to as 1a − [001] chains) -as other physical quantities are expected to make only minor differences -by measuring the magnetic ground state using spin-polarized (SP)-STM and by resolving the in-gap band structure including a topological gap.…”

Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors

“…We also want to emphasize that our findings are only relevant for long helical spin chains consisting of many rotation periods as, for instance, weakly coupled YSR states in short trivial ferromagnetic chains can be tuned close to zero energy for certain exchange-coupling strengths [47,[100][101][102]. Nonetheless, it is a significant benefit that zero-energy bound states can be more conclusively identified as MBSs in helical spin chains compared to in semiconductor nanowires, especially since atomic chains have a reduced tunability in comparison to semiconductor nanowire devices and so the phase space of a purported MBS signal is more difficult to explore.…”

“…A single magnetic adatom on the surface of a superconductor leads to the formation of a Yu-Shiba-Rusinov (YSR) state, which is well studied in theory [82][83][84][85][86][87][88][89][90] and experiment [91][92][93][94][95][96][97][98]. Current experiments exploit an atom by atom construction technique to build the atomic chains, allowing great control over the chain length [47,[98][99][100][101][102][103] compared to self-assembled chains [104][105][106]. Here we will focus on long chains of magnetic adatoms that possess a helical ordering [77].…”