1
Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a
Superconductor
Stevan Nadj-Perge*
1
, Ilya K. Drozdov*
1
, Jian Li*
1
, Hua Chen*
2
, Sangjun Jeon
1
, Jungpil
Seo
1
, Allan H. MacDonald
2
, B. Andrei Bernevig
1
and Ali Yazdani
1
1
Joseph Henry Laboratories & Department of Physics, Princeton University, Princeton,
NJ 08544, USA.
2
Department of Physics, University of Texas at Austin, Austin, TX 78712, USA.
*
These authors contributed equally to this work
To whom correspondence should be addressed. Email: yazdani@princeton.edu
Abstract
Majorana fermions are predicted to localize at the edge of a topological superconductor, a
state of matter that can form when a ferromagnetic system is placed in proximity to a
conventional superconductor with strong spin-orbit interaction. With the goal of
realizing a one-dimensional topological superconductor, we have fabricated
ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using
high-resolution spectroscopic imaging techniques, we show that the onset of
superconductivity, which gaps the electronic density of states in the bulk of the Fe chains,
is accompanied by the appearance of zero energy end states. This spatially resolved
signature provides strong evidence, corroborated by other observations, for the formation
of a topological phase and edge-bound Majorana fermions in our atomic chains.
2
Topological superconductors are a distinct form of matter that is predicted to host
boundary Majorana fermions (1-3). These quasi-particles are the emergent condensed
matter analogs of the putative elementary spin-1/2 particles originally proposed by Ettore
Majorana (4) with the intriguing property of being their own anti-particles. Super-
symmetric theories in particle physics and some models for dark matter in cosmology
motivate an ongoing search for free Majorana particles (5, 6). The search for Majorana
quasi-particle (MQP) bound states in condensed matter systems is motivated in part by
their potential use as topological qubits to perform fault-tolerant computation aided by
their non-Abelian characteristics (7, 8). Spatially separated pairs of MQP pairs can be
used to encode information in a nonlocal fashion, making them more immune to quantum
decoherence. Early proposals for the detection of MQPs were based on the properties of
superfluid
3
He, on exotic fractional quantum Hall states, or on correlated superconductors
(9-12). The focus in the last few years has shifted to the search for these exotic fermions
in weakly interacting synthetic systems in which proximity to a conventional Bardeen-
Cooper-Schrieffer (BCS) superconductor is used in concert with other electronic
properties to create the topological phase that hosts MQPs.
The idea that MQPs can be engineered in the laboratory grew from the theoretical
observation that proximity induced superconductivity on the surface state of a topological
insulator is topological in nature (13). Pairing on a spin-less Fermi surface (1), created
in this case by the spin-momentum locking of topological surface states, must be
effectively p-wave to satisfy the pair-wavefunction anti-symmetry requirement and is
therefore topological. This approach was later extended to systems in which a
semiconductor nanowire with strong spin orbit interactions in a parallel magnetic field is
in contact with a superconductor (14, 15). Experimental efforts to implement the
nanowire proposal have uncovered evidence for a zero bias peak (ZBP) in tunneling
spectroscopy studies of hybrid superconductor-semiconductor nanowire devices, as
expected in the presence of the MQP states of a topological superconductor (16-19).
However, the ZBPs detected in such devices could also be caused by the Kondo effect or
disorder (20-24). A key disadvantage of the nanowire studies is that they lack the ability
to spatially resolve ZBP features in order to demonstrate that they are localized at the
3
boundary of a gapped superconducting phase. Here we introduce a method of fabricating
one-dimensional topological superconductors and detecting their MQPs that achieves
both spatial and spectral resolution.
Magnetic Atomic Chains as a Platform for Topological Superconductivity
Magnetic atom chains on the surface of a conventional s-wave superconductor
have been proposed to provide a versatile platform for the realization of topological
superconductors (25). This platform lends itself to the detection of MQPs using the
spectroscopic imagining techniques of scanning tunneling microscopy (STM). In the
absence of intrinsic spin-orbit coupling, (25) and related theoretical work (26-30) showed
that a topological phase emerges in an atomic chain when its magnetic atoms have a
spatially modulated spin arrangement, for example a spin helix. The spin texture of the
chains emulates the combination of spin-orbit and Zeeman interactions required to create
a topological phase. Helical spin configurations are however much less common in
atomic chains than simple ferromagnetic and antiferromagnetic ones or may be more
influenced by disorder (31). We therefore explore an alternate, more realizable scenario
by placing a Fe chain on the surface of Pb (Fig. 1A). We will show that the essential
ingredients for topological superconductivity in this scenario are the ferromagnetic
interaction between Fe atoms realized at the Fe-Fe bond distance and the strong spin-
orbit interaction in superconducting Pb (32). Our approach is related to earlier proposals
for topological superconductivity using half-metal ferromagnets or metallic chains placed
in contact with superconductors in the presence of spin-orbit interactions (33-35).
To illustrate the key ingredient of our approach, we first consider an idealized
ferromagnetic chain of Fe atoms described by a tight-binding model calculation (Section
1 of (36)). We use hopping parameters appropriate for d orbitals of bulk Fe to compute
the band structure of a freely suspended linear Fe chain (Fig. 1B). The large exchange
interaction results in a fully occupied majority spin band with the Fermi level (E
F
)
residing in the minority spin bands. Coupling the Fe chain to a BCS superconductor with
strong spin-orbit interaction (such as Pb), we find that the spin-orbit interactions lift many
of the degeneracies in the chain’s band structure shown in Fig. 1B, while at the same time
allowing for the occurrence of p-wave superconductivity (Section 1 of (36)). Since only
4
the Fe d-bands will be strongly spin-polarized, other bands are unlikely to influence the
topological character of the system, whether they reside mainly on the Fe chains or on the
substrate. Remarkably, for large exchange interaction, topological superconductivity is
ubiquitous to the type of band structure shown in Fig. 1B—occurring for nearly all values
of the chemical potential (Fig. 1C, (36) for details). In this idealized situation, the number
of minority spin bands which cross the Fermi level is almost always odd, making the
presence of MQPs at the ends of the chains almost guaranteed.
We consider another idealized situation for topological superconductivity by
modeling a ferromagnetic chain embedded in a 2D superconductor, which allows us
identify its signatures in STM measurements (Section 2 of (36)). The spatially resolved
density of states (DOS) of this 2D model at positions on the chain differs from that of a
BCS superconductor by the presence of Yu-Shiba-Rusinov in-gap states (Fig. 1, C and D)
(37-41). These calculations also exhibit the spatial and spectroscopic signatures of MQPs
at the chain ends (Fig. 1, D and E). Other more realistic models for our experimental
system are also worth exploring (see below) and non-topological phases can occur for
some chain geometries. These model studies of proximity-induced superconductivity on
Fe chains demonstrate that topological states can be identified using STM by
establishing: 1) ferromagnetism on the chain, 2) spin-orbit coupling in the host
superconductor (or at its surface) 3) a superconducting gap in the bulk of the chain, and
finally 4) a localized ZBP due to MQPs at the ends of the chain. One can over constrain
these conditions by providing evidence that the system has an odd number of band
crossings at E
F
. The disappearance of edge-localized ZBPs when the underlying
superconductivity is suppressed provides an additional check to show that the MQP
signature is associated with superconductivity and not with other phenomena, such as the
Kondo effect (20-22).
Ferromagnetic Fe Atomic Chains on the Pb(110) Surface
To fabricate an atomic chain system on the surface of a superconductor with
strong spin-orbit coupling, we used a Pb (110) single crystal, which we prepare with
cycles of in situ sputtering and annealing. Following sub-monolayer evaporation of Fe on
the Pb surface at room temperature and light annealing, STM images (temperature was
5
1.4K for all experiments reported here) show large atomically ordered regions of the Pb
(110) surface, as well as islands and chains of Fe atoms that have nucleated on the
surface (Fig. 2A). The islands appear to provide the seed from which chains self-
assemble following the anisotropic structure of the underlying surface. Depending on
growth conditions, we find Fe chains as long as 500 , usually with an Fe island in the
middle (inset, Fig. 2A). In longer chains, the ends are separated from the islands in the
middle by atomically ordered regions that are 200 long. High-resolution STM images
show that the chains (with an apparent height of about 2 ) are centered between the
atomic rows of Pb (110), display weak atomic corrugation (5-10 pm) and strain the
underlying substrate (Fig. 2, B-D). Approximate periodicities of 4.2 and 21 measured
on the chain show that the Fe chain has a structure that is incommensurate with that of
the underlying Pb surface. To identify the atomic structure of our chains, we performed
density functional theory (DFT) calculations of Fe on the Pb (110) surface which show
that strong Fe-Pb bonding results in a partially submerged zigzag chain of Fe atoms
between Pb (110) atom rows (Fig. 2, E and F; see Section 3 of (36) for DFT details).
From these calculations, we find that among several candidate structures with the
experimental periodicity, a three-layer Fe zigzag chain partially submerged in Pb has the
lowest energy and gives contours of constant electron density most consistent with our
STM images.
We use a combination of spectroscopic and spin-polarized measurements to
demonstrate that Fe atomic chains on Pb (110) satisfy the criteria (conditions 1-4 above)
required to demonstrate a one-dimensional topological superconductor. First, we discuss
spin-polarized STM studies that show experimental evidence for ferromagnetism on the
Fe chains and strong spin-orbit coupling on the Pb surface (Fig. 3, A-C). Using Cr STM
tips, which have been prepared using controlled indentation of the tip into Fe islands, we
measured tunneling conductance (dI/dV) at a low bias (V = 30 mV) as a function of
magnetic field perpendicular to the surface on both the chains and on the Pb substrate
(Fig. 3, A and B). Our preparation of spin-polarized tips were validated by also
performing experiments on Co on Cu (111), now a standard system (40) for verifying