Manipulating superconductivity of $1T$-TiTe$_2$ by high pressure

1.1 MB·

by  R. C. Xiao

Manipulating superconductivity of 1T-TiTe by high pressure
2
R.C.Xiao,1,2W.J.Lu,1,∗D.F.Shao,1J.Y.Li,1,2M.J.Wei,1,2H.Y.Lv,1P.Tong,1X.B.Zhu,1andY.P.Sun3,1,4,†
1Key Laboratory of Materials Physics, Institute of Solid State Physics,
Chinese Academy of Sciences, Hefei 230031, China
2University of Science and Technology of China, Hefei, 230026, China
3High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
4Collaborative Innovation Center of Microstructures, Nanjing University, Nanjing 210093, China
7 Superconductivity of transition metal dichalcogenide 1T-TiTe2 under high pressure was investi-
1 gated by thefirst-principles calculations. Our results show that the superconductivity of 1T-TiTe2
0
exhibitsvery different behavior underthehydrostatic and uniaxial pressure. The hydrostatic pres-
2
sure is harmful to the superconductivity, while the uniaxial pressure is beneficial to the supercon-

n ductivity. SuperconductingtransitiontemperatureTC atambientpressureis0.73K,anditreduces
a monotonouslyunderthehydrostaticpressureto0.32Kat30GPa. WhiletheTC increasesdramat-
J ically under the uniaxial pressure along c axis. The established TC of 6.34 K under the uniaxial
4 pressureof 17GPa, belowwhich thestructuralstability maintains, isabovetheliquid helium tem-
1 peratureof4.2K.TheincreaseofdensityofstatesatFermilevel,theredshiftofF(ω)/α2F(ω)and
thesofteningoftheacousticmodeswithpressureareconsideredasthemainreasonsthatleadtothe
] enhancedsuperconductivityunderuniaxialpressure. Inviewofthepreviouslypredictedtopological
n
o phase transitions of 1T-TiTe2 under the uniaxial pressure [Phys. Rev. B 88, 155317 (2013)], we
c consider1T-TiTe2asapossiblecandidateintransitionmetalchalcogenidesforexploringtopological
- superconductivity.
r
p
PACSnumbers: 73.20.At,74.20.Pq,71.15.Mb
u
s
.
at I. INTRODUCTION cal phenomena can be realized via various kinds of ma-
m nipulation. Anomalous electron transport was found
in the back-gated field-effect transistors with 1T-TiTe
- Transitionmetaldichalcogenides(TMDCs)MX ,with 2
d 2 thin-film channels.22 Large negative magnetoresistance
M a transition metal (e.g. M = Ti, Mo, Ta, W) and
n was reported in two-dimensional spin-frustrated 1T-
o X a chalcogen atom (S, Se, Te), is an emerging fam- TiTe I .23 Bulk and monolayer 1T-TiS Te show
c ily of layered materials. The intra layer is composed 2−x x 2−x x
topologicalphasesundercertainconcentrationofS/Te.24
[ by X-M-X sandwich structure, which is attracted by the
1T-TiTe was recently predicted to undergo series of
van der Waals forces between the inter layers. TMDCs 2
2 topological phase transitions under high pressure.25 1T-
v material that can be semiconductor, metal, charge den-
TiTe isasemimetalwithanoverlapofvalenceandcon-
8 sitywave(CDW) system,orsuperconductorhas become 2
ductionbandsof0.6eV,26howeverthesuperconductivity
9 a rich playground to discover new materials with di-
hasnotbeenexperimentallyfounddownto 1.1Katam-
7 verse physical phenomena and properties. Broad appli-
1 bient pressure.27
cationprospectsofTMDCssuchastransistors,photode-
0
tectors, electroluminescent devices,1 van der Waals het- Pressure, an important controllable parameter that
.
1 erostructures with high on/off current ratio,2 and topo- can effectively tune the lattice structures and the cor-
0 logicalfield-effecttransistorsbasedonquantumspinHall responding band structure, has become an effective way
7 effect,3 have been triggered great attention. to introduce superconductivity and study the relation-
1
: MTe2 is a typical material with rich physical ship between the superconductivity and other physical
v properties and exhibits unique properties compared phenomena in TMDCs. For instance, the metallization
Xi with MS2/MSe2 due to the strong p-d hybrid and andthehighestonsetTC of11.5KwererealizedinMoS2
r spin-orbit coupling effect. For instance, the com- under high pressure;28,29 the relationship between CDW
a petition between the charge/orbital density wave andsuperconductivityin1T-TaS230,31 and1T-TiSe232,33
(CDW/ODW) and superconductivity was observed in was studied under high pressure; the pressure driven su-
IrTe ;4,5 topological Dirac point was found in the perconductivity and suppressed magnetoresistance were
2
HfTe2/AlN epitaxial system;6 large and non-saturating observed in WTe214,15 and MoTe2.16,34
magnetoresistance,7–9type-IIWeylpoints,10–13andpres- In this work, we focus on the possibility of super-
sure driven superconductivity14–16 were observed in conductivity of 1T-TiTe under high pressure by first-
2
WTe2 and MoTe2; topologically nontrivial surface state principles calculations. Our results show that the TC at
with Dirac cone was found in PdTe2 superconductor;17 ambient pressure is 0.73 K, and it reduces under the hy-
andthetype-IIDiracFermionsinPtTe218,19wasrecently drostaticpressureto0.32Kat30GPa. Whiletheuniax-
theoretically proposed and confirmed by experiment. ialpressurealongcaxiscanincreasetheT dramatically
C
1T-TiTe is a textbook Fermi-liquid system.20,21 to6.34Kmaximally. Weexplainedthedifferentbehavior
2
Though it is a simple physical system, abundant physi- ofsuperconductivityunderthehydrostatic/uniaxialpres-
2
surebasedonthevarietiesofelectronic/phononstructure
and the electron-phonon coupling effect.
II. METHODS
Thefirst-principlescalculationsbasedondensityfunc-
tionaltheory(DFT)werecarriedoutusingQUANTUM-
ESPRESSO package.35 The ultrasoft pseudo-potentials
FIG.1: (Coloronline)(a)Crystalstructureand(b)Brillouin
and the local density approximation (LDA) according
zone of 1T-TiTe2.
to the PZ functional were used. The energy cutoff for
the plane wave (charge density) basis was set to 35
Ry (350 Ry). The Brillouin zone (BZ) was sampled
with a 16×16×8 mesh of k-points. The Vanderbilt- 3.7 4.0
(a) (b)
Marzari Fermi smearing method with a smearing pa- ¯)3.6 ¯) 3.9
rameter of σ = 0.02 Ry was used. The lattice con- (a3.5 (a 3.8
3.4
stants and ions were optimized using Broyden-Fletcher- 3.3 3.7
Goldfarb-Shanno(BFGS)quasi-newtonalgorithm. Elec- 6.4
tronic properties are calculated including the spin-orbit ¯)6.2 ¯) 6.0
couplingeffect. Sincethespin-orbitcouplingeffectisless c (6.0 (c 5.6
important in describing the vibrational properties,36,37 5.8 5.2
the calculation of phonon dispersion is carried out ne- 0 10 20 30 0 5 10 15
Pressure (GPa) Pressure (GPa)
glecting this effect. The phonondispersionandelectron-
FIG. 2: (Color online) Lattice parameters under the (a) hy-
phononcoupling constants werecalculatedusing density
functionalperturbationtheory(DFPT)38withan8×8×4 drostatic pressure and (b) uniaxial pressure along caxis.
mesh of q-points. The double Fermi-surface averages of
electron-phononmatrixelementswerecalculatedusinga
32×32×16 mesh of k-points.
cated at the Γ and L points, respectively. The calcu-
lated phonon dispersion is shown in Fig. 3(d). The
irreducible representations of the Γ point phonons are
III. RESULTS AND DISCUSSION Γ=E +A +2E +2A , and the corresponding op-
g 1g u 2u
tical vibration modes are illustrated in Fig. 4(a). The
1T-TiTe has a layered structure with space group E andA areRamanactivemodes,andthe calculated
2 g 1g
P¯3m1 (1T-CdI structure), with one Ti atom and two frequencies of 105/150 cm−1 for E /A are very close
2 g 1g
Te atoms located at (0, 0, 0) and (1/3, 2/3, ±z) sites, to 102/145 cm−1 observed in experiment.41
respectively. The crystalstructure and BZ are displayed Applying pressure reduces the lattice parameters and
in Fig. 1. The optimized lattice parameters are 3.677 ˚A enhances the atom interaction, making the band struc-
and 6.331 ˚A for a and c respectively. The lattice param- turemoredispersiveandincreasingtheoverlapoftheva-
etersareslightlyunderestimatedby2.4%comparedwith lence bandsandconductionbands. The electronicstruc-
the experimentally obtained ones,21,39 and such under- ture and phonon dispersion under the hydrostatic pres-
estimation exists normally in the LDA calculations. As sureof30GPaareshowninFigs. 3(a)and(b),wherethe
expected, when the hydrostatic pressure is applied the CBMof electronic structure is changedfromthe L point
lattice is suppressed, as shown in Fig. 2(a). Due to the to the M point. With the lattice parameters and Ti-Te
weak van der Waals coupling between adjacent layers, bond length decreasing,the frequencies of Γ phonons in-
the reduction of c is more substantialthan that of a. By creasemonotonouslyunderthepressureasdemonstrated
fitting the pressure-energydata to the Birch-Murnaghan in Fig. 4(b), and especially the variation of A is more
2u
equationofstate,thebulkmodulusB anditsderivative evidently. Meanwhile, the phonons of the whole BZ also
0
B′ for1T-TiTe werecalculatedtobe51.1GPaand4.54 shift to higher frequency with the hydrostatic pressure,
0 2
respectively. as illustrated for the phonon density of states F(ω) in
Thecalculatedelectronicstructureof1T-TiTe atam- Fig. 6(a).
2
bient pressure is shown in Fig. 3(c), which is reasonable Though the band structures are more dispersive, the
agreement with the previously experimental and theo- N(E ) decreases with the hydrostatic pressure (Fig.
F
retical reports.26,40 The density of states (DOS) near 5(a)). TorevealthepressureeffectontheorbitalsatE ,
F
the Fermi level (E ) are mostly contributed by the Ti the partialDOS at E (NP(E )) is shownin Figs. 5(b)
F F F
d and Te p orbitals. The electronic structure shows and(c). TheNP(E )ofTiddecreasesdramaticallyun-
F
the semimetal feature with the DOS at Fermi level der the uniaxial pressure (Fig. 5(b)), and the NP(E )
F
(N(E )) of 1.6 states/eV. The valence band maximum of Te p +p and p increase and decrease respectively
F x y z
(VBM) and conduction band minimum (CBM) are lo- under the hydrostatic pressure (Fig. 5(c)). The charge
3
30 GPa (hydrostatic) Ambient pressure 15 GPa (uniaxial)
3 3 3
(a) (c) (e)
2 2 2
V) V) V)
E-E (eF01 E-E (eF 01 E-E (eF 01
-1 -1 -1
-2 -2 -2
-3 -3 -3
M K A L H AA M K A L H A M KK A L H AA
400 400 400
(b) (d) (f)
300 300 300
-1 m) -1 m) -1 m)
(c200 (c 200 (c 200
100 100 100
0 0 0
M K A L H AA M K A L H A M K A L H A
FIG. 3: (Color online) Electronic structures and phonon dispersions of 1T-TiTe2 under the (a, b) hydrostatic pressure of 30
GPa,(c,d)ambientpressureand(e,f)uniaxialpressureof15GPa. Thereddotsin(d)denotetheRamanfrequenciesobserved
in experiment (Ref. 41). For the convenience of comparison, the valence and conduction bands crossing the EF decorated by
blueand red respectively.
equation42
ω 1.04(1+λ)
T = log exp − , (1)
c 1.2 (cid:18) λ−µ∗−0.62λµ∗(cid:19)
wheretheCoulombpseudopotentialµ∗ issettoatypical
value of 0.1.33,43,44 The logarithmicallyaveragedcharac-
teristic phonon frequency ω is defined as
log
2 dω
ω =exp α2F(ω)logω . (2)
log
(cid:18)λZ ω (cid:19)
The total electron-phonon coupling constant λ can be
obtained by
α2F(ω)
λ= λ =2 dω, (3)
qv
Z ω
Xqv
FIG.4: (Coloronline)(a)Schematicillustrationoftheoptical where the Eliashberg spectral function is
vibration modes at Γ point, Ti and Te are denoted by blue
1 γ
and dark yellow balls, respectively. (b)Phonon frequencies α2F(ω)= δ(ω−ω ) qv . (4)
at Γ point and Ti-Te bond length under the hydrostatic and 2πN(EF)Xqv qv ~ωqv
uniaxial pressure.
The T at ambient pressure is calculated to be 0.73
C
K, coinciding with the fact that the superconductiv-
ity was not found above 1.1 K in the experiment.27 As
densityatE on(110)planeunderthe hydrostaticpres-
F discussed above, applying hydrostatic pressure increases
sure of 30 GPa and ambient pressure are also shown in
thephononfrequencies,thereforetheDebyetemperature
Figs. 5(g) and (h).
raises, so does the ω (see Fig. 7(a)). Similar to the
log
We estimated the superconducting transition temper- F(ω), Eliashberg function α2F(ω) shifts to higher fre-
ature T based on the Allen-Dynes-modified McMillan quency with the increase of hydrostatic pressure (Fig.
C
4
0 GPa 0 GPa
(a) 10 GPa (c) 9 GPa
20 GPa 15 GPa
) (a.u.) 30 GPa ) (a.u.) 17 GPa
F( F(
(b) (d)
u.) u.)
a. a.
) ( ) (
F( F(
2 2
0 100 200 300 400 0 100 200 300
-1 -1
(cm ) (cm )
FIG.6: (Color online)(a)/(c) PhonondensityofstatesF(ω)
and (b)/(d) Eliashberg function α2F(ω) under hydrostatic
pressure (left) and uniaxial pressure (right).
FIG. 5: (Color online) N(EF) and NP(EF) (in states/eV)
uTdnrhodesetrcahttaihcregpe(raed)se-sn(ucsr)ietyhoyfadt3r0oEsFtGaPtoianc,(a(1nh1d)0)a(dmp)lb-a(infee)ntuunnpidraeexsrisautlhreepra(egns)sduhr(yei)-. (K)log 221400(a) (K)log 111258000 (d)
uniaxialpressureof15GPa. Thedifferencebetweentwocon- 180 90
0.40
tourlinesin(g)-(i)issettothesame. TiandTearedenoted 0.9 (e)
0.38
by blueand dark yellow balls, respectively. (b)
0.36 0.6
0.34
0.3
6(b)). Therefore, according to Eq. (3), the λ decreases K) 0.8 K) 6 (f)
withthehydrostaticpressure(seeFig. 7(b)). Asaresult, ( C 0.6 (c) (C 4
0.4 2
the T decreases monotonously with the pressure from
C
0.2 0
0.73 K at ambient pressure to 0.32 K at 30 GPa (Fig. 0 5 10 15 20 25 30 0 5 10 15 20

7(c)), indicating that the hydrostatic pressure does not P (GPa) P (GPa)
benefit to introduce the experimentally detected super- FIG.7: (Coloronline)Calculatedλ,ωlog andTC of1T-TiTe2
conductivity,whichisunlikethecasesofemergingsuper- underthe(a)-(c) hydrostatic and (d)-(f) uniaxial pressure.
conductivity in the semimetal WTe and MoTe 14–16,34
2 2
under hydrostatic pressure.
Due to the layer structure, uniaxial pressure along c be attributed to the combination of the expansion of ab
axis can be easily applied in experiment. Therefore the plane andthe slowdecreaseof the Ti-Te length(see Fig.
superconductivity under the uniaxial pressure along c 4(b)). Meanwhile,thevariationofE andA underthe
u 2u
axis is studied as well in our research. When the uni- uniaxial pressure is less significant than that under the
axial pressure along c axis is applied, the c axis reduces hydrostaticpressureduetothefactthatthereductionof
meanwhile a axis expands (Fig. 2(b)). The variations of Ti-Telengthismuchlessthanthatunderthehydrostatic
a and c are more evidently than that under the hydro- pressure.
staticpressure. TheaveragePoisson’sratiov =−∆a/∆c TheuniaxialpressureraisestheN(E )verymuch(see
F
in the range of our study is 0.23. The electronic struc- Fig. 5(d)). The NP(E ) of Ti d +d increases dra-
F zx zy
ture is less dispersive and the overlap is reduced with matically under the uniaxial pressure (Fig. 5(e)), and
theuniaxialpressure. Theelectronicstructureunderthe the trend of NP(E ) of Te p +p and p under the uni-
F x y z
uniaxial pressure of 15 GPa is shown in Fig. 3(e), where axial pressure (Fig. 5(f)) is opposite to that under the
the CBM is changed from the L point to the M point. hydrostatic pressure. The increase of the NP(E ) of Te
F
The phonon dispersion under the uniaxialpressure of 15 p andTid +d willincreasetheorbitaloverlapofTi-
z zx zy
GPa is shown in Fig. 3(f), where the acoustic modes Te atoms at E as shown in Fig. 5(i), while the orbital
F
soften. overlap is not such case under the hydrostatic pressure
As demonstrated in Fig. 4(b), with the increase of (Fig. 5(g)). The strong σ bands crossing the EF due to
uniaxial pressure, both Eg and A1g modes that only in- the orbital overlap at EF is one of the main reasons of
volve the vibrations of Te atom increase monotonously. high TC of superconductors MgB244–46 and H3S.47,48
While, the E and A modes increase at first and then As shown in Fig. 6(c), even though some optical
u 2u
decreaseasthepressurelargerthan8.9GPa,whichcould phonon F(ω) peaks shift to higher frequency in some
5
ofhydrostaticpressureanduniaxialpressureonthecrys-
tal, electronic and phonon structures (Fig. 8). Both
a, c and Ti-Te bond are compressed under the hydro-
staticpressure(Fig. 8(a)). Thestrongerbanddispersion
makes the N(E ) reduce. The phonon density of states
F
F(ω) shifts to higher frequency. The decrease of N(E )
F
and the blueshift of F(ω) are not in favor of supercon-
ductivity, as discussed above. While under the uniaxial
pressure c is suppressed and a is expanded accordingly
(Fig. 8(b)). Thebanddispersionbecomesweaker,there-
fore the N(E ) increases with the increase of uniaxial
F
pressure. The acoustic phonon modes soften, and F(ω)
shiftstolowerfrequency. Thesetwofactors(theincrease
of N(E ) and the redshift of F(ω)) are in favor of su-
F
perconductivity,asdiscussedabove. We think this phys-
icalscenariois notonly applicable to 1T-TiTe , but also
2
to other layered semimetal TMDC materials. We pro-
pose that the uniaxial pressure can provide an alterna-
tive method for enhancing or finding superconductivity
FIG.8: (Coloronline)Schematicdiagramoftheeffectsof(a) in TMDCs.
hydrostatic pressure and (b) uniaxial pressure on the crystal
The previous investigation shows that 1T-TiTe is
(top), electronic (middle) and phonon (bottom) structures. 2
The gray symbols in each graph denote the corresponding topological trivial at ambient pressure, but it was pre-
states at ambient pressure. Ti and Te are denoted by blue dicted to undergo series of topological phase transitions
and dark yellow balls, respectively. underpressure,whichisrelatedtothebandinversionsat
different points of the BZ.25 Therefore applying the uni-
axial pressure, one can expect to obtain the topological
cases,the overallF(ω)shifts tolowerfrequencywiththe phase and the enhanced superconductivity in 1T-TiTe
2
increase of uniaxial pressure, especially for the acoustic at the same time. As suggested, introducing supercon-
phononsandtheωlog decreaseswithuniaxialpressureas ductivity into the topological material could make them
well (Fig. 7(d)). Similar to the F(ω), α2F(ω) shifts to to be topological superconductor,49,50 which has a full
lower frequency (Fig. 6(d)), and the proportion of its pairing gap in the bulk and a gapless surface state con-
low frequency part increases with the uniaxial pressure sisting of Majorana fermions. The possible topological
duotothesofteningoftheacousticmodes. Accordingto superconductivity in 1T-TiTe under pressure is needed
2
Eq. (3), the mode with lower frequency and the larger tobe studied inthe furtherexperimentalandtheoretical
α2F(ω) will strongly contribute to the electron-phonon studies.
coupling. Therefore, as shown in Fig. 7(e), the λ ba-
sically increases with the increase of uniaxial pressure.
Consideringoveralleffects,theT changesslowlyatfirst
C
while it increases dramatically as the uniaxial pressure
larger than 8.9 GPa (Fig. 7(f)). The N(E ) decreases
F
withthehydrostaticpressure,andincreasesdramatically IV. CONCLUSION
under the uniaxial pressure (Figs. 5(a) and (d)). The
varying trend of T with pressure coincides with that of
C
N(E ) (Figs. 7 (c) and (f)). This result is consistent Using the first-principles calculations, we demon-
F
with the scenario that, as a general rule of BCS, larger strated that the superconductivity of 1T-TiTe is sup-
2
N(E ) is in favor of higher T . pressedunderthehydrostaticpressureandenhancedun-
F C
Superconductivity with a relatively high T often der the uniaxial pressure. The increase of N(E ), the
C F
emerges in the vicinity of structural instability. Just be- redshift of F(ω)/α2F(ω) and the softening of the acous-
neath the structural instability, the T of 6.34 K under tic phonon modes with the uniaxial pressure contribute
C
the uniaxial pressure of 17 GPa is estimated, above the to the enhanced superconductivity. When the uniaxial
liquid helium temperature of 4.2 K. Under higher uniax- pressure of 17 GPa is applied, the maximum T of 6.34
C
ial pressure, the structure is no longer stable, which is Kinourresearchisobtained. Theuniaxialpressurepro-
estimated from the calculated imagine frequency in the vides analternativemethod to manipulate superconduc-
acoustic modes. Our results show that the hydrostatic tivity in TMDCs. Under reasonable pressure, the topo-
pressure is harmful to the superconductivity, while the logical state and superconductivity may appear at the
uniaxial pressure is beneficial to the superconductivity sametimein1T-TiTe . Thesuperconductivityandtopo-
2
of 1T-TiTe . logical property in 1T-TiTe under pressure will expand
2 2
We draw a schematic diagram to describe the effects its physics and applications.
6
Acknowledgments Innovation Promotion Association of CAS (2012310),
Key Research Program of Frontier Sciences of CAS
This work was supported by the National Key Re- (QYZDB-SSW-SLH015) and Hefei Science Center of
search and Development Program of China under Con- CAS (2016HSC-IU011). The calculations were partially
tractNo. 2016YFA0300404,theNationalNatureScience performedattheCenterforComputationalScience,CA-
Foundation of China under Contract Nos. 11674326, SHIPS.
11404340, 11274311, 11404342 and U1232139, Youth
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