A perfect gap in Majorana's world
Experiments conducted at the University of Hamburg reveal how electronic bands form inside the band gap of an elemental superconductor when magnetic chains are assembled on its surface. By probing the band dispersion, information about the topology of the electronic states were extracted enabling the prediction which of the bands are topologically non-trivial and thus expected to host an exotic Majorana mode. Astonishingly, one of the bands which clearly has a topological gap still shows no sign of a Majorana mode. This apparent contradiction with topological band theory might be explained by a more complex multi-orbital band structure of the chain which is neglected in oversimplified theories. The study was published in the journal Nature Physics.
In recent years, huge efforts have been made in order to find unquestionable signatures of Majorana modes in condensed matter systems, since they could eventually serve as a building block for a new generation of robust quantum computers. As one example, they are predicted to emerge at the boundaries of magnetic chains on a superconducting surface if the electronic bands in these chains have non-trivial topology. A combined observation of a non-trivial band topology in the bulk together with localized modes at the boundaries would therefore provide very strong evidence that the boundary modes are indeed Majoranas. However, measurements of the bands in magnet-superconductor-hybrids turn out to be very challenging.
Recently, a team of physicists led by PD Dr. Jens Wiebe in the research group of Prof. Roland Wiesendanger has found a way to resolve the dispersion of these low-energy bands. They studied how the electronic structure of atomic Manganese chains emerges when the chains are assembled atom-by-atom on a superconducting Niobium(110) surface. The wave-like character of quasiparticles confined within the perfectly defect-free chains leads to a quantum interference effect. This leads to a series of confined quantum states, reminiscent of the famous particle-in-a-box problem introduced in basic quantum mechanics classes (Fig. 1). From these patterns, energy and momentum of the quasiparticles can be related and thus, information about the band dispersion can be extracted (Fig. 2). A dominant band is visible, which appears to be gapped around zero-energy. It is found that this band gap cannot be attributed to normal but only to an unconventional type of superconductivity. Notably, measurements without momentum resolution would not be able to distinguish between these two cases. This type of superconductivity should lead to the emergence of Majorana modes at the two boundaries of the chain. Unexpectedly, the team did not find any signature of a Majorana mode from this particular band. The apparent contradiction is most probably explained by an additional band with Dirac-like dispersion appearing inside the unconventional gap of the former band (Fig. 2), which can be assigned to another orbital of the Manganese atoms. The more complex multi-orbital band structure puts additional constraints to the realization of Majorana modes in the magnetic chain platform.
“Accessing all this information enables an unprecedented microscopic understanding of topologically superconducting phases in magnetic chains - directly from experimental measurements”, says first author Lucas Schneider, who is a PhD candidate in the research group. Furthermore, it can help to characterize the nature of superconductivity in similar systems.
Figure 1: Topography (upper panel) and energy resolved local density of states (lower panel) along the center of a chain consisting of 17 individual Mn atoms. Confined quantum states with 1 - 6 maxima along the chain are observed at different energies. The energy of the states is determined by the dispersion of the relevant band. Image: UHH/MIN/Schneider
Figure 2: Extracted dispersion (momentum vs. energy) of the low-energy bands in Manganese chains on Niobium. The signature of a nearly parabolic band is found, which is gapped in an energy interval ?. This gap is assigned to an unconventional superconducting pairing which should lead to the emergence of Majorana modes at the two ends of the chain. An additional band with a Dirac-like dispersion crossing the gap might prevent the formation of the Majorana mode of the former band. Image: UHH/MIN/Schneider
L. Schneider, P. Beck, T. Posske, D. Crawford, E. Mascot, S. Rachel, R. Wiesendanger and J. Wiebe,
Topological Shiba bands in artificial spin chains on superconductors,
Nature Physics (2021).
PD Dr. Jens Wiebe
Department of Physics
University of Hamburg
Phone: 040 / 42838-3282