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015

Resonance-state-induced superconductivity at high Indium contents in In-doped SnTe

Neel Haldolaarachchige, Quinn Gibson, Weiwei Xie, Morten Bormann Nielsen, Satya Kushwaha and R. J. CavaDepartment of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

We report a reinvestigation of superconducting Sn1−xInxTe at both low and high In dopinglevels. Analysis of the superconductivity reveals a fundamental change as a function of x : thesystem evolves from a weakly coupled to a strongly coupled superconductor with increasing indiumcontent. Hall Effect measurements further show that the carrier density does not vary linearly withIndium content; indeed at high Indium content, the samples are overall n-type, which is contraryto expectations of the standard picture of In1+ replacing Sn2+ in this material. Density functionaltheory calculations probing the electronic state of In in SnTe show that it does not act as a trivialhole dopant, but instead forms a distinct, partly filled In 5s - Te 5p hybridized state centered aroundEF , very different from what is seen for other nominal hole dopants such as Na, Ag, and vacant Snsites. We conclude that superconducting In-doped SnTe therefore cannot be considered as a simplehole doped semiconductor.

PACS numbers: ——–

I. INTRODUCTION

SnTe and other II-VI materials with the rock-saltstructure type have long attracted attention as modelsof small band gap semiconductors, and have been of re-newed recent interest due to the discovery of topologi-cal crystalline insulators.1,2 Hole-doped SnTe is also of-ten considered a model system for superconductivity ina rock-salt type small band gap semiconductor.3–8 It isknown, however, that SnTe shows very different super-conducting Tc’s when self-hole-doped (i.e. Sn1−δTe),and chemically doped (i.e. Sn1−xInxTe), to the samehole-densities.8–11 Moreover, Indium-doped SnTe main-tains the cubic rock-salt structure type up to very highIndium contents (about 50%). At such high indium lev-els, the Sn1−xInxTe system can no longer be consideredas a doped semiconductor because, at such high x, nor-mal charge balance rules based on Sn2+, In1+ and Te2−

are strongly violated; i.e. for Sn0.5In0.5Te the In contentis an order of magnitude too high for that to be a rea-sonable model for the system. These observations raisethe fundamental question: ”What is the real nature ofIndium in Sn1−xInxTe?”

Many reports on this materials system postulate thatIn1+ replaces Sn2+. This behavior has been well sup-ported experimentally up to about a 9% Indium dopinglevel and a good correlation is found between the chemi-cal In content and the experimentally observed hole car-rier densities.11 (assuming that each In1+ donates onehole to the system when substituting for Sn2+). Ithas also been reported that the superconducting Tc ofSn1−xInxTe continues to increase up to a very high levelof doping (50% of In). Unlike the case for the lowerdoping levels, however, there do not appear to be anyreports of a correlation between In content and carrierdensity in this composition regime; only Tc’s and uppercritical fields are presented. This therefore raises anotherquestion: ”If Sn1−xInxTe is the model system for hole-doping induced superconductivity in a rock salt structuresemiconductor, then does the superconducting Tc scale

with hole-density, even at high doping levels?”To test these two questions, we have revisited Indium-

doped SnTe. Our experimental investigations have re-vealed unanticipated new details of the electronic behav-ior of the system, leading us to suggest that Indium is nota trivial dopant in SnTe. Motivated by the experiments,analysis of our electronic band structure calculations in-dicates that unlike the case for other monovalent dopants,the In(s) states in Sn1−xInxTe are prevalent at the Fermilevel, supporting a resonant-level-type model in which In-dium has a mixed oxidation state in the system, i.e. thatit has partially filled 5s states and thus is neither In1+ norIn3+. Indium as a resonant level dopant has previouslybeen proposed in SnTe14–16 (along with the analogousTl-doped PbTe system12). Here we strongly support thisviewpoint - we show from both experimental studies andDFT calculations that superconducting Sn1−xInxTe can-not be viewed as a simple hole doped semiconductingmaterial.

II. EXPERIMENT AND CALCULATION

Polycrystalline samples of Sn1−xInxTe were preparedby a single step solid state reaction method, starting withultra-high purity (5N, 99.999%) elemental Sn, In andTe. The starting materials were placed in quartz glasstubes and sealed under vacuum. The tubes were heated(180 0C per hour) to 1100 0C and held at that temper-ature for about 5 hrs. They were then rapidly cooledto 850 0C, and held there about 10 hrs after which theywere again rapidly cooled to room temperature. The pu-rity and cell parameters of the samples were evaluated bypowder X-ray diffraction (PXRD) at room temperatureon a Bruker D8 FOCUS diffractometer (Cu Kα) and unitcell parameters were determined by least squares fittingof the peak positions with the MAUD program.17 Fur-ther investigation of the sample purity was done withEnergy Dispersive Spectroscopy (EDS) by using a FEIXL30 FEG-SEM system equipped with an EVEX EDS.

2

EDS studies on the In-doped samples indicated that thenominal and actual In-doping concentrations are closelymatched. Therefore, the nominal concentrations are usedthroughout this manuscript. Single crystal X-ray diffrac-tion measurements on a single crystal of Sn0.6In0.4Teextracted from the characterized polycrystalline samplewere carried out at 100 K on a Bruker Apex II diffrac-tometer with Mo radiation. Details of the data collectionand analysis are found in the supplementary informationfile.The electrical resistivities were measured using a stan-

dard four-probe method with an excitation current of10 mA; small diameter Pt wires were attached to thesamples using a conductive epoxy (Epotek H20E). Datawere collected from 300 - 0.4 K in magnetic fields up to 5T using a Quantum Design Physical Property Measure-ment System (PPMS) equipped with a 3He cryostat. HallEffect measurements were similarly made with a 4-wireconfiguration geometry, in an applied field of ± 1 T tosubtract off the possible longitudinal resistive contribu-tion. Specific heats were measured between 0.4 and 50 Kin the PPMS, using a time-relaxation method, at 0 and 5Tesla applied magnetic fields. The magnetic susceptibil-ities were measured in a DC field of 10 Oe; the sampleswere cooled down to 1.8 K in zero-field, the magneticfield was then applied, and the sample magnetization wasfollowed on heating to 6 K [zero-field-cooled (ZFC)], andthen on cooling to 1.8 K [field-cooled (FC)] in the PPMS.The electronic structure calculations were performed

by density functional theory (DFT) using the WIEN2Kcode with a full-potential linearized augmented plane-wave and local orbitals [FP-LAPW + lo] basis18–21 to-gether with the PBE parameterization22 of the GGA,with spin orbit coupling (SOC). The plane-wave cutoffparameter RMTKMAX was set to 7 and the Brillouinzone was sampled by 100 k points. Supercells were cre-ated to accommodate the dopant impurity atoms. The3% doping level was simulated with a primitive cubic unitcell, and the 12% doping level was simulated with a facecentered cubic unit cell, both with one impurity atom perunit cell, placed as a substitution on the Sn site.

III. MATERIALS CHARACTERIZATION

Fig. 1 shows the powder X-ray diffraction (PXRD) pat-terns obtained for the Sn1−xInxTe materials. The pat-terns are a good match to the NaCl-type structure ofSnTe (x = 0, Fm-3m, a = 6.32 A), with a composition-dependent unit cell parameter shift. The main panel ofFig. 1 shows that a single phase material with the cu-bic NaCl structure is maintained in the Indium dopedsamples up to a very high doping level (40%). The up-per right inset of Fig. 1 shows an expanded view of thediffraction peak near 2θ = 40 degrees. Systematic peakshifts are observed, indicating a systematic shrinking ofthe unit cell as a function of In content. This behavioris further highlighted by plotting the lattice parameter

Inte

nsity

1/2 (

arb.

u.1/2 )

807060504030

2θ (°)

Sn1-xInxTex = 0

x = 0.01

x = 0.05

x = 0.10

x = 0.20

x = 0.25

x = 0.30

x = 0.40

x = 0.15

6.32

6.30

6.28

6.26

a (Å

)

0.40.20.0x

Inte

nsity

(ar

b.u.

)

41.040.02θ (°)

x =

0

x =

0.4

0

FIG. 1. (Color online) Powder X-ray diffraction (PXRD)data for the Indium doped SnTe. Upper left inset shows sys-tematic peak shift with increasing In doping and lower leftinset shows lattice parameter variation of Sn1−xInxTe sam-ples in the range of 0 ≤ x ≤ 0.4.

variation with composition (see lower right inset of theFig. 1), which shows continuous shrinking of the unit cell.A similar shrinkage of the lattice parameter with indiumcontent was found in previous studies of Sn1−xInxTe upto the 50% doping level.10 The data support the widelyheld belief that In systematically replaces the Sn atoms inSnTe to create a single phase NaCl-type structure mate-rial. The composition dependence of the lattice parame-ter variation (see lower right inset of the Fig. 1), however,shows that

(

dadx

)

changes slope at around the 9% dopinglevel, indicating that there are changes in the system near9% In content. This structural change around 9-10 % in-dium doping is well correlated with other observations ofthe electronic properties, as described later in this paper.

Due to the extremely high In content that can be sub-stituted for Sn in SnTe, and the changes in the cellparameter vs. composition behavior described above,we considered the possibility that the crystal structureof Sn1−xInxTe for high x might not be a simple NaCltype. To maintain the charge neutrality expected forsemiconductors, for example, a highly defective mate-rial of composition Sn1−xInxTe1−(0.5x) could conceivably

3

be formed at high x. Alternatively, even if the mate-rial is essentially stoichiometric at Sn1−xInxTe, at veryhigh x values some or all of the In could be found intetrahedral interstitial positions in the rocksalt frame-work, rather than substituting on the octahedral siteoccupied by Sn, in other words the structural formulacould be [Sn(octahedral)1−xIn(tetrahedral)x]Te for highx. To test these possibilities, a very careful single crys-tal structure determination was performed on a singlecrystal of formula Sn0.6In0.4Te at 100 K. The crystal wasfound, to high precision, to have the perfect, stoichiomet-ric rocksalt structure with all ideal atomic sites fully oc-cupied and In simply substituting for Sn. Further, therewere no displacements of the atomic positions from thehigh symmetry ideal rocksalt structure positions. ThusSn1−xInxTe is structurally and chemically exactly as ithas been assumed to be in previous studies: its crystalstructure can confidently be assigned to a simple, stoi-chiometric NaCl-type. The details of the data collection,structural analysis procedure, and results can be foundin the supplementary information.

The upper right inset of Fig. 2.(a) shows the mag-netic susceptibility characterization of the superconduct-ing transitions of Sn1−xInxTe. The superconductingshielding can be observed in the zero-field-cooled (ZFC-shielding) and field-cooled (FC-Meissner) data in the fig-ure. The large volume fractions observed confirm thebulk superconductivity, and a systematic increase of su-perconducting Tc is easily observed in the high In contentrange of 20-40%. Very similar superconducting transi-tion temperature values can be observed in both resistiv-ity and magnetization data on the 20-40% Indium dopedsamples. This is a good indication of the homogeneousquality of the polycrystalline samples studied.

The main panel of Fig. 2.(a) shows the detailed anal-ysis of the lower critical field behavior for Sn0.6In0.4Te.The 40% Indium doped material is selected for this studybecause it has the highest Tc in the series of samples pre-pared here. The lower left inset of Fig. 2.(a) shows themagnetization as a function of applied magnetic field atseveral temperatures below the zero field superconduct-ing Tc. The behavior confirms the type-II superconduc-tivity. The solid line in the figure shows the fitting to

the conventional formula Hc1(T ) = Hc1(0)

[

1−(

TTc

)2]

.

The lower critical field can be extracted as Hc1(0) = 21Oe.23

The upper right inset of Fig. 2.(b) shows the resistiv-ity variation for Sn1−xInxTe. Pure SnTe shows metallic-

like behavior(

dρdT > 0

)

with p-type carrier density (1020

cm−3) (not shown here), which agrees well with previ-ously published data.9,11 The material becomes super-conducting immediately with small amounts of Indiumdoping. Our data agrees well with the data reported inthe literature. The upper right inset of Fig. 2(b) showsthat the superconducting Tc is in the 1-2 K range at lowdoping levels of Indium (x < 0.1) and increases linearly

30

25

20

15

10

5

Hc1

(Oe)

Hc1 = Hc1(0)[1-(T/Tc)2]

1.0

0.8

0.6

0.4

0.2

0.0

m0H

c2 (T

)

4.54.03.53.02.52.0T (K)

dHc2/dTc = - 0.48 T/K

-2.0

-1.5

-1.0

-0.5

0.0

4πc

v

5.04.03.02.0T (K)

x =

0.2

5

x =

0.3

0

x =

0.4

0

-16

-12

-8

-4

M (

10-3

em

u)

4020H (Oe)

2 K

4 K

1.0

0.8

0.6

0.4

0.2

0.0

ρ/ρ 5

Κ

54321T (K)

x =

0.0

5

x =

0.7

5

x =

0.1

5

x =

0.2

5

x =

0.3

5

x =

0.4

0

1.0

0.8

0.6

0.4

0.2

0.0

ρ/ρ 5

Κ

5.04.03.02.0T (K)

0.9T

0 T

(a)

(b)

FIG. 2. (Color online) (a) Lower critical field and (b) uppercritical field analysis of 40% Indium doped SnTe sample. Theupper left inset of (a) shows the magnetic susceptibility dataand the lower right inset of (a) shows the magnetization as afunction of magnetic field at temperatures below the zero fieldsuperconducting temperature. The main panel of (a) showsthe conventional fitting for determining the lower critical field.The upper inset of (b) shows the resistivity as function dop-ing and shows the resistivity as a function of temperature atdifferent applied magnetic fields. (d) shows the WHH fittingto the upper critical field values.(a) Resistivity, (b) magneticsusceptibility and (c) carrier density behavior as function oftemperature for Sn1−xInxTe.

with In content. Also, the superconducting Tc increaseslinearly as a function of doping at higher doping levels(x > 0.1). There is a very clear change in the slope ofTc vs. x that can be observed at around the 9-10% In-dium doping level. This behavior is consistent with theobserved anomaly in lattice parameter variation shownin Fig. 1.

Continuing the characterization of the superconduc-tivity for the highly doped material, the main panelof Fig. 2.(b) shows analysis of upper critical field ofSn0.6In0.4Te. The width of the superconducting tran-sition decreases systematically with increasing magneticfield (see lower left inset of Fig. 2.(b)). Selectingthe 50% normal state resistivity point as the transi-tion temperature, we estimate the orbital upper critical

4

50

40

30

20

10

0

C/T

(m

J/m

ole

K2 )

65432T (K)

Sn0.6In0.4Te

m0Η = 0 Tm0Η = 5 T

1086420

Cel

e/T

(mJ/

mol

e K2 )

4.54.03.53.0T (K)

3

2

1

0

C/T

(m

J/m

ole

K2 )

2.01.61.20.8T (K)

Sn0.95In0.05Te

m0Η = 0 T m0Η = 5 T

0.86

0.84

0.82

C/T

(mJ/

mol

e K2 )

0.80.40.0T (K)

m0Η = 5 T

3.0

2.0

1.0

0.0

Cel

e/T

(mJ/

mol

e K2 )

1.20.8T (K)

20

10

0

C/T

(mJ/

mol

e K2 )

100 T2 (K

2)

m0Η = 5 T

(a)

(b)

FIG. 3. (Color online) Heat capacity analysis of (a) 5% and(b) 40% Indium doped SnTe samples. The upper left insetsof both panels show the superconducting phase transitions inthe electronic heat capacity, and the lower right insets showthe heat capacity at 5 Tesla applied magnetic field.

field, µ0Hc2(0), from the Werthamer-Helfand-Hohenberg(WHH) expression µ0Hc2(0) = −0.693 Tc

dHc2

dT |T=Tc.

This expression is widely used to calculate the up-per critical field of a variety of superconductors in-cluding intermetallic, heavy metal and oxide based ma-terials.24–27 A very linear relationship is observed inthe main panel of Fig. 2(b) between µ0Hc2 and Tc.

The slope(

dµ0Hc2

dTc

= −0.48 T/K)

is used to calculate

µ0Hc2(0) = 1.46 T. This value of µ0Hc2(0) is smaller thanthe weak coupling Pauli paramagnetic limit µ0H

Pauli =1.82 Tc = 7.56 T for this system.

The upper critical field value µ0Hc2(0) can be used to

estimate the coherence length ξ(0) =√

Φ0/2πHc2(0) =

150 A, where Φ0 = hc2e is the magnetic flux quantum.29,30

Similarly, from the relation of Hc1(0) = φ0

4πλ2 lnλξ , we

find the magnetic penetration depth λ(0) = 5000 A.A Ginzburg-Landau parameter κ = λ

ξ = 33 is then

calculated. Using these parameters and the relationof Hc2(0)Hc1(0) = Hc(0)

2[lnκ(0) + 0.08], the ther-modynamic critical field Hc(0) was found to be 0.85mT. All the superconducting parameters determined forSn0.6In0.4Te are summarized in Table. I.Fig. 3 shows the analysis of the superconducting

transition by specific heat measurements for p-typeSn0.95In0.05Te and n-type Sn0.6In0.4Te. The main panelof Fig. 3.(a) shows C

T as a function of T for Sn0.95In0.05Te,characterizing the specific heat jump at the thermody-namic transition. This jump is completely suppressedunder a 5 T applied magnetic field. The supercon-ducting transition temperature Tc = 1.18 K is shownin the upper left inset of Fig. 3.(a), as extracted bythe standard equal area construction method. We findthat the low temperature normal state specific heat canbe well fitted with C

T = γn + βT 2, where γnT repre-sents the electronic contribution in the normal state andβT 3 describe the lattice-phonon contributions to the spe-cific heat. The solid line in the lower right inset inFig. 3.(a) shows the fitting; the electronic specific heatcoefficient γn = 0.82 mJ

mol K2 and the phonon contribution

β = 0.45 mJmol K3 are extracted from the fit. The value of

γn for this p-type superconductor is consistent with thepreviously reported values.9,11

The main panel of Fig. 3.(b) shows CT as a function of

T for Sn0.6In0.4Te, characterizing the specific heat jumpat the thermodynamic transition. This jump is com-pletely suppressed under a 5 T applied magnetic field.The superconducting transition temperature Tc = 4.2 Kis shown in the upper left inset of Fig. 3.(b), as extractedby the standard equal area construction method. Wefind that the low temperature normal state specific heatcan be well fitted with C

T = γn + βT 2, where γnT rep-resents the electronic contribution in the normal stateand βT 3 describes the phonon contribution to the spe-cific heat. The solid line in the lower right inset inFig. 3.(b) shows the fitting; the electronic specific heatcoefficient γn = 2.47 mJ

mol K2 and the phonon contribution

β = 0.97 mJmol K3 are extracted from the fit. The value

of γn for this highly In-doped n-type superconductor ismuch higher than that of the low level Indium doped p-type sample. The specific heat data are a clear indicationthat some very specific difference is present between thelow and high level Indium doped samples.The ratio ∆C

γTc

can be used to measure the strength of

the electron-phonon coupling.31 The specific heat jump∆CTc

for Sn0.95In0.05Te is about 1.2 mJmol K2 , which results

in the value of ∆Cγ Tc

of 1.45. This value is about the

same as the BCS prediction for weakly electron-phononcoupled superconductors and also agrees with previouslyreported values of low level of Indium doped samples.9,11

However, The specific heat jump ∆CTc

for the sample

of Sn0.6In0.4Te is about 4.9 mJmol K2 , which results in a

5

value of ∆Cγ Tc

of 1.98. This is higher than that of the

weak-coupling limit for conventional BCS superconduc-tors. Therefore, the results suggest that Sn0.6In0.4Te is astrongly electron−phonon coupled superconducting sys-tem. The observed values of ∆C

γ Tc

show that the low and

high doping levels of Indium in SnTe make two distincttypes of superconductors.

In a simple Debye model for the phonon contributionto the specific heat, the β1 coefficient is related to the De-bye temperature ΘD through β = nNA

125 π4RΘ−3

D , where

R = 8.314 Jmol K , n is the number of atoms per formula

unit and NA is Avogadro’s number. The calculated De-bye temperatures are thus 204 K and 162 K for 5% and40% Indium doped samples. These values of the De-bye temperatures are similar to the previously reportedvalues on chemically doped SnTe, PbTe and related sys-tems.9,12,13 An estimation of the strength of the electron-phonon coupling can be derived from the McMillan for-

mula λep =1.04+µ∗ln

ΘD

1.45Tc

(1−0.62µ∗)lnΘD

1.45Tc−1.04

. The McMillan model

contains the dimensionless electron-phonon coupling con-stant λep, which, in the Eliashberg theory, is relatedto the phonon spectrum and the density of states.32,33

This parameter λep represents the attractive interaction,while the second parameter µ∗ accounts for the screenedCoulomb repulsion. Using the Debye temperature ΘD

and the critical temperature Tc, and making the com-mon assumption that µ∗ = 0.15,32 the electron-phononcoupling constants (λep) are 0.52 and 0.79 for 5% and40% Indium doped samples. Thus, our characterizationof the superconducting transitions supports the conclu-sion that the 5% Indium doped sample can be categorizedas a weakly coupled superconductor and the 40% Indiumdoped sample can be categorized as a strongly coupledsuperconductor.

The value of γ extracted from the measured specificheat data corresponds to a normalized electronic densityof states at the Fermi energy N(EF ). The following val-ues for the density of states, 0.44 and 1.17 states/(eVf.u.) (f.u. stands for formula unit) for 5% and 40% In-dium doped samples are thus estimated from the relationγ = π3/2k2BN(EF )(1 + λep). The value of N(EF ) for the5% In-doped samples is consistent with previous reportsfor low In doping levels but N(EF ) for the 40% dopedsample is much higher, consistent with the fact that thathigher In content samples show much higher supercon-ducting Tc’s than the lower In content samples.

Fig. 4 (a, b and c) is a summary that shows the lat-tice parameter variation, carrier density variation, andsuperconducting temperature variation as a function ofIndium doping in SnTe. It can clearly be seen that thereis a change at the 9-10% Indium doping level in Fig. 4.(a)that is well correlated with the p to n type crossoverthat is seen in Fig. 4(b). At low doping levels of Indium(x < 10%) the system remains p-type, which agrees wellwith previous reports. However, when the doping levelgoes beyond a critical doping level (x = 10%), the sys-tem shows anomalous behavior of the carrier density. At

4

3

2

1

Tc

(K)

0.40.30.20.10.0x (In Doping)

Tc_RT Tc_MT Tc_RT_Ref-9 Tc_RT_Ref-10

-15

-10

-5

0

5

10

15

Car

rier

Den

sity

(1020

cm-3

)

@ 50K

Carr. Dens. from Hall data

CIn cal with In1+

CIn cal with In3+

6.32

6.30

6.28

6.26

a (Å

)

Sn1-xInxTe

Discontinuity close to 8% doping

8

4

0

-4

Car

rier

Den

sity

(1020

cm-3

)

6050403020T (K)

Sn1-xInxTe x = 0 x = 0.08 x = 0.10 x = 0.15 x = 0.30 x = 0.40

FIG. 4. (Color online) the (a) Lattice parameter variation,(b) carrier density variation and volume density of Indiumatoms in the doped system, and (c) superconducting transi-tion temperature variation, as a function of fractional indiumcontent in the cubic In-doped SnTe crystal system. The insetof (b) shows the raw data for the carrier density determinationat low T. Solid lines in all panels are guides to the eye.

higher doping levels of Indium (x > 10%), the systemchanges to n-type and the composition dependence of thecarrier density saturates quickly. This change should beconnected to some kind of Fermi surface reconstruction;the behavior is not consistent with the conventional pic-ture of hole-doping through In1+ substitution for Sn2+,which we find to be true only up to about 9% Indiumdoping. Fig. 4(b) also shows the volume density expectedby assuming that every dopant Indium atom donates ahole, or an electron, into the SnTe unit cell. In such casesthe carrier density as a function of dopant concentrationshould linearly increase in a positive direction for In1+

substitution or increase in a negative direction for In3+

substitution. However, the behavior in this system ismuch more complicated than that. In doping results inthe unexpected suppression of the p-type carrier densityat high x and, that at a very high doping level, the car-rier type changes to n-type. More detailed experimentalstudies of single crystals in this composition regime tocharacterize this crossover in more detail would be aninteresting avenue for future work.

6

TABLE I. Superconducting Parameters of the cubic p-typeand n-type Indium doped SnTe systems

.

Parameter Units Sn0.95In0.05Te Sn0.6In0.4Te

Tc K 1.18 4.2dHc2

dT|T=Tc

T K−1 -0.48

µ0Hc1(0) Oe 21

µ0Hc2(0) T 1.46

µ0HPauli T 2.23 7.81

µ0H(0) mT 0.85

ξ(0) A 150.2

λ(0) A 5000

κ(0) A 33.28

γ(0) mJ

mol K2 0.94 2.47∆CγTc

1.27 1.98

ΘD K 204 162

λep 0.52 0.79

N(EF )eVf.u.

0.44 1.17

It can be observed that the superconductivity emergesimmediately with Indium doping into SnTe Fig. 4(c).The superconducting Tc continuously increases as a func-tion of doping. However, there is a clear deviation at9-10% Indium doping level in the rate of increase ofthe superconducting temperature as a function of dop-

ing;(

dTc

dxIn

)

is higher at lower doping levels of Indium

(x < 0.1) and becomes smaller when x > 0.1. This pointof deviation around 10% Indium is well correlated withthe lattice parameter and carrier density variations.

IV. ELECTRONIC STRUCTURE

Future experimental investigation of the higher In con-tent materials will be of interest, but here we look inmore detail at the apparent complexity of the electronicsystem by performing electronic band structure studieson model materials that simulate the effects of dopingin SnTe. In order to theoretically investigate the elec-tronic structure of doped SnTe, DFT calculations wereperformed on supercells containing different levels of In,Ag, Na and Sn-vacancies; the latter dopants are con-sidered for comparison to the In case. Fig. 5 shows theelectronic band structure for 3% doped SnTe with In, Ag,Na and vacancy dopants. Quite dramatically, the Ag, Naand Sn-vacancy doped models are qualitatively very sim-ilar, with the Fermi energy about 200 meV deep in thevalence band. However, the model for the In doped ma-terial is qualitatively different. The Fermi energy is lessdeep in the valence band, and there is a new, distinctin-gap state not seen in the other calculations. The fatbands, which allow the orbital origin of this in-gap stateto be determined, show that it is due to the contribu-tions from the In 5s orbital. Further analysis shows this

band to be composed primarily of In 5s and Te 5p or-bitals. This in-gap bands cuts through the Fermi energyat multiple points, and thus contributes to the electronicproperties of the material. This already indicates an un-usual doping mechanism. While In is creating holes inthe valence band manifold, it is simultaneously creatingother electron and hole pockets through the creation ofan impurity band centered around EF .

This effect is even more pronounced at higher dopinglevels. Fig. 6 shows the electronic structures for In, Ag,Na and vacancy doped SnTe at 12 percent doping. Here,again, the Na, Ag and Sn vacancy doped compoundsare very similar, whereas the Indium doped compoundis qualitatively very different. For one, the Fermi energyis considerably deeper in the valence band for the Ag, Naand defect-doped compounds than for In. Furthermore,the same in-gap state present in the 3 percent doped cal-culation is present here. Indeed, this band traverses theentire band gap. This compound cannot be considered tobe a doped semiconductor, as artificially adding electronswill not bring the Fermi level into a band gap. Finally,the Fermi level is about the same depth in the valenceband as is seen for the 3 percent In doping level. Whilethese calculations cannot be directly compared, as the 12percent and 3 percent calculations needed different unitcell symmetries, this certainly indicates that there is anonlinear dependence of hole concentration on Indiumdoping level, at least at high doping levels. This is in-deed what is observed experimentally. In fact, as the Inimpurity band is creating its own Fermi surface, at highdoping levels, it may not be meaningful to distinguishbetween different hole concentrations, as the Fermi sur-face is now more complex than a single pocket. What isstriking is that in both cases, the In dopant is creating animpurity band that is relatively well-separated from theother bulk bands, and which is also not very dispersivein energy. This is characteristic of a resonant level typedopant, as has been discussed in the thermoelectric andrelated literature.12,14–16

The resonant aspect of this impurity state is also ap-parent in the Density of States. Fig. 7 shows the DOSfor the In, Ag, and Na doped compounds at both the 3percent and 12 percent doping levels. Again, near EF ,the Ag and Na samples resemble each other well, whilethe In one is different. The In doped compound at 3 per-cent has a small ”doublet” peak, which sits right at EF ,that is not present in the others. At 12 percent, this hasevolved into a tall, well separated peak that is bisectedby the Fermi energy. Further analysis show that both ofthese peaks have nontrivial In 5s character, along withTe 5p character. This indicates that the impurity statethat is so important in In doped SnTe appears to comefrom a hybridization of In 5s and Te 5p orbitals. Dueto the inert pair effect, it is very unusual to have 5s or6s states at the Fermi level (indeed, in SnTe the Sn 5sstates appear about 5 eV below EF ); some well-knowncompounds that do, such as K doped BaBiO3, exhibitsuperconductivity.37 It is therefore very likely that the

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hybrid state created by the In 5s and Te 5p orbitals playa significant role in the superconductivity. This wouldexplain why In doped SnTe exhibits an order of magni-tude higher Tc than self-doped SnTe, even at the samenominal hole concentration. Further calculations indi-cate that if In were also to occupy an interstitial tetra-hedral site rather than replacing an Sn atom, it wouldact as an n-type dopant while still inducing the samein-gap 5s state as seen in the previously discussed calcu-lations. This calculation was part of our motivation forthe detailed crystallographic study we performed, whichshowed that In in tetrahedral interstitial sites cannot befound in (Sn,In)Te.Finally, we note that In has been used as dopant to

achieve very high resisitivities in Pb1−xSnxTe. This isconsistent with the picture of Indium forming an in-gapstate. At very low concentrations, this state would berelatively localized, and would pin the Fermi energy tothe gap, acting as a carrier concentration buffer, muchlike Sn does in Sn:Bi2Te2Se.

34–36

V. CONCLUSION

We have shown, through experimental observationsand DFT calculations, that Indium doped SnTe can-not be thought of as a simple hole doped semiconductor.The nature of the superconductivity and the carrier typechange as a function of Indium doping, going from over-all p-type to overall n-type and from a weakly coupled to

a strongly coupled superconductor. Furthermore, the In5s states are shown by theory to be present at the Fermilevel and therefore affect the electronic properties. Giventhat Indium doped SnTe has been studied as a supercon-ducting doped topological crystalline insulator, this workindicates that the nature and influence of the In 5s statesmust be taken into account. This may also suggest thataside from allowing for insulating behavior or improvingthermoelectric performance, resonant level dopants canaffect superconducting properties. Future studies couldelucidate further the nature of resonant level doping inSnTe. It is interesting that a very simple structure typecan show both weakly and strongly coupled supercon-ductors. Therefore we also argue that the high In-doped,strongly coupled superconductor in this system is worthyof further investigation.

VI. ACKNOWLEDGMENTS

The materials synthesis and physical property char-acterization of this superconductor were supported bythe Department of Energy, division of basic energy sci-ences, Grant DE-FG02-98ER45706. The single crystalstructure determination was supported by the Gordonand Betty Moore Foundation, EPiQS initiative, grantGBMF4412, and the electronic structure calculationswere supported by the ARO MURI on topological In-sulators, grant W911NF-12-1-0461.

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FIG. 5. (Color online) calculated electronic band structure for 3% In, Ag, Na and vacancy doped SnTe. The resonant bandat EF can be observed only in the In doped case.

FIG. 6. (Color online) calculated electronic band structure for 12% In, Ag, Na and vacancy doped SnTe. The resonant bandat EF can be observed only in the In doped case.

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FIG. 7. (Color online) Density of states as a function of E-EF for (a) 3% and (b) 12% In, Ag, and Na doped SnTe systems.Vacancy doping yields a DOS that is very similar to that seen for Ag and Na doping, with vacancies being a two-hole dopantrather than a single-hole dopant.