Spectral signatures of a unique charge density wave in Ta 2NiSe 7 Matthew D. Watson1Alex Louat1Cephise Cacho1Sungkyun Choi2 3Young Hee Lee2 4Michael Neumann2 3and Gideok Kim2 3

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Spectral signatures of a unique charge density wave in Ta2NiSe7

Matthew D. Watson,1, ∗Alex Louat,1Cephise Cacho,1Sungkyun

Choi,2, 3 Young Hee Lee,2, 4 Michael Neumann,2, 3 and Gideok Kim2, 3

1Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot, OX11 0DE, UK

2Center for Integrated Nanostructure Physics (CINAP),

Institute for Basic Science (IBS), Suwon 16419, Republic of Korea

3Sungkyunkwan University, Suwon 16419, Republic of Korea

4Department of Energy Science, Sungkyunkwan University, Suwon 16419, Republic of Korea

(Dated: June 12, 2023)

Charge Density Waves (CDW) are commonly associated with the presence of near-

Fermi level states which are separated from others, or "nested", by a wavector of q.

Here we use Angle-Resolved Photo Emission Spectroscopy (ARPES) on the CDW ma-

terial Ta2NiSe7and identify a total absence of any plausible nesting of states at the

primary CDW wavevector q. Nevertheless we observe spectral intensity on replicas

of the hole-like valence bands, shifted by a wavevector of q, which appears with the

CDW transition. In contrast, we ﬁnd that there is a possible nesting at 2q, and asso-

ciate the characters of these bands with the reported atomic modulations at 2q. Our

comprehensive electronic structure perspective shows that the CDW-like transition of

Ta2NiSe7is unique, with the primary wavevector qbeing unrelated to any low-energy

states, but suggests that the reported modulation at 2q, which would plausibly connect

low-energy states, might be more important for the overall energetics of the problem.

Introduction

Charge density wave (CDW) instabilities, originally formulated by Peierls for a single 1D band

at half-ﬁlling, can be naively generalised to real materials by the concept of Fermi surface nesting

(FSN) [1–3]. If some portions of the Fermi surface can be mapped to others by a wavevector

q, a joint electronic and lattice instability with that periodicity can occur when a ﬁnite electron-

phonon coupling is considered. However it has been argued that the FSN picture is very often

∗matthew.watson@diamond.ac.uk

arXiv:2210.00447v2 [cond-mat.str-el] 9 Jun 2023

insufﬁcient to understand the emergence of charge density waves (CDWs) in real materials, and

that the momentum-dependence of the electron-phonon coupling is equally, if not more, important

[4–7]. Still, for the CDW to be energetically favourable, one would generically expect at least

some low-energy states to be separated by the CDW wavevector q, in order for their hybridisation

in the modulated phase to lead to an overall electronic energy gain.

At ﬁrst glance, the structural phase transition in Ta2NiSe7[8,9] appears superﬁcially similar to

prototypical FSN-driven CDWs as found in e.g. ZrTe3[10,11], with a moderate transition tem-

perature of ∼63 K, incommensurate periodicity [9], a sharp bump-shaped anomaly in resistivity

[12,13], and sensitivity of Tcto disorder [12,14,15]. Several literature reports therefore naively

assume the FSN picture to be applicable, and the observed modulations at q[9] and 2q [16] have

been sometimes referred to as “2kF" and “4kF" respectively [14]. However, there is actually a lack

of support for this scenario from an electronic structure perspective. Early tight-binding models

[17] and recent DFT calculations [13,18], as well as transport measurements [12,13], agree that

the starting point is a semimetal with small hole- and electron-like Fermi surfaces, very far from

the Peierls paradigm of a single metallic band at half-ﬁlling. Furthermore, the Fermi surfaces in-

ferred from semimetallic-like magnetotransport behaviour [12] and calculations [12,13,18] are

small, seemingly inconsistent with the ordering at a large wavevector of q=(0,0.483,0). Thus, the

driving force for the incommensurate CDW in Ta2NiSe7cannot be easily ascribed to a FSN-driven

CDW, while the 2qstructural modulation [16] is another intriguing component, previously only

reported in organics [19].

In this work, we reveal the 3D Fermi surface of Ta2NiSe7using high-resolution ARPES and

conﬁrm the scenario of small hole- and electron-like Fermi surfaces. Importantly, we identify the

total absence of any plausible nesting of states at q. We nevertheless observe a backfolding of

valence bands in the CDW phase by a wavevector of q, with the backfolded bands appearing in a

projected band gap. Thus Ta2NiSe7exhibits the extremely peculiar phenomenology of a prominent

backfolding of spectral weight with a wavevector that does not seem to connect any low energy

states. However, we ﬁnd that there is a possible nesting at 2q, and associate the characters of these

bands with the reported atomic modulations at 2q. The results lead us to speculate that the CDW

may be best understood as a unique instability involving both qand 2q, suggesting an intricate and

unique microscopic mechanism that qualitatively differs from the paradigmatic CDW materials.

Results

The structure of Ta2NiSe7consists of three distinct chains, as shown in Fig. 1(a). The Ta1 atoms

have bicapped trigonal prismatic coordination (BTP), similar to trichalcogenides such as TaSe3

[20], forming double-chain units. The Ta2 sites take octahedral (OCT) coordination (as in 1T-

TaSe2), and also form double chains of edge-sharing octahedra, akin to those found in Ta2NiSe5.

In between, Ni atoms form chains of extremely distorted octahedra (d-OCT) with substantially

varying bond lengths. The seven Se sites are all inequivalent, leading to a rich structure in mea-

surements of the Se 3d core levels (Supplemental Information, [21]).

While possessing the quasi-1D chain structures along b, Ta2NiSe7can also be considered a 2D

material, with a staggered van der Waals gap which yields neutral cleavage in the b−cplane.

However the sawtooth-like structure gives an intrinsically three-dimensionality to the system, and

some relatively short interlayer Se-Se distances allow for some inter-layer hopping, meaning the

3D character is also important, both structurally and electrically. Thus one might fairly describe

the dimensionality as “1+1+1D", or a “dimensional hybrid" [22]. The layers stack according to the

aaxis, orthogonal to bbut not to c, and the overall structure is described by a centered monoclinic

space group C2/m (number 12).

Substitution of Ni for Pt to form Ta2PtSe7was reported in the original synthesis paper of Sun-

shine and Ibers [8], but no further stoichiometries have been reported in this "217" structure.

Structural similarities with FeNb3Se10 were previously mentioned [9,15], but a more contempo-

rary analogy is with Ta4Pd3Te16, recently discovered to exhibit both an incommensurate CDW and

superconductivity [22–25], which has the same space group as Ta2NiSe7and similarly contains

two distinct Ta chains.

We measured the resistivity of our samples to characterise the Tcand their overall quality. For

the sample presented in Fig. 1(b), we ﬁnd Tc, deﬁned by the peak in dρ/dT , at 59.5 K, and a

residual resistivity ratio (RRR) of 5.2; a second sample (not plotted) showed slightly lower values

of 58.8 K and 4.54 respectively [21]. These values align well with the literature [12] and indicate

a good sample quality, albeit that some previous samples achieved slightly improved purity with

Tcup to 62.5 K [13] or 63 K [14]. There is a slight hysteresis in the temperature-dependent

resistivity, which has been also observed in previous measurements [12,15] and discussed as an

impurity-related effect [26].

To give an overview of the electronic structure, we present the calculated density of states in

Fig. 1(c). The occupied states have primarily Se 4pand some Ni 3dcharacter. Interestingly, the

DOS exhibits a pronounced dip near EF, although remaining ungapped. Conceptually, this can

be attributed to a slight overlap of the topmost Se/Ni-derived valence band and the bottom-most

Ta2-derived conduction bands [17]. For the rest of this paper we focus on these low-energy states

at and near EF, but we emphasise that the global picture for the normal state electronic structure

of Ta2NiSe7is certainly a semimetal.

For an in-depth understanding of the 3D Fermi surface, it is ﬁrst necessary to consider the

somewhat complex geometry of the Brillouin zone, shown in Fig. 2(a). From the Γpoint, a

path along the chain direction, kch direction ﬁrst intersects the Brillouin zone boundary and then

encounters the Y point at (0,2π/b,0). Note that although we use the notation of the conventional

unit cell for describing the real space lattice and the CDW ordering wavevector, for convenience

and consistency with previous studies, in k-space it is essential to consider the primitive reciprocal

lattice vectors and correct Brillouin zone. Importantly, Fig. 2(a) shows that the Y point, outside

of the ﬁrst Brillouin zone, is related to a formally equivalent point Y1on the boundary of the ﬁrst

Brillouin zone, by a primitive reciprocal lattice vector translation.

We align our samples such that the kch direction is parallel to the entrance slit of our analyser.

Then the normal protocol for Fermi surface mapping, i.e. rotating the sample perpendicular to

the analyser entrance slit, corresponds to a map in the ki.p.-kch plane. Here ki.p. is the in-plane

direction, parallel to the caxis of the real space structure, however in reciprocal space this is not

any kind of high-symmetry direction, instead corresponding to the cut shown by the 2D and 3D

projections of the calculated Fermi surface in Fig. 2(d). With the photon energy tuned to a bulk

Γpoint, and remaining within the ﬁrst Brillouin zone, we can use this geometry to nicely map

the the larger hole-like Fermi surface around Γin Fig. 2(e), revealing a shape consistent with

the calculations. Since ki.p. is not a high-symmetry direction in k-space, however, this direction is

somewhat awkward to make use of, as it will not strictly intersect any other high-symmetry points,

and it becomes an even more complicated cut to interpret outside of the ﬁrst Brillouin Zone. A

related feature of the Ta2NiSe7structure is that there is no rotational or mirror symmetry about the

normal to the the cleavage plane, as seen by the lack of symmetry in Fig. 2(e) (i.e. positive and

negative ki.p are not equivalent). Thus, azimuthal rotation of the sample by 180 degrees - typically

an innocuous operation on needle-like samples - does not result in equivalent spectra, as explained

further in the SI [21].

Since the calculations shown in Fig. 2(b,c) predict a 3D electronic structure, and additionally

ki.p. is not the most intuitive direction to probe in this case, it is especially important to make

full use of the out-of-plane direction, k⊥, which at normal emission corresponds to a path along

Γ-Y1-Γ. Relying on the nearly free electron ﬁnal state model, (which seems to work adequately

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SpectralsignaturesofauniquechargedensitywaveinTa2NiSe7MatthewD.Watson,1,∗AlexLouat,1CephiseCacho,1SungkyunChoi,2,3YoungHeeLee,2,4MichaelNeumann,2,3andGideokKim2,31DiamondLightSourceLtd,HarwellScienceandInnovationCampus,Didcot,OX110DE,UK2CenterforIntegratedNanostructurePhysics(CINAP),InstituteforBasi...

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Spectral signatures of a unique charge density wave in Ta 2NiSe 7 Matthew D. Watson1Alex Louat1Cephise Cacho1Sungkyun Choi2 3Young Hee Lee2 4Michael Neumann2 3and Gideok Kim2 3

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