Electronic band structure of a superconducting nickelate probed by the Seebeck coefficient in the disordered limit G. Grissonnanche1 2 3 G. A. Pan4H. LaBollita5D. Ferenc Segedin4Q. Song4H. Paik6 7C. M. Brooks4E.

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Electronic band structure of a superconducting nickelate

probed by the Seebeck coeﬃcient in the disordered limit

G. Grissonnanche,

1, 2, 3, ∗

G. A. Pan,

H. LaBollita,

D. Ferenc Segedin,

Q. Song,

H. Paik,

6, 7

C. M. Brooks,

Beauchesne-Blanchet,

J. L. Santana Gonz´alez,

A. S. Botana,

J. A. Mundy,

and B. J. Ramshaw

1, 8, †

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

Laboratoire des Solides Irradi´es, CEA/DRF/lRAMIS, CNRS,

Ecole Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau, France

Department of Physics, Harvard University, Cambridge, MA, USA

Department of Physics, Arizona State University, Tempe, AZ, USA

Platform for the Accelerated Realization, Analysis,

and Discovery of Interface Materials, Cornell University, Ithaca, NY, USA

School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA

Canadian Institute for Advanced Research, Toronto, Ontario, Canada

(Dated: August 29, 2024)

Superconducting nickelates are a new family of strongly correlated electron materials with a phase

diagram closely resembling that of superconducting cuprates. While analogy with the cuprates is nat-

ural, very little is known about the metallic state of the nickelates, making these comparisons diﬃcult.

We probe the electronic dispersion of thin-ﬁlm superconducting 5-layer (

= 5) and metallic 3-layer

(

= 3) nickelates by measuring the Seebeck coeﬃcient,

. We ﬁnd a temperature-independent and

negative

S/T

for both

= 5 and

= 3 nickelates. These results are in stark contrast to the strongly

temperature-dependent

S/T

measured at similar electron ﬁlling in the cuprate La

1.36

0.4

0.24

CuO

The electronic structure calculated from density functional theory can reproduce the temperature

dependence, sign, and amplitude of

S/T

in the nickelates using Boltzmann transport theory. This

demonstrates that the electronic structure obtained from ﬁrst-principles calculations provides a

reliable description of the Fermiology of superconducting nickelates, and suggests that, despite

indications of strong electronic correlations, there are well-deﬁned quasiparticles in the metallic state.

Finally, we explain the diﬀerences in the Seebeck coeﬃcient between nickelates and cuprates as

originating in strong dissimilarities in impurity concentrations. Our study demonstrates that the

high elastic scattering limit of the Seebeck coeﬃcient reﬂects only the underlying band structure of a

metal, analogous to the high magnetic ﬁeld limit of the Hall coeﬃcient. This opens a new avenue

for Seebeck measurements to probe the electronic band structures of relatively disordered quantum

materials.

PACS numbers: 74.72.Gh, 74.25.Dw, 74.25.F-

I. INTRODUCTION

Unconventional superconductivity remains one of the

most active and challenging subﬁelds of strongly corre-

lated electron research, with cuprates posing some of the

toughest experimental and theoretical challenges over the

past three decades [

]. The origin of high-

supercon-

ductivity in the cuprates remains a mystery in part due

to the complex interplay of several competing states and

relatively strong disorder. One approach to understand-

ing the physics of high-

is to replace copper entirely,

for example with ruthenium or nickel, while maintain-

ing the same square-lattice, transition metal oxide motif.

RuO

is a success of this approach [

], but it does not

share the complex phase diagram of the cuprates.

The recent discovery of superconductivity in strontium-

doped NdNiO

[

–

] and stoichiometric Nd

[

]

presents an opportunity to explore the key ingredients

∗gael.grissonnanche@polytechnique.edu

†bradramshaw@cornell.edu

for unconventional superconductivity by contrasting the

physical properties of the nickelates with the cuprates.

The nickelates contain cuprate-like NiO

planes, and the

family we study here is Nd

n+1

2n+2

, where

indicates

the number of NiO

planes per unit cell [

–

]. While

nickel in the

∞

member of the series—NdNiO

—

has the same nominal 3

electronic conﬁguration as

copper does in the cuprates, the ﬁnite-

members have

the nominal conﬁguration of 3

d9−δ

, where

= 1

. This

oﬀers a mechanism for exploring the hole-doped phase

diagram without introducing cation disorder.

Superconducting nickelates exhibit many similarities

with the cuprates. These include a phase diagram with

a superconducting dome maximized around similar 3

d8.8

electron concentrations, evidence for a nodal supercon-

ducting gap [

], magnetism[

], charge density waves

[

], and even a strange metal phase [

] (Fig. 1a).

Conspicuously absent from this list are experimental com-

parisons of the electronic structure. To understand which

aspects of the electronic dispersion are favorable for un-

conventional superconductivity, one must ﬁrst understand

how electrons interact in the normal metallic state.

arXiv:2210.10987v3 [cond-mat.supr-con] 28 Aug 2024

The central diﬃculty is that most of the experimental

techniques used to study electronic structures are incom-

patible with current superconducting nickelate samples.

There have been attempts to measure the angle-integrated

density of states [

], and there are recent angle-resolved

photoemission spectroscopy (ARPES) measurements on

non-superconducting, single crystal nickelates [

], but

ARPES remains out of reach for superconducting nickelate

ﬁlms due to surface quality issues. Similarly, quantum

oscillations require metals with a defect density lower

than what is currently available in even the cleanest ﬁlms.

This calls for the use of other techniques that are sensitive

to the electronic structure and that are compatible with

higher levels of elastic scattering from defects and with

thin ﬁlms.

Thermoelectricity—as measured by the Seebeck coeﬃ-

cient

—provides an alternative to probe the electronic

band structure of a material. Unlike electrical transport,

which is only sensitive to the electronic states in the

immediate vicinity of the Fermi energy (

) (Fig. 2a),

the Seebeck eﬀect is sensitive to details of the electronic

dispersion away from

. Speciﬁcally, the Seebeck coeﬃ-

cient reﬂects the asymmetry of the dispersion above and

below

—it probes the asymmetry between occupied

and unoccupied states (Fig. 2b), also called particle-hole

asymmetry or energy asymmetry [

]. In general,

the Seebeck coeﬃcient is deﬁned by both the band struc-

ture and the energy dependence of the scattering rate.

However, we will demonstrate that this coeﬃcient is only

determined by the band structure in the disordered limit,

which is analogous to how the Hall coeﬃcient becomes

independent of scattering rate in the high-ﬁeld limit. As

the high-ﬁeld limit is usually inaccessible in most metals,

this makes the Seebeck eﬀect a new powerful probe of the

electronic dispersion of relatively disordered materials.

To investigate the electronic structure of the nickelates,

we measured the Seebeck coeﬃcient of a superconducting

5-layer nickelate Nd

(

= 5 nickelate) with a

transition onsetting at

Tc≈

10 K (Fig. 1b)—as well as a

more-overdoped, non-superconducting, 3-layer nickelate

(

= 3 nickelate) for comparison (Fig. 1b).

We ﬁnd that both the

= 5 and

= 3 nickelates share a

similar temperature independent, negative

S/T

. We show

the electronic dispersion obtained from density functional

theory (DFT) accounts for both the magnitude and sign

of the temperature-independent Seebeck coeﬃcient for

the two compounds when calculated in the disordered

limit.

To justify the disordered limit, we compare the nickelate

data to previous measurements of the Seebeck coeﬃcient

in hole doped cuprates with a similar electron count to the

= 5 nickelate. First, we compare with measurements

performed on a single crystal of La

1.36

0.4

0.24

CuO

(Nd-LSCO

= 0

24) [

] with a Seebeck coeﬃcient that is

positive and qualitatively diﬀerent from that of the nicke-

lates. Second, we compare with measurements performed

on a single crystal of (Bi,Pb)

(Sr,La)

CuO

6+δ

(Bi2201

= 0

23) [

] with an almost identical Seebeck co-

150

300

8.68.78.88.99

3d electron count

Temperature ( K )

Cuprates

Nickelates

AF SC

Nd-LSCO

Bi2201

n = ∞

n = 5

n = 3

FIG. 1. (a) Schematic temperature versus 3delectron count

phase diagrams of cuprates (top) and nickelates (bottom).

Diﬀerent phases are displayed: superconducting phase (SC,

dark grey), strange metal (light grey delimited by dashed

lines [

]), antiferromagnetism (AF). The location in these

phase diagrams of the studied sample are represented by verti-

cal dashed lines Nd

(Ni

1.2+

: d

8.8

, red) and Nd

(Ni

1.33+

: d

8.67

, green), indicated as

= 5 and

= 3, respec-

tively, Nd-LSCO

= 0

24 (purple), Bi2201

= 0

23 (orange).

(b) In-plane resistivity vs

= 0 T of Nd

(

= 5

nickelate, red), Nd

(

= 3 nickelate, green) as measured

by Pan et al. [6].

eﬃcient to the nickelates. Despite their disparities, we

show that the diﬀerences in Seebeck coeﬃcients between

nickelates and cuprates come from strong dissimilarities

in impurity concentrations, and not necessarily from fun-

damental diﬀerences in the nature of the metallic state.

Despite the presence of strong electronic correlations, the

success of DFT and semi-classical transport calculations

in our study provides evidence of well-deﬁned quasipar-

ticles responsible for charge and heat transport in both

nickelates and cuprates.

II. METHODS

Samples. The perovskite-like parent Nd

n+1

3n+1

ﬁlms (

= 5 and

= 3) were synthesized by molecular

a b

FIG. 2. Sketch of a band dispersion, highlighting the elec-

tronic states that contribute the most to (a) resistivity and

(b) the Seebeck coeﬃcient, as indicated by the color gradients.

The states are selected by the weighting factors (

−df

) and

−E(df

dE ) from the equations B1 for the resistivity and B2 for

the thermoelectric coeﬃcient, respectively, at a given temper-

ature

. The states that contribute most to the resistivity

(Seebeck coeﬃcient) are located at the Fermi level (on either

side of the Fermi level). In the case of the Seebeck coeﬃcient,

the contributions of states above the Fermi level are subtracted

from the contributions of states below the Fermi level—-hence

the Seebeck coeﬃcient is a measure of the particle-hole asym-

metry.

beam epitaxy on (110)-orientated NdGaO

. The growth

process used distilled ozone, substrate temperatures of

∼

650-690

◦

C, and the NdNiO

calibration procedure de-

scribed in Ref. [

]. This synthesis was followed by a

reduction process contained in a sealed glass ampoule, op-

timized with a process at

∼

290

◦

C lasting three hours in

order to reach the square-planar Nd

n+1

2n+2

phases

(this process is similar to the procedure in Ref. [

]). Us-

ing an electron-beam evaporator, contacts consisting of

a 10 nm chromium sticking layer and 150 nm of gold

were deposited in a Hall bar geometry such that the ap-

plied thermal gradient and measured Seebeck voltage were

along the [001]-direction of the substrate.

The substrate material NdGaO

has a high thermal

conductivity that increases 30-fold between room tem-

perature and

∼

30 K [

], weakening the applied thermal

gradient along the nickelate ﬁlm. To mitigate this eﬀect,

we polished the NdGaO

substrate to reduce its thickness

from 500 microns down to

∼

100 - 150 microns using dia-

mond lapping ﬁlm. This served to increase the thermal

gradient that generates the Seebeck voltage, which allowed

us to measure the Seebeck eﬀect down to

∼

60 K, below

which the thermal gradient becomes too small and the

experiment cannot be performed reliably. This process

necessarily involves a brief heat exposure during sample

mounting. We minimized the degradation risk to the

sample [

] by using low temperature crystal wax and

mounting in an argon glove box; resistivity measurements

taken before and after polishing showed no substantial

changes.

Measurements. We measured the Seebeck coeﬃcient

using an AC technique used previously for cuprates [

An AC thermal excitation is generated by passing an

electric current at frequency

ω∼

1 Hz through a 5

kΩ strain gauge used as a heater to generate a thermal

gradient in the sample. While the heat is carried primarily

by the substrate, this also generates a thermal gradient

∆

TAC

along the ﬁlm. We detect this AC thermal gradient

at frequency 2

, as well as the absolute temperature shift,

using two type E thermocouples. An AC Seebeck voltage,

∆

VAC

, is also generated at a frequency 2

in response

to the thermal gradient. We measure this voltage with

phosphor-bronze wires attached to the same contacts

where the thermocouples measure ∆

TAC

: this eliminates

uncertainties associated with the geometric factor.

The thermocouple and Seebeck voltages were ampliﬁed

using EM Electronics A10 preampliﬁers and detected us-

ing a MCL1-540 Synktek lock-in ampliﬁer at the thermal

excitation frequency 2

. The Seebeck coeﬃcient is then

given by

−

∆

VAC/

∆

TAC

. The frequency

was ad-

justed so that the thermoelectric voltage and the thermal

gradient remained in phase.

Band structure calculations. The paramagnetic

electronic structure of the

= 5 and

= 3 layered nicke-

lates was calculated using density functional theory (DFT)

combined with the projector augmented wave method, as

implemented in the Vienna ab-initio simulation package

[

]. We used a pseudopotential that treats the Nd 4

elec-

trons as core electrons. The in-plane lattice parameters

were set to match the NdGaO

substrate, and we opti-

mized the out-of-plane lattice parameter. See Appendix A

for more details on the band structure calculations.

Boltzmann transport. We ﬁt a tight-binding model

(Tables Iand II) to the DFT band structure calculated

for the nickelates (Fig. 6). We combined the tight-binding

model and Boltzmann transport theory to calculate the

Seebeck coeﬃcient. We applied the same algorithm that

was used successfully in the cuprates [

–

] to numer-

ically evaluate the Seebeck coeﬃcient for the nickelates.

III. RESULTS

Seebeck coeﬃcient. Fig. 3b shows the in-plane See-

beck coeﬃcient of both the

= 5 and

= 3 samples.

Both samples show an

S/T

that is similar in magnitude,

negative, and independent of temperature. We repro-

duced the Seebeck coeﬃcient of the

= 5 layer nickelate

on a second sample (Appendix C), and the measured

S/T

of the

= 3 sample is similar to what was measured

previously on the 3-layer nickelate La

above its

metal-to-insulator transition at 105 K [31].

The Seebeck coeﬃcients of both nickelate samples are

also comparable in magnitude and sign to that of the

overdoped cuprate Bi2201

= 0

23 [

]. All of these

measurements contrast with the optimally-doped cuprate

Nd-LSCO

= 0

24 [

], whose Seebeck coeﬃcient is

strongly temperature dependent and changes sign near

room temperature (Fig. 3b). Both cuprates have a similar

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ElectronicbandstructureofasuperconductingnickelateprobedbytheSeebeckcoefficientinthedisorderedlimitG.Grissonnanche,1,2,3,∗G.A.Pan,4H.LaBollita,5D.FerencSegedin,4Q.Song,4H.Paik,6,7C.M.Brooks,4E.Beauchesne-Blanchet,3J.L.SantanaGonz´alez,3A.S.Botana,5J.A.Mundy,4andB.J.Ramshaw1,8,†1LaboratoryofAtomicand...

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Electronic band structure of a superconducting nickelate probed by the Seebeck coefficient in the disordered limit G. Grissonnanche1 2 3 G. A. Pan4H. LaBollita5D. Ferenc Segedin4Q. Song4H. Paik6 7C. M. Brooks4E..pdf

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Electronic band structure of a superconducting nickelate probed by the Seebeck coefficient in the disordered limit G. Grissonnanche1 2 3 G. A. Pan4H. LaBollita5D. Ferenc Segedin4Q. Song4H. Paik6 7C. M. Brooks4E.

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