Geometry-induced spin-ltering in photoemission maps from WTe 2surface states Tristan Heider1Gustav Bihlmayer2Jakub Schusser3 4Friedrich Reinert4 Jan Min ar3Stefan Bl ugel2Claus M. Schneider1 5 6and Lukasz Plucinski1

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Geometry-induced spin-ﬁltering in photoemission maps from WTe2surface states

Tristan Heider,1Gustav Bihlmayer,2Jakub Schusser,3, 4 Friedrich Reinert,4

Jan Min´ar,3Stefan Bl¨ugel,2Claus M. Schneider,1, 5, 6 and Lukasz Plucinski1, ∗

1Peter Gr¨unberg Institut (PGI-6), Forschungszentrum J¨ulich GmbH, 52428 J¨ulich, Germany

2Peter Gr¨unberg Institut (PGI-1) and Institute for Advanced Simulation (IAS-1),

Forschungszentrum J¨ulich and JARA, 52428 J¨ulich, Germany

3New Technologies-Research Center, University of West Bohemia, 30614 Pilsen, Czech Republic

4Experimentelle Physik VII and W¨urzburg-Dresden Cluster of Excellence ct.qmat, Universit¨at W¨urzburg, W¨urzburg, Germany

5Fakult¨at f¨ur Physik, Universit¨at Duisburg-Essen, 47048 Duisburg, Germany

6Physics Department, University of California, Davis, CA 95616, USA

(Dated: October 21, 2022)

We demonstrate that an important quantum material WTe2exhibits a new type of geometry-

induced spin-ﬁltering eﬀect in photoemission, stemming from low symmetry that is responsible for

its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemis-

sion Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted

from the surface states of WTe2. Such asymmetries are not present in the initial state spin textures,

which are bound by the time-reversal and crystal lattice mirror plane symmetries. The ﬁndings are

reproduced qualitatively by theoretical modeling within the one-step model photoemission formal-

ism. The eﬀect could be understood within the free-electron ﬁnal state model as an interference due

to emission from diﬀerent atomic sites. The observed eﬀect is a manifestation of time-reversal sym-

metry breaking of the initial state in the photoemission process, and as such it cannot be eliminated,

but only its magnitude inﬂuenced, by special experimental geometries.

Introduction.—WTe2is a semi-metallic two-

dimensional (2D) quantum material that exhibits a

non-saturating magnetoresistance up to 60 T [1]. It

has been debated, whether the bulk electron and hole

pockets in WTe2slightly overlap leading to the Weyl

type-II topological phase [2, 3], with a conjecture that

the surface electronic structure would be virtually

indistinguishable for a topological and trivial phases [4].

When thinned down to a monolayer, WTe2enables the

realization of high-temperature quantum Hall phases

[5] and gate-controlled superconductivity [6, 7]. In

non-magnetic systems the ﬁrst-order Hall response

vanishes at zero magnetic ﬁeld due to symmetry ar-

guments. However, the second-order correction leads

to the recently discovered [8–11] non-linear Hall eﬀect

(NLHE) in systems of reduced symmetry. Few-layer

WTe2has been the ﬁrst system in which the NLHE has

been demonstrated [9, 10] due to the presence of a single

mirror plane, and a related existence of polar axes both

in-plane and out-of-plane of the layers.

Early high resolution angle-resolved photoemission

(ARPES) on WTe2[12, 13] have focused on imaging

bulk electron and hole pockets with the motivation to ex-

plain the non-saturating magnetoresistance, pointing to a

possible full charge compensation at lower temperatures.

The prediction of possible type-II Weyl states in WTe2

[2] have further motivated the research on its electronic

structure. The reduced symmetry of WTe2results in in-

equivalent top and bottom surfaces along the c-axis. The

general shape of the experimental WTe2band dispersions

over the scale of 2 eV below the Fermi level is well repro-

duced by ab initio calculations, however, as pointed out

in an early study [12], density functional theory (DFT)

calculations are not able to quantitatively reproduce crit-

ical features of the WTe2electronic structure near the

Fermi level. In particular, this concerns the positions of

the electron and hole pockets and related sizes of their

Fermi surfaces [14] which play a critical role in under-

standing the magnetoresistance properties [12, 15]. This

lack of agreement, despite occurring on a small energy

scale of only 50 meV, is surprising because WTe2(001)

surfaces are clearly very stable under UHV yielding quan-

titatively consistent results in high-resolution ARPES for

the set of dispersive occupied features located near the

Fermi level [4, 12–14, 16–18].

Using the newly-developed high resolution laser-

driven spin-polarized ARPES (SARPES) spectrometer

we demonstrate for the ﬁrst time the spin texture of the

Fermi level photoemission map measured with 6 eV pho-

tons. Previous SARPES studies only probed selected

regions in the Brillouin zone (BZ) [19–21]. We further

demonstrate that the symmetry of the ARPES spin tex-

ture reﬂects the WTe2surface symmetry with a sin-

gle mirror plane present, and not the initial state spin

symmetry. Therefore, we directly demonstrate that the

ARPES photocurrent carries additional information be-

yond the initial band structure spin texture, due to what

we call the geometry-induced spin ﬁltering eﬀect.

The results are analyzed by comparison to the dedi-

cated theoretical DFT calculations. The results obtained

within the linearized-augmented plane-wave (LAPW)

scheme show that the initial state spin texture follows

the expected axial vector transformation rules of a single

mirror plane and time-reversal. Further one-step model

photoemission calculations within the Korringa-Kohn-

Rostoker (KKR) scheme reproduce the (broken) symme-

arXiv:2210.10870v1 [cond-mat.mtrl-sci] 19 Oct 2022

FIG. 1. (a-b) Spin-integrated laser ARPES Fermi surface maps measured with p- and s-polarized light. (c-d) Corresponding

energy dispersions E(kx) for ky= 0 as indicated by the dashed lines in (a) and (b). (e-f) Experimental laser-SARPES 57 ×89

pixel Fermi surface maps taken at two nearby spots on the same cleave. The false color scale refers to the spin polarization Sf y

in the ensemble of the photoemitted electrons. (g) Schematic geometry of the SARPES experiment. The maps were measured

using the lens deﬂector system collecting the emission angles indicated by the yellow cone with the sample rotated by θ= 25◦

with respect to the lens axis using p-polarized light and probing the spin along the yaxis, as deﬁned in (g).

try properties of the experimental data. Finally, within

the free-electron ﬁnal state ARPES model we identify the

origin of the observed asymmetries as an interference of

the emission from diﬀerent atomic sites.

Methods.— The sample (Td-WTe2single crystal, space

group P mn21, purchased from HQ graphene) was glued

to the molybdenum sample plate by a silver-epoxy. We

used p- or s-polarized light from the LEOS Solutions con-

tinuous wave laser with hν = 6.02 eV focused down to

∼50 µm, the MB Scientiﬁc A1 hemispherical electron

analyzer and the exchange-scattering Focus GmbH FER-

RUM spin detector [22]. Spectrometers based on a sim-

ilar design are in operation at synchrotron light sources

[23, 24]. The mirror plane of WTe2was aligned parallel to

the entrance slit of the A1 spectrometer. The mechano-

electrostatic lens deﬂector system of A1 allows mapping

the emission angle over approx. ±15◦in both kxand ky

directions, therefore allowing for point-by-point kxvs. ky

mapping in the spin-polarized mode without rotating the

sample. All measurements were carried out at ∼15 K at

the pressure in the analyzer chamber <5×10−11 mbar.

The initial state band structure was calculated using

DFT in the generalized gradient approximation [25]. We

use the full-potential LAPW method in ﬁlm geometry

as implemented in the FLEUR code [26]. Photoemission

calculations were performed within the one-step model

formalism as implemented in the fully relativistic KKR

method [20, 27].

Further details on methods are provided in the Section

SI of the Supplemental Material.

Results.—Figure 1(a-d) shows the high-resolution

FIG. 2. Crystal geometry and initial state spin textures. (a)

The 3D impression of the WTe2crystal structure. (b) The

probed surface with two possible terminations, which we label

D1 and D2. (c) The Sycomponent of the theoretical Fermi

level spin texture, which is the same for both domains. The

size of the symbols corresponds to the spin-polarization in

the ﬁrst layer (containing two formula units). (d) The surface

state charge density in real space at kx=−0.3˚

A−1and initial

energy −25 meV (see Supplemental Material Fig. S6).

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Geometry-inducedspin-lteringinphotoemissionmapsfromWTe2surfacestatesTristanHeider,1GustavBihlmayer,2JakubSchusser,3,4FriedrichReinert,4JanMinar,3StefanBlugel,2ClausM.Schneider,1,5,6andLukaszPlucinski1,1PeterGrunbergInstitut(PGI-6),ForschungszentrumJulichGmbH,52428Julich,Germany2PeterGrunberg...

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Geometry-induced spin-ltering in photoemission maps from WTe 2surface states Tristan Heider1Gustav Bihlmayer2Jakub Schusser3 4Friedrich Reinert4 Jan Min ar3Stefan Bl ugel2Claus M. Schneider1 5 6and Lukasz Plucinski1.pdf

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Geometry-induced spin-ltering in photoemission maps from WTe 2surface states Tristan Heider1Gustav Bihlmayer2Jakub Schusser3 4Friedrich Reinert4 Jan Min ar3Stefan Bl ugel2Claus M. Schneider1 5 6and Lukasz Plucinski1

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