Direct probing of a large spin-orbit coupling in the FeSe superconducting monolayer on STO Evidence for nontrivial topological states Khalil Zakeri1Dominik Rau1Jasmin Jandke2Fang Yang2Wulf Wulfhekel2 3and Christophe Berthod4

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Direct probing of a large spin-orbit coupling in the FeSe superconducting monolayer on STO:

Evidence for nontrivial topological states

Khalil Zakeri,1, ∗Dominik Rau,1Jasmin Jandke,2Fang Yang,2Wulf Wulfhekel,2, 3 and Christophe Berthod4

1Heisenberg Spin-dynamics Group, Physikalisches Institut,

Karlsruhe Institute of Technology, Wolfgang-Gaede-Str. 1, D-76131 Karlsruhe, Germany

2Physikalisches Institut, Karlsruhe Institute of Technology,

Wolfgang-Gaede-Str. 1, D-76131 Karlsruhe, Germany

3Institute for Quantum Materials and Technologies,

Karlsruhe Institute of Technology, D-76344, Eggenstein-Leopoldshafen, Germany

4Department of Quantum Matter Physics, University of Geneva, 1211 Geneva, Switzerland

Abstract

—————————————————————————————————————————————————–

In condensed-matter physics spin-orbit coupling (SOC) is a fundamental physical interaction, which describes

how the electrons’ spin couples to their orbital motion. It is the source of a vast variety of fascinating phenomena

in solids such as topological phases of matter, quantum spin Hall states, and many other exotic quantum states.

Although in most theoretical descriptions of the phenomenon of high-temperature superconductivity SOC has

been neglected, including this interaction can, in principle, revise the microscopic picture of superconductivity

in these compounds. Not only the interaction leading to Cooper pairing but also the symmetry of the order

parameter and the topological character of the involved states can be determined by SOC. Here by preforming

energy-, momentum-, and spin-resolved spectroscopy experiments with an unprecedented resolution we demon-

strate that while probing the dynamic charge response of the FeSe monolayer on strontium titanate, a prototype

two dimensional high-temperature superconductor using slow electrons, the scattering cross-section shows a

considerable spin asymmetry. We unravel the origin of the observed spin asymmetry by developing a model in

which SOC is taken into consideration. Our analysis indicates that SOC in this two dimensional superconductor

is rather strong. We anticipate that such a strong SOC can have several serious consequences on the electronic

structures and can lead to the formation of topological states. Moreover, a sizable SOC can compete with other

pairing scenarios and is crucial for the mechanism of high-temperature superconductivity.

——————————————————————————————————————————————————–

I. INTRODUCTION

The fundamental interaction describing the microscopic coupling mechanism between the spin and orbital degrees of

freedom of electrons in solids is the so-called spin-orbit coupling (SOC) [1,2]. This interaction, which is a relativistic

eﬀect, is an essential ingredient for describing many emergent phenomena observed in condensed-matter systems. For

instance, a large SOC in combination with other symmetry aspects can lead to the appearance of topological phases

in solids. Examples of this kind are the topological insulators, where a large SOC leads to the formation of the

topologically protected surface states and spin momentum locking [3–7]. Likewise in magnetically ordered solids SOC

in the absence of inversion symmetry can result in the formation of topologically protected spin textures in the form

of chiral domain walls, skyrmions, antiskyrmions, hopﬁons, etc. [8].

In order to ﬁgure out whether or not a material exhibits topological electronic states and to which topological

classes these states belong, one requires to quantify the strength of SOC. Assuming that the symmetry considerations

are fulﬁlled, the presence of a suﬃciently large SOC would, in principle, give rise to the formation of nontrivial

topological states in the system. Although the phenomenon of high temperature superconductivity is, by itself, a

fascinating phenomenon, combined with topological aspects of matter it would lead to an even more exotic state

of matter e.g., topological superconductivity and the formation of the Majorana states [9–11]. These states which

obey non-Abelian statistics can be used to realize topological quantum computers [12]. In most of the proposals

for realizing these interesting concepts it is suggested to attach a low-dimensional superconductor to a topological

material or semiconductor heterostructures with a large SOC [10]. However, under some circumstances if SOC in

a low-dimensional superconductor is suﬃciently large, one expects to observe topological states in a single material

∗khalil.zakeri@kit.edu

arXiv:2210.02810v1 [cond-mat.supr-con] 6 Oct 2022

[13]. An ideal candidate for such an observation would be a single layer of FeSe grown on SrTiO3(001), an ideal two-

dimensional high temperature superconductor (HTSC) [14–20]. In the case of ultrathin ﬁlms the inversion symmetry

in the direction perpendicular to the surface is broken. A large SOC together with the broken inversion symmetry

can provide the necessary fundamental basis required for the observation of topological states in the system [21,22].

Hence a direct probing of SOC in this class of materials is essential in connection with the possibility of the formation

of topological states. Unfortunately, the strength of SOC in such two-dimensional superconductors is hitherto fully

unknown.

Irrespective of the importance of SOC for the topological superconductivity, the presence of this interaction is of

prime importance to understand the underlying physics of HTSC in general [21,23]. In most theoretical approaches

describing the microscopic mechanism of superconductivity and Cooper pairing of electrons SOC is assumed to be very

small and, therefore, has been neglected. There are only a few theoretical models which include SOC in bulk HTSCs,

showing that the presence of this interaction is essential in the determination of the symmetry of the order parameter as

well as the electronic states involved in superconductivity [21,23]. Generally the impact of SOC becomes increasingly

important when reducing the systems’ dimensionality. This is due to the emergence of new symmetry aspects in

low-dimensional solids. Surprisingly, so far no direct signature of SOC and its impact in ultrathin (two-dimensional)

HTSCs have been reported experimentally. A direct measure of SOC would, therefore, be extremely valuable in the

context of microscopic physical mechanism behind high temperature superconductivity in low-dimensional HTSCs.

Here by performing high resolution spectroscopy of spin-polarized slow electrons on epitaxial FeSe monolayers

grown on Nb-doped strontium titanate SrTiO3(001), a prototypical two-dimensional superconductor, we demonstrate

that the frequency and momentum dependent scattering cross-section depends strongly on the spin of the incoming

electron. A careful analysis of the spectra reveals that the observed eﬀect is due to the presence of a considerably

large SOC in this system. Such a large SOC together with other symmetry aspects provides the required ingredients

for the formation of topologically nontrivial states and would shed light on the mysterious origin of superconductivity

in this system.

II. RESULTS

The epitaxial FeSe monolayer was grown by molecular beam epitaxy on Nb-doped SrTiO3(001) (hereafter STO).

The dynamic charge response of the system was probed by means of spin-polarized high-resolution electron energy-

loss spectroscopy (SPHREELS) (see Sec. V A of Materials and Methods for details on the substrate preparation, ﬁlm

growth and SPHREELS experiments). The scattering geometry is sketched in Fig. 1a. The scattering plane was

chosen to be parallel to the [100]-direction of STO(001), as indicated in Fig. 1band c. This would allow probing

the dynamic response of the system along the high symmetry ¯

Γ–¯

X direction of the surface Brillouin zone (SBZ). In

order to be sensitive to the spin-dependent eﬀects associated with the broken inversion symmetry in the direction

perpendicular to the surface, we used a longitudinally spin-polarized electron beam with the spin orientation being

parallel and antiparallel to the scattering’s plane normal vector n(see Supplementary Note 1 for an explanation).

These incoming spin states are denoted by |+iand |−i, respectively. Figure 1dshows the spin-resolved spectra

recorded in the superconducting state of the sample and using an incident electron beam energy Ei= 4.07 eV. The

spectra were recorded at the ¯

Γ–point of SBZ. Beside the so-called zero loss peak at the energy-loss ~ω= 0, one

observes several features as a result of the excitation of several collective modes. The peaks with lower intensity at

~ω= 11.8, 20.5, 24.8 and 36.7 meV represent the various phonon modes of the FeSe ﬁlm itself [24–26]. More obviously

the so-called Fuchs-Kliewer (FK) phonon modes of the underlying STO substrate can also be recognized at the loss

energies ~ω= 59.3 and 94.5 meV [27,28].

Generally the spectral function S(q, ω) measured by SPHREELS directly reﬂects the dynamic response of the

collective charge excitations in the system. This quantity is proportional to the imaginary part of the dynamic

charge susceptibility Imχ(q, ω) [29–31]. The electrons are scattered by the total charge distribution of the sample

and, hence, the scattering intensity carries information regarding collective excitations of the lattice i.e, phonons,

collective electronic excitations i.e., plasmons and any type of excitation representing a hybrid mode of these two [31].

The most interesting observation here is that S(q, ω) depends strongly on the spin. The spin asymmetry deﬁned as

A=I|+i−I|−i/I|+i+I|−iis shown in the lower part of Fig. 1d. Here I|+iand I|−i denote the intensity of the

scattered electrons when the incoming electron’s spin is parallel and antiparallel to n, respectively.

In order to shed light on the origin of the observed spin asymmetry, its dependency on the physical variables e.g.,

temperature, incident energy, and wavevector transfer qwas measured and the results are summarized in Fig. 2.

Data presented in Fig. 2aclearly demonstrate that the spin asymmetry does not depend on temperature. In both

superconducting and normal states one observes a value as large as 11%. This fact indicates that the spin asymmetry

is not related to the superconducting (or magnetic) phase transition and is due to the intrinsic SOC of the system.

Next we check the dependence of the spin asymmetry on the incident beam energy Ei. Generally for very low incident

𝐸𝑖, 𝒌𝑖𝐸𝑓, 𝒌𝑠

Ti OFe Se



𝑖



𝑠



𝑖+



𝑠

Detector

Intensity (x103 Counts/s)

0100 200

Asymmetry (%)

Energy Loss (meV)

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−

Figure 1.Evidence of a large SOC in FeSe ML on STO. a The scattering geometry used for probing the dynamic charge

response. The electrons are represented by the blue and red balls. Their spin in the laboratory frame is shown by the red and

blue arrows. The incident energy and wavevector are denoted by Eiand ki, respectively. The energy and the wavevector after

the scattering event are given by Efand ks, respectively. The laboratory frame is depicted by black arrows with x, y, and z

labels. The incident and outgoing angles are called θiand θs. The total scattering angle is θ0and was set to 80◦.bThe top view

of STO(001) and the FeSe(001) ﬁlm. The spin polarization of the beam is either parallel or antiparallel to the y-axis that is the

[010]-direction of the STO(001) surface. These spin states are called |+iand |−i, respectively. cAtomically resolved scanning

tunneling microscopy topography image of the FeSe surface, showing the atomic resolution of the topmost Se atoms, indicated

by the gray balls in b. The ﬁeld of view is 7 ×4.5 nm2. The constant current topography image was recorded at T= 0.9 K and

using a tunneling current of 180 pA and a bias voltage of 1.0 V. The corresponding reciprocal lattice is shown in the right side.

The ¯

Γ–point represents the SBZ center and the ¯

X and ¯

M points represent the edges of SBZ. dBlue upward and red downward

triangles represent the experimental spectra recorded for the spin of the incoming beam being parallel and antiparllel to the

y-axis, respectively. The open circles denote the spin asymmetry A=I|+i−I|−i/I|+i+I|−i. The spectra were recorded

at the specular geometry i.e., the wavevector of q= 0, at the ¯

Γ–point. The error bars represent the statistical uncertainties.

energies (Ei<3 eV) the intensity may be inﬂuenced by the space charge eﬀects. On the other hand for incident

energies higher than 12 eV the intensity is determined by the multiple scattering and electron diﬀraction processes

(the so-called low-energy electron diﬀraction or LEED states). Hence, the relevant energy window would be between

3 and 11 eV. Such data are presented in Fig. 2b. For this set of measurements ﬁrst the incident and scattered beam

angles were ﬁxed to θi=θs= 40◦(see Fig. 1a). The incident beam energy Eiwas precisely deﬁned and the electrons

with the ﬁnal energy Ef=Ei±δE were collected. Here δE represents the energy width of the elastic scattering (the

hatched area in Fig. 2a). In order to make sure that all the elastically scattered electrons are collected, we recorded

the intensity for δE = 8 meV (this value is two times the energy resolution). The spin asymmetry shows a strong

dependence on the incident beam energy and exhibits a maximum near 4 eV. As the next physical variable we check

the dependence of the spin asymmetry on q. Spectra recorded for diﬀerent values of qnear the zone center (in the

vicinity of the ¯

Γ–point) indicate that the spin asymmetry does not depend on q. This is demonstrated in Figs. 2cand

d, where the spin asymmetry recorded for diﬀerent values of qis presented. The data shown in Fig. 2cwere recorded

with an incident beam energy of Ei= 6.0 eV and those in Fig. 2dwere recorded with Ei= 7.25 eV. A careful

inspection of the data shown in Figs. 2cand dindicates that although the spin asymmetry depends strongly on Ei,

it does not depend on q. The strong Ei-dependence of spin asymmetry and its q-independence is an unambiguous

evidence that the observed spin asymmetry is originating from a substantially large SOC at the surface (see the

discussion below).

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Directprobingofalargespin-orbitcouplingintheFeSesuperconductingmonolayeronSTO:EvidencefornontrivialtopologicalstatesKhalilZakeri,1,DominikRau,1JasminJandke,2FangYang,2WulfWulfhekel,2,3andChristopheBerthod41HeisenbergSpin-dynamicsGroup,PhysikalischesInstitut,KarlsruheInstituteofTechnology,Wolfgang-G...

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Direct probing of a large spin-orbit coupling in the FeSe superconducting monolayer on STO Evidence for nontrivial topological states Khalil Zakeri1Dominik Rau1Jasmin Jandke2Fang Yang2Wulf Wulfhekel2 3and Christophe Berthod4.pdf

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Direct probing of a large spin-orbit coupling in the FeSe superconducting monolayer on STO Evidence for nontrivial topological states Khalil Zakeri1Dominik Rau1Jasmin Jandke2Fang Yang2Wulf Wulfhekel2 3and Christophe Berthod4

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