Structural and Electronic Properties of the 2D Superconductor CuS with 1 1/3-valent Copper

1.1 MB·English

by  I. I. Mazin

Structural and Electronic properties of the 2D Superconductor CuS with 11-valent
3
Copper
I.I. Mazin
Code 6390, Naval Research Laboratory, Washington, DC 20375, USA
WepresentfirstprinciplecalculationsofthestructuralandelectronicpropertiesoftheCuScovel-
litematerial. Symmetry-loweringstructuraltransitioniswellreproduced. However,themicroscopic
origin ofthetransition isunclear. Thecalculations firmlyestablish thatthesofarcontroversialCu
valencyinthiscompoundis1.33. Wealsoarguethatrecentlyreportedhigh-temperaturesupercon-
2
ductivityinCuSisunlikelytooccurinthestoichiometricdefect-freematerial,sincethedetermined
1
Cu valency is too close to 1 to ensure proximity to a Mott-Hubbard state and superexchange spin
0
fluctuations of considerable strength. On the other hand, one can imagine a related system with
2
more holes per Cu in thesame structural motif (e.g., dueto defects or O impurities) in which case

n combination ofsuperexchangeandan enlarged compared toCuSFermisurface maylead touncon-
a ventionalsuperconductivity,similar to HTSC cuprate, but,unlikethem,of an f-wavesymmetry.
J

3 PACSnumbers:
1

] Coppersulfide inthe so-calledcovellitestructure(Fig. Structural properties of the covellite are also intrigu-
i
c 1) has recently attracted attention due to a new re- ing. At roomtemperature it consists of triangularlayers
s port about possible superconductivity at 40 K1. This ofCuandS,stackedasfollows,usingstandardhexagonal
-
l report has been met with understandable skepticism, stacking notation: Cu1 and S1 form layers A and B, at
r because previous researches2,3 reported reproducible su- the same height, so that Cu1 has coordination of three
t
m perconductivity at rather low temperatures, around 1-2 and no direct overlap. Cu2 and S2 form layersB and C,
. K. On the other hand, inspection of the literature re- so that Cu2 is directly above S1 and bonds with it, too,
t
a veals that reported physical properties of covellite are albeit more weakly than to S2. Thus, compared to the
m drastically different in different papers. For instance, S2 layer,the Cu2 layer is closer to the Cu1+S1 one, and
- one paper reported a well defined Curie-Weiss magnetic Cu2appearstobeinsideatetrahedron,closertoitsbase.
d susceptibility4, while others observed a nearly constant ThenextlayerisagainC,sothattwoS2atomsareright
n
behavior consistent with the Pauli susceptibility in ab- on top of each other and form a strongly covalent bond,
o
sence of any local moments. the shortest bond in this system, essentially making up
c
[ an S2 molecule.

At T = 55 K the system spotaneously undergoes a
2
transitionfroma hexagonalstructure to a lower symme-
v
try orthorhombic structure. To a good approximation,
6
5 the transition amounts to sliding the Cu2-S2 plane with
9 respecttotheCu1-S1planeby0.2˚A,andthetwoneigh-
0 boringCu2-S2planesby0.1˚Awithrespecttoeachother,
1. in the same direction. The bond lengths changevery lit-
1 tle, one of the three Cu2-S2 bonds shortens by 0.04 ˚A,
1 and the S2-S2 bonds lengthens by 0.05 ˚A, and all other
1 bonds remain essentially unchanged. Note that such
:
v transitions are quite uncommon for metals, but rather
i characteristic of insulating Jahn-Teller systems. Trans-
X
port properties are hardly sensitive to this transition,
r which is however clearly seen in the specific heat.
a
Thustherearethreequestionstobeasked. First,what
isthenatureofthelowtemperaturesymmetry-lowering?
Second, why some experiments indicate pure Pauli sus-
ceptibility, while others observe local moments (through
Curie-Weissbehavior)? Third,whyoneparticularexper-
iment sees indications of high temperature superconduc-
tivity, while others do not? Of, course, there is always a
FIG. 1: (color online) Crystal structure of covellite in the
chance the “outliers” experiments are simply incorrect,
high-symmetry phase. Large yellow spheres indicate sulfure,
and blue spheres copper. The dark spheres form the pla- butitisalwaysworthaskingthequestion,whethersome
narCuS layers(Cu1), and thelight spheresform thewarped sample issues may
Cu2S2 bilayers (Cu2). Fat yellow sticks indicate strong cova- possibly account for such discrepancies.
lent bonds inside theS2-S2 dumbells. Inordertoadressthefirstquestion,wehaveperformed
2
ically, a lower symmetry is stabilized in a metal if it re-
TABLEI:Thecalculatedtotalenergy(meV/cell) ofthelow-
sults in a reduced density of states at the Fermi level
temperatureorthorhombicandthehigh-temperaturehexago-
(“quasinesting mechanism”). However, the density of
nalstructure,usingeithertheexperimentalorthecalculated
states at the Fermi level does not change at this tran-
optimized parameters. Structural parameters used, as well
as selected bond length (˚A) are also shown. Note that one sition (Fig. 2), and the states below Fermi actually shift
unitcellincludes6formulaunits. Thecellvolumeisgivenin slightly upward. Thus, one-electron energy is not the
˚A3 The last column corresponds to the orthorhombic struc- reasonfor the transition. A look at the calculatedFermi
ture with internal coordinates optimized, while keeping the surfaces(Fig. 4) showsthat while they become more 2D
experimental unit cell. in the orthorhombic structure (the in-plane plasma fre-
H-exp O-exp H-calc O-calc O-c.o. quency remains the same, ≈ 4.0 eV, while that out of
plane, 1.36 eV, drops by 12%), there is no shrinkage in
a 3.789 3.760 3.807 3.793 3.760
their size.
b 3.789 6.564 3.807 6.623 6.564
c 16.321 16.235 16.496 16.453 16.235
80
ortho
zCu2 0.1072 0.1070 0.1069 0.1077 0.1083 hex
70
zS2 0.0611 0.0627 0.0639 0.0646 0.0651
yCu1 n/a 0.6377 n/a 0.6227 0.6077 60
yCu2 n/a 0.3372 n/a 0.3410 0.3413 ell 50
yS1 n/a 0.3068 n/a 0.2917 0.2760 es/c
at 40
yCSu21-S1 n3×/a2.19 02.×0020.188 n3×/a2.20 02.×0026.240 02.×0026.290 N(E), st 30
2.17 2.19 2.19
20
Cu2-S1 2.33 2.33 2.36 2.33 2.34
Cu2-S2 3×2.31 2×2.30 3×2.31 2×2.30 2×2.30 10
2.28 2.33 2.33 0
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1
S2-S2 1.99 2.04 2.11 2.13 2.12
E-EF, eV
Volume 202.9 200.3 207.0 206.7 207.3
Energy 0 -85 -258 -265 -189
FIG. 2: (color online) Calculated density of states in
thehigh-temperature(“hex”)andlowtemperature(“ortho”)
density functional calculations (DFT) of both hexago- structures, using in both cases optimized parameters.
nal (H) and orthorhombic (O) structure. First, we op-
timized the crystal structure using the standard VASP
We cannot say definitively what causes the low-
programwithdefaultsettings(includinggradientcorrec-
temperature symmetry lowering in CuS, but we can say
tions), and starting from the experimental structure as
confidentlythatitisnotvanderWaalsinteractionascon-
reported in Ref. 4.
jectured in Ref. 5 (for one, it would not be reproduced
After that, all calculations in the determined crystal inLGA/GGAcalculationswithrequestedaccuracy,and,
structureswereperformedusingthestandardall-electron also, as dicussed below, the interplanar bonding is cova-
LAPW code WIEN2k. We have also verified that the lent, and not van der Waals), and not a typical metallic
calculated forces in the optimized structures are small mechanism driven by Fermi surface changes. One can-
enough. As a technical note, to obtain full convergences didate is ionic Coulomb interaction. Indeed the calcu-
in the energydifferences we hadto go up to RKmax =9. latedEwaldenergyisnoticeablylowerintheorthorhom-
TheresultsareshowninTable1. Eventhoughthereis bic structure. However the Ewald energy is only part
some discrepancy between the calculated and the exper- of total electrostatic energy, so from this fact alone one
imental low-temperature structures (mostly in terms of cannot derive definitive conclusions.
anoveralloverestimationoftheequilibriumvolume),the Let us now discuss the electronic structure. Since the
correct symmetry lowering is well reproduced. In fact, differencesbetweenthetwostructuresareverysmall,we
giventhatonlyonepaperhasreportedinternalpositions shalllimitourdiscussionbythehigh-temperaturehexag-
fortheorthorhombicstructre,andthe samepaperfound onal structure. The calculated band structure is shown
a Curie-Weiss law, suggesting, as discussed below, crys- in Fig. 3. Note two sets of bands, one at -7 eV and
tallographic defects in their sample, it is fairly possible the other at 1 eV, of strong S2-p character. These are
z
that the calculations predict the structure of an ideal bonding and antibonding bands of the S2-S2 dumbells.
material better than this one experiment has measured. Historically, there has been a heated discussion of the
A more important question now is, what the mech- Cu valency in this compound, and what is an appro-
anism for this well-reproduce symmetry lowering can priate ionic model. Both (Cu+1) (S−2)(S−1) (Ref. 4)
3 2
be? Ionicsymmetry-loweringmechanisms(suchasJahn- and (Cu+1) (S−1)(S−2) (Ref. 5) have been discussed,
3 2
Teller)areexcludedinawidebandmetallikeCuS.Typ- assuming monovalent copper. On the other hand, XPS6
3
and NQR7 data indicated Cu valency larger than 1, but
3.0
smallerthan1.5. Fromourcalculationsitisimmediately
2.0
1.0 obvious that S1 is divalent, while S2 is monovalent (the
V) -01..00 EF athnetibFeornmdiinlgevpezl,bwahnildeoaflltSh1e-dSe2r-iSve2ddbimanedrsisar1e beVeloawbothvee
nergy (e ---234...000 Fpreiramteilieovneilc),msoodtehlaitsC(Cuuh+a4s/v3a)3le(nSc−2y2)1(.S3−32,)a.ndthe appro-
E -5.0
-6.0
-7.0
-8.0 Γ M K ΓA L H A
This means that the Cu d−band has 1/3 hole per Cu
1.0 ion,2.5timesfewerthaninthehigh-Tccuprates(optimal
doping corresponds to 0.8-0.85 holes). This may be too
0.0 EF farfromhalffillingforstrongcorrelationeffects,butitis
V) nevertheless suggestive of possible spin fluctuations. We
y (e -1.0 will return to this point later.
g
er
n
E -2.0
Inorderto understandthe Cud bands nearthe Fermi
-3.0 Γ M K ΓA L H A level, let us consider a simple tight binding model with
two d orbitals,with m=±2 (correspondingto combina-
tions of the x2−y2 and xy cubic harmonics, which be-
longto the samerepresentationinthehexagonalgroup).
FIG.3: Calculated banddispersionsinthehexagonalstruc- Since these orbitals are the ones spread most far in the
ture. ThepointsΓ,MandKareinthecentralplane(kz =0) plane,theirhybridizationwithSisthestrongestandthey
and A, L and H in the basal plane (kz = π/c). In the top form the highest antibonding states near the Γ point,
panel,thewidthofthelinesisproportionaltotheamountof crossing the Fermi level. Integrating out the S p or-
x,y
theS2-pz character in thecorresponding states. bitals we arrive at the following model band structure:
1
E = (3t2 +4t2 ) cos(k·R )±(3t2 −4t2 ) cos2(k·R )− cos(k·R )cos(k·R ) ,
k 2(ε −ε ) pdσ pdπ i pdσ pdπ i i j 
d p i s i i>j
X X X
 (1)
where t are the Cu-S hopping amplitudes, and R are Cu, too small to form a magnetic state, even in LDA+U
i
the three standardtriangularlattice vectors, R =0. with U ∼ 8 eV (as verified by direct calculations). For-
i i
Note that these bands are degenerate at Γ, unless spin- mation of an ordered magnetic state is additionally hin-
P
orbit coupling is taken into account. Near the top of the deredbythe factthatsupexchangeisthiscaseisantifer-
band the dispersion is isotropic, and away from it the romagnetic,and frustrated,as it should be ona triangu-
Fermisurfacedevelopsacharacteristichexagonalrosette lar lattice. One may think that additional hole doping,
shape (Fig. 4). achieved through Cu vacancies, broken S-S bonds or in-
Let us now look at the calculated bands (Fig. 3). It terstitialoxygen(note that this structuresincludes large
is more instructive to concentrate on the righ hand side pores, one per formula unit, in each Cu-S layer) should
of Fig. 3, where the k dispersion does not obscure the bringthed−bandsclosertohalf-occupancyandpromote
z
states degeneracy. We see, as predicted by the model, localmagneticmoments. Notethatinatleastoneexper-
three sets of nearly parabolic bands, each four times de- imental paper a Curie-Weiss behavior was reported, cor-
generate at the point A=(0,0,π/c). One of them is be- responding to 0.28 µB/Cu4, and in another a weak, but
low the Fermi level and two above,forming the eight FS inconsistentwiththePaulilaw,temperaturedependence
sheets we see in Fig. 4. The middle bands are predomi- was found8, while other authors reported temperature-
nantly formedby the Cu1 andthe lower(fully occupied) independent susceptibility.
andupperonesbytheCu2,althoughthereissubstantial One can speculate that the unexpected high-
mixture of all three Cu orbitals. The average occupa- temperature superconductivity observed by Raveau et
tion of Cu d orbitals, as described above,is 1/3 hole per al1 is a phenomenon of the same sort, namely that this
4
-
+ +
- -
+
FIG.5: (coloronline)AmodelFermisurface,calculatedusing
Eq. 1,overlappedwiththewavevectorscorrespondingtosu-
perexchangeonatriangularlattice. Thesignsshowapossible
f−wavepairingstate,consistentwithsuperexchnage-induced
spin fluctuations.
change) would be pairing for a triplet f−state shown in
the same picture9. Indeed, the superexchange vectors
always span the lobes of the order parameter with the
same sign. Since in a triplet case spin-fluctuations gen-
erate an attractive interaction, it will be pairing for the
geometry shown in Fig. 5. Note that this is opposite to
high-T cuprates, where the superexchange interaction
c
FIG.4: (coloronline)CalculatedFermisurfacesinthehexag- spans parts with the opposite parts of the d−wave or-
onal(top)andorthorhombic(bottom)structure,viewedalong der parameter, but in a singlet channel this interaction
thec-axis. Note reduced kz dispersion in the bottom panel. is repulsive, and therefore pairing when the correspond-
ing parts of the Fermi surface have opposite signs of the
order parameter.
superconductivity forms in a portion of a sample, the
While the model Fermi surface shown in Fig. 5 is
same portion where some previous researchers observed
roughly similar to that calculated in the stoichiometric
localmagneticmoments. Asdiscussedabove,itishighly
CuS,thesystematthisdopingistoofarfromtheordered
unlikely that a stoichiometric, defectless CuS sample
magnetism to let us assume sizeable superexchange-like
would support either local moments or unconventional
magnetic fluctuations. As mentioned, our attempts to
superconductivity. However, it is of interest to consider
stabilize an antiferromagnetic (more precisely, ferrimag-
ahypotheticalsituationthatwouldtakeplaceifsuchmo-
netic, since we only tried collinear magnetic patterns)
ments were present. Indeed in that case one can write
using a triple unit cell failed, even in LDA+U. One may
downthe superexchangeinteractionbetweenthe nearest
thinkofaholedopedsystem,wheresuperexchangeisop-
neighbors as antiferromagnetic Heisenberg exchange, in
erativeandtheinnerFermisurfaces(albeitnottheouter
whichcaseinthe reciprocalspaceit willhavethe follow-
ones) have geometry similar to that featured in Fig. 5.
ing functional form:
Of course,it may not be possible to stabilize a system
J(q)=J cos(k·R ). (2) at sufficient hole doping and retain the required crystal-
i lography. We prefer to think about the model discussed
i
X in the perevious paragraphs as inspired by the CuS cov-
In Fig. 5 we show an example of a Fermi surface gen- ellite, bit not necessary applicable to actual materials
erated for the model band structure (Eq. 1), for the derived from this one. The reason we paid so much at-
simplest case of t = 0. The wave vectors correspond- tentiontoitisthatthisisasimplegenericmodel,describ-
pdπ
ing to the peaks ofthe superexchangeinteraction(2)are inganytriangularplanarstructurewithtransitionmetals
shown by arrows. An interesting observation is that for andligands inthe same plane,as in the covellite,in case
thisparticulardopingthissuperexchangeinteraction(or, where correlations are sufficiently strong to bring about
bettertosay,spinfluctuationsgeneratedbythissuperex- spinfluctuationscontrolledbysuperexchange. Itisquite
5
exciting that, compared to the popular spin-fluctuation f, as opposed to singlet d. This finding may have im-
scenario of superconductivity in cuprates, to which it is plications far beyound this particular material and (yet
conceptuallysosimilar,this simplegenericmodelresults unconfirmed) superconductivity in it.
in a completely different superconducting state, triplet
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(1988). SigristandUeda10,withthebasisfunctionsˆz(ky(ky2−3kx2)
5 W. Liang, M.H. Whangbo, Solid State Comm. 85, 405 or kz[(ky2−kx2)yˆ−2kxkyxˆ].
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