Indium substitution effect on the topological crystalline insulator family (Pb$_{1-x}$Sn$_{x}$)$_{1-y}$In$_{y}$Te: Topological and superconducting properties

TL;DR

This study explores how indium substitution influences the structural, topological, and superconducting properties of (Pb,Sn)Te topological crystalline insulators, revealing a transition from metallic to insulating and superconducting states with increasing indium content.

Contribution

It provides new insights into the effects of indium doping on the electronic phases and topological surface states in (Pb,Sn)Te TCIs, highlighting the emergence of superconductivity.

Findings

Indium doping induces a transition from weak-metallic to insulating behavior.

Superconductivity appears at higher indium levels with Tc up to 4.7 K.

Indium modifies the bulk electronic structure, affecting topological surface states.

Abstract

Topological crystalline insulators (TCIs) have been of great interest in the area of condensed matter physics. We investigated the effect of indium substitution on the crystal structure and transport properties in the TCI system (Pb$_{1-x}$Sn$_{x}$)$_{1-y}$In$_{y}$Te. For samples with a tin concentration $x\le50\%$, the low-temperature resisitivities show a dramatic variation as a function of indium concentration: with up to ~2% indium doping the samples show weak-metallic behavior, similar to their parent compounds; with ~6% indium doping, samples have true bulk-insulating resistivity and present evidence for nontrivial topological surface states; with higher indium doping levels, superconductivity was observed, with a transition temperature, Tc, positively correlated to the indium concentration and reaching as high as 4.7 K. We address this issue from the view of bulk electronic structure modified by the indium-induced impurity level that pins the Fermi level. The current work summarizes the indium substitution effect on (Pb,Sn)Te, and discusses the topological and superconducting aspects, which can be provide guidance for future studies on this and related systems.

Figures

a). Due to the unchanged crystal structure, the crystal point group symmetries that are essential to maintain the topological surface states remain the same. Because of the difference in lattice constants of the end members (PbTe ¿ SnTe ¿ InTe)[Springer ](#bib.bib37), the lattice parameters of (Pb*1-x*Sn*x*)*1-y*In*y*Te compounds vary with $x$ and $y$. Figure 1b shows the XRD patterns of SnTe ($x=1$, $y=0$, black), Pb*0.5*Sn*0.5*Te ($x=0.5$, $y=0$, blue) and (Pb*0.5*Sn*0.5*)*0.7*In*0.3*Te ($x=0.5$, $y=0.3$, red), respectively. Compared to the parent compound SnTe, with a lattice constant $a=6.

b shows that we get a good fit to the 20-K data for the $x=0.35$, $y=0.02$ sample with $\alpha=0.37$ and $l_{\phi}=51$ nm. Moving to $T=5$ K in Fig. 3d, the low-field data can be described by keeping $\alpha$ fixed and increasing $l_{\phi}$ to 58 nm; however, the data also exhibit a large oscillation about the calculated curve for $|B|>0.2$ T. This may be due to a Landau level crossing the Fermi energy[Serbyn2014 ](#bib.bib45). Turning to the $x=0.5$, $y=0.06$ sample, the 5-K data in Fig. 3d are well described by the WAL formula for $|B|<1$ T, with $\alpha=2.25$ and $l_{\phi}=100$ nm, but at l

a shows examples of the resulting crystals (before removal from the quartz tubes).

Equations

$$\Delta G=\frac{\alpha }{\pi }\frac{e^2}{h}[\ln (B_{\varphi }/B)-\psi (\frac{1}{2}+B_{\varphi }/B)],$$

Full text

I Introduction

Topological insulators (TIs) are a class of materials that are currently the focus of considerable attention since they represent a new state of matter in which the bulk is an insulator with an ”inverted” energy gap induced by a strong spin-orbit coupling (SOC), which leads to the emergence of unusual gapless edge or surface states protected by time-reversal-symmetryHasan2010 ; Qi2011 ; Ando2013 ; Kane2011 . First discovered in two-dimensional systems, one of the simplest topological insulators is the quantum spin Hall state, in which the SOC plays the same role as the magnetic field in the quantum Hall effect. In the quantum Hall effect, the bulk conductance is zero while the edge states are conducting with current flowing in one direction around the edge of the system. Similarly, in the quantum-spin-Hall state, the bulk is still insulating while edge-state electrons with opposite spins propagate in opposite directions, consistent with time-reversal symmetry. Theoretical concepts were soon generalized to three dimensions and shown experimentally in materials such as Bi1-xSbxFu2007 . As in the 2D case, the direction of an electron’s motion along the surface of a 3D topological insulator is locked to the spin direction, which now changes continuously as a function of propagation direction, resulting in an unusual ”planar metal”. In the bulk of a TI, the electronic band structure resembles that of an ordinary band insulator, with the Fermi level falling between the conduction and valence bands. On the surface of a TI there are special states that fall within the bulk energy gap and allow surface metallic conduction. Although ordinary band insulators can also support conductive surface states: the locking of the spin and propagation directions eliminates the possibility of backscattering from nonmagnetic impurities.

The first key experiment in this field was the observation of the 2D quantum-spin-Hall effect in a quantum-well structure made by sandwiching a thin layer of mercury telluride (HgTe) between layers of mercury cadmium telluride (HgxCd1-xTe), following a theoretical predictionBernevig2006 . The first 3D TI to be probed using angle-resolved photoemission spectroscopy (ARPES) was the semiconducting alloy Bi1-xSbxHsieh2008 . Simpler versions of the 3D TI were theoretically predicted in Bi2Te3, Sb2Te3Zhang2009 and Bi2Se3Zhang2009 ; Xia2009 compounds with a large bulk gap and a gapless surface state consisting of a single Dirac cone. Later ARPES experiments indeed observed the linear dispersion relation of these surface statesXia2009 ; Chen2009 . These discoveries confirmed the ubiquitous existence in nature of this new topological state.

In 2011, the notion of ”topological crystalline insulators (TCIs)” was introduced to extend the topological classification of band structures to include certain crystal point group symmetriesFu2011 . This new state of matter features metallic surface states with quadratic band dispersion on high symmetry crystal surfaces, and it was shown that such a situation is realized in an insulating crystal having rocksalt structure. It has caused quite a sensation since the first example, SnTe, has been theoreticallyHsieh2012 and experimentallyTanaka2012 confirmed to exhibit topological surface states in ¡001¿, ¡110¿ and ¡111¿ surfaces. Soon after this discovery, the topological surface state in the Pb-doped Pb1-xSnxTe and Pb1-xSnxSe have been verified by ARPES and Landau level spectroscopy using scanning tunneling microscopy and spectroscopyDziawa2012 ; Xu2012 ; Yan2014 , thus expanding the range of relevant materials. Alongside SnTe and the related alloys Pb1-xSnxSe/Te, other chalcogenides such as SnS and SnSe that incorporate lighter elements have also been predicted to be TCIs even without the SOCSun2013 . In theory, by applying external pressure, normal IV-VI rocksalt chalcogenides can be tuned into TCIsBarone2013 . Besides the materials with rocksalt crystal structure, Hsieh $et.al.$ predicted that the antiperovskite family are also promising materials for exploring the topological and other related propertiesHsieh2014 . More recently, a new phase of Bi is stablized by strain, has been found to be a TCI based on mirror symmetry, similar to SnTeMunoz2016 .

The discovery of TIs and TCIs has also stimulated the search for topological superconductors (TSCs), whose surfaces should exhibit Majorana fermionsQi2011 . Superconductors derived from TIs by doping have been considered as TSC candidates, such as CuxBi2Se3Fu2010odd ; Hor2010sc . Since the topological surface states are protected from backscattering by disorder, it should be safe to tune the chemical potential through chemical substitution. The ARPES studies performed on Sn1-xInxTe (SIT) at $x$ = 0.045 confirmed that the topological surface states remain intact after In dopingSato2013 . In fact, SnTe becomes a superconductor upon substituting 2% or more of Sn with In, which introduces hole carriersErickson2009 ; Balakrishnan2013 ; Zhong2013 ; Novak2013 . Similarly, doping the TCI Pb0.5Sn0.5Te with ¿ 10% indium also induces superconductivityZhong2014 . This spurs interest in searching for the superconducting analogue, a time-reversal-invariant topological superconductor (TSC), in this system. Point-contact spectroscopy experiments performed on SIT with varies In concentrations found that a zero-bias conductance peak is observed only in the cleanest samples with $x\approx$ 0.04, suggesting that there is competition between topological and non-topological superconducting states, and that disorder may determine the outcomeNovak2013 .

A challenge for characterizing the transport properties of surface states in TI/TCI materials such as Bi2Se3 and SnTe is the dominance of a pronounced bulk conductanceSkinner2012 ; Butch2010 . Despite considerable efforts to reduce the bulk carrier density, such as modifying crystal growth methodJia2011 , reducing sample thicknessPeng2009 and chemical counterdopingHor2009 ; Analytis2010 ; Checkelsky2011 , the bulk conduction has proved difficult to suppress. Inspired by the goal of finding truly bulk-insulating topological materials, we have found that indium doping the TCI materials (Pb,Sn)Te can yield a huge bulk resistivity while maintaining topological surface statesZhong2015 .

In this article, we present a review of the effects of indium substitution on the crystal structure, resistivity behavior, and electronic band structure in the TCI family (Pb1-xSnx)1-yInyTe (PSIT). By varying the indium concentration, samples show an extreme range of low-temperature resistivities: with a few percent indium doping, the samples show weak-metallic behavior; with $\sim$6% indium doping, samples have true bulk-insulating resistivity and present evidence for nontrivial topological surface states; with higher indium doping levels, superconductivity with a transition temperature $T_{c}$ positively correlated to the indium concentration was observed. We consider this behavior from the standpoint of the localized impurity states associated with the indium dopants.

II Results

II.1 Crystal structure

SnTe is a IV-VI semiconductor that crystallizes in the cubic rocksalt structure at room temperature, and maintains this structure after a certain degree of substitution of Sn with Pb and/or In (Figure 1a). Due to the unchanged crystal structure, the crystal point group symmetries that are essential to maintain the topological surface states remain the same. Because of the difference in lattice constants of the end members (PbTe ¿ SnTe ¿ InTe)Springer , the lattice parameters of (Pb1-xSnx)1-yInyTe  compounds vary with $x$ and $y$. Figure 1b shows the XRD patterns of SnTe ($x=1$, $y=0$, black), Pb0.5Sn0.5Te ($x=0.5$, $y=0$, blue) and (Pb0.5Sn0.5)0.7In0.3Te ($x=0.5$, $y=0.3$, red), respectively. Compared to the parent compound SnTe, with a lattice constant $a=6.32$ Å, Pb-doping increases the lattice constant ($a=6.39$ Å for Pb0.5Sn0.5Te). Subsequent In-doping can then decrease the lattice constant ($a=6.36$ Å for (Pb0.5Sn0.5)0.7In0.3Te). Similarly, a systematic shrinking of the unit cell as a function of In content has been observed in previous studies of SITZhong2013 ; Haldo2016 . The measured lattice parameters listed on the figure for the various compositions are qualitatively consistent with Vegard’s law and the differences in radii of the ionic components. With more Sn or Pb atoms being replaced by In, the distortion of the crystal structure gets larger, and eventually the solubility limit is reached, indicated by the appearance of the secondary phase InTe.

Common tools to characterize the surface states include angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). To apply these techiques, one typically needs atomically-flat and well-oriented surfaces. For the topological insulator Bi2Se3, this is not be a problem, since it can be easily cleaved due to weak coupling between its layers. In the case of SnTe related compounds, however, the situation is more challenging due to their isotropic cubic structures. To illustrate, Figures 1c-1e show microscope photos of pristine surfaces. The flat, shiny planes are cleaved surfaces, and they become smaller with increasing Pb/In substitution. Thus, it appears that substitution of Pb or In atoms introduces lattice distortion and leads to smaller cleaved surfaces for surface-sensitive studies. STM studies of SIT single crystal samples have been successfully performedSato2013 , as discussed in Sec. 2.5. Direct ARPES studies of PSIT single crystals are few, and it has proved more practical to perform measurements on thin films evaporated from previously characterized bulk samplesDu2015 ; Zhong2015 .

II.2 Resistivity behaviors of In-doped Pb1-xSnxTe

The evolution of the electronic properties with composition have been investigated through transport measurements. Here we take (Pb0.5Sn0.5)1-yInyTe as an example to illustrate the effect of indium substitution. As shown in Figure 2, pure Pb0.5Sn0.5Te shows a metallic-like behavior with a $p$-type carrier density similar to SnTe. By introducing increasing amounts of indium into the Pb0.5Sn0.5Te system, single crystal samples show quite divergent, nonmonotonic variations in resistivity in the normal state. For the samples with one percent or less indium, the resistivity is weakly metallic, just like the resistivity behavior of pure SnTeZhong2013 or Pb1-xSnxTe without indium dopingDixon1968 . Increasing $y$ to 0.06, we observe that the resistivity at 10 K rises by five orders of magnitude. With further increases of $y$, the resistivity drops, but remains semiconducting, consistent with earlier studiesZhong2014 ; Vul1978 ; Kozub2006 ; Shamshur2008 . This resistivity behavior in the normal state is quite different from the case of In doped SnTeZhong2013 , where all samples are weakly metallic in the normal sate. At low temperature, samples show true bulk-insulating resistivity and and present evidence for nontrivial topological surface statesZhong2015 . With higher indium doping levels, superconductivity with a transition temperature $T_{c}$ positively correlated to the indium concentration was observed, and the highest $T_{c}$, $\sim 4.7$ K, was achieved for 45% indium doped SnTe samples Zhong2013 ; Balakrishnan2013 and 30% indium doped Pb0.5Sn0.5Te samples Zhong2015 .

The effect of indium substitution is similar for other (Pb,Sn)Te compositions. Nonmonotonic variation in the normal-state resistivity with $y$ is also found in transport measurements of PSIT for many series with different $x$ values. Specifically, $x$=0.5 is not the only system that shows large bulk resistance when doped with a low concentration of indium. In the whole family of (Pb1-xSnx)1-yInyTe, maximum resistivities that surpass 10${}^{6}\ \Omega$cm are observed for $x$=0.25-0.30. Even for $x$=0.35, doping with 6% In results in a rise in resistivity by 6 orders of magnitude at low temperature. These phenomena can be well explained in a picture where the chemical potential is pinned within the band gap, which will be discussed in detail in a later section.

A common test of the topological character of surface states involves measurements of magnetoresistance (MR) at low temperatureBansal2012 . The symmetry-protected coupling of spin and momentum for surface states makes them immune to weak localization effects. Application of a transverse magnetic field breaks time-reversal symmetrySerbyn2014 , thus removing the topological protection and leading to a field-induced increase in resistance. Figure 3a shows data for $\Delta R=R(B)-R(0)$ measured at several temperatures for a magnetic induction $|B|\leq 7$ T applied perpendicular to the $(001)$ surface of the (Pb0.65Sn0.35)0.98In0.02Te sample. At temperatures of 30 K and below, the field dependence of the induced resistance has a form qualitatively consistent with that expected for weak anti-localization (WAL) of two-dimensional electron states.The MR curve at 5K (black) clearly shows a cusp near zero field, which is a sign of the WAL effect and suggests the dominance of topological surface states. At elevated temperature, the cusp disappears, and the curves in the low-field regime (not shown) are dominated by the parabolic $B$-dependence of the bulk statesAkiyama2014 ; Kim2011WAL , which is a reflection of the bulk carriers under a Lorentz force in a perpendicular field. The magnitude of the MR changes monotonically with temperature, a fact that needs further study to fully understand.

In order to clarify the nature of surface states in samples with different compositions, in Fig. 3b, 3c we compare the MR behavior at 5 K between (Pb0.8Sn0.2)0.94In0.06Te (red), (Pb0.65Sn0.35)0.98In0.02Te (black), and (Pb0.5Sn0.5)0.94In0.06Te (blue). In the low-field regime, the $x$=0.35 sample clearly shows a WAL effect even with a few percent indium, which is consistent with the ARPES evidence that the topological surface states of In-doped SnTe are maintained when In doping concentration is roughly 4.5%Sato2013 . To be more quantitative, we convert the data to conductance, $G$, and compare with the theoretical formula for WALHikami1980 ,

[TABLE]

where $\psi$ is the digamma function and $\alpha$ is a number equal to $1/2$ times the number of conduction channels; $B_{\phi}=\Phi_{0}/(8\pi l_{\phi}^{2})$, with $\Phi_{0}=h/e$ and $l_{\phi}$ being the electronic phase coherence length. For our system, one expects four Dirac cones crossing the Fermi surfaceSerbyn2014 ; Assaf2014 , which would give $\alpha=2$. Figure 3b shows that we get a good fit to the 20-K data for the $x=0.35$, $y=0.02$ sample with $\alpha=0.37$ and $l_{\phi}=51$ nm. Moving to $T=5$ K in Fig. 3d, the low-field data can be described by keeping $\alpha$ fixed and increasing $l_{\phi}$ to 58 nm; however, the data also exhibit a large oscillation about the calculated curve for $|B|>0.2$ T. This may be due to a Landau level crossing the Fermi energySerbyn2014 . Turning to the $x=0.5$, $y=0.06$ sample, the 5-K data in Fig. 3d are well described by the WAL formula for $|B|<1$ T, with $\alpha=2.25$ and $l_{\phi}=100$ nm, but at larger $|B|$ we need an additional component that varies as $-B^{2}$. The latter contribution might come from bulk states.

II.3 Phase diagram

To summarize the effect of indium substitution on PSIT materials, we present in Fig. 4, a ternary phase diagram of the system to illustrate trends for several properties: the character of the low-temperature resistivity (metallic, insulating, superconducting) and the solubility limit. Here, the end members are SnTe, PbTe, and InTe. The closer to the end member, the higher concentration of that component. Each of the six dashed lines starting with the same end member InTe represent a series of PSIT with the fixed Sn:Pb ratios, as labeled by $x$.

For low indium doping (blue region), samples show weak metallic resistivity, as in SnTe. A few percent indium doping turns the Pb1-xSnxTe samples into true insulators (orange region). By increasing the In content further, superconductivity may be achieved (green region). When the indium content exceeds the solubility limit in the system (marked with white crosses), where additional In is no longer simply substituting for Pb/Sn, an impurity phase of InTe, with a tetragonal crystal structure, appears and the samples are no longer single crystals. The critical In concentrations that divide these various regions are illustrated with dashed lines.

From the resistivity behavior in the phase diagram, it can be seen that the In substitution effect shows consistent trends. Superconductivity emerges almost immediately with indium doping in SnTe. In Pb1-xSnxTe, though, with increasing Pb content the amount of In needed to induce superconductivity goes up, and the range of superconductivity with respect to In-doping shrinks. Meanwhile, the bulk insulating region is broadens with increased Pb, and the maximum bulk resisitvity that can be achieved in the PSIT family is found in the $x$=0.30 and $x$=0.25 seriesZhong2015 . Those materials along with previous reported bulk insulating TIs Sn-Bi1.1Sb0.9Te2SKushwaha2016 could provide good platforms to study the true topological ’insulators’, in which bulk conduction would not dominate the transport behavior, assuming that their surface states remain topological.

II.4 Bulk band structure

To address the divergent resistivity behaviors, it is helpful to consider the bulk electronic structure. SnTe and other IV-VI materials with the rocksalt structure have long attracted attention as a model for small band gap semiconductors. The topologically distinct band structure of SnTe (nontrivial, $x$ = 1) and PbTe (trivial, $x$ = 0) involves a change in the ordering of the conduction and valence bands at $L$ points. This implies that the band gap of the alloy Pb1-xSnxTe first closes and then re-opens as $x$ increases, as shown in Fig. 5Ravich2002 ; Kaidanov1985 ; Pankratov1987 . It follows that there must be a topological quantum phase transition upon varying the Pb/Sn ratio in Pb1-xSnxTe, and experiments indicate that it occurs near $x_{c}\approx 0.35$ at low temperatureDimmock1966 ; Kaidanov1985 ; Pankratov1987 ; Gao2008 ; Xu2012 ; Tanaka2013 .

Generally, it is believed that each In dopant will provide one less valence electron than Sn2+ and Pb2+, so that indium should be considered as a $p$-type dopant. In the case of SnTe, one begins with a $p$-type semiconductor due to Sn vacancies. With In doping, the number of cation vacancies decreases, which partially compensates the expected impact of the In; nevertheless, the $p$-type carrier density initially grows with increasing In concentration Zhang2013_SnTe ; Novak2013 . The situation becomes more complicates for an Indium concentration above 10%, where the sign of the Hall resistivity changes Haldo2016 , suggesting the possibility that two types of carriers are simultaneously present. In fact, in indium doped PbTe and Pb1-xSnxTe, In-doping results in far less than 1 electron per impurity atom, which suggests In doping also introduces an impurity band that causes the effect of pinning the Fermi levelBushmarina1991 ; Heremans2012 . Evidence for the quasi-localized character of indium-induced states has been provided by a recent nuclear magnetic resonance study on Sn0.9In0.1TeMaeda2017 .

In this scenario, the large bulk resistivity in series with $x=0.25-0.35$ is a consequence of indium sites introducing localized impurity states that pin the chemical potentialKaidanov1985 ; Ravich2002 ; the electronic properties then depend on the position and width of the indium level. In the region of compositions where the localized impurity band lies in the band gap, or a position that is very close to the band edge, the free carrier concentration is extremely low at low temperature, which is reflected in the very large bulk resistivities for $x\sim 0.30$ that we observe in the transport measurements.

According to the schematic evolution of the band structure of Pb1-xSnxTe and the energy of the In impurity level in Fig. 5, the chemical potential sits in the valence band on the Sn side, consistent with $p$-type metallic behavior, while it moves to the conduction band on the Pb-rich side. With a very small amount of indium doping on the Pb-rich side, the opposing trends of decreasing cation vacancies and increasing In-substitution initially lower the carrier density, leaving the system weakly metallic. With further increases in In content, the Fermi level drops into the band gap, where it gets pinned by the impurity state level. The magnitude of the resistivity will then depend largely on the size of the band gap, which is determined by the Sn content, $x$, instead of the indium content, $y$Ravich2002 . Figure 6 gives a summary of the variation in resistivity as a function of $x$ in PSIT compounds with either 3% or 6% indium doping. The same trends are found as a function of $x$, although the low-temperature resistivities tend to be higher for $y=0.06$.

It is worth mentioning that a long relaxation time was observed in the bulk resistance for several samples, especially those that are truly bulk insulators, i.e. $x=0.25$, 0.30, 0.35. After a sample was quenched down to low temperature (liquid-helium), its resistivity gradually decreased with time. This relaxation phenomenon can last for days until the resistivity reaches a stable value. Previous studies on Pb1-xSnxTe doped with group-III elements revealed similar time-dependent behavior, and it was explained in terms of the interaction between the crystal lattice and the non-equilibrium electron densities associated with the pinned chemical potential at the impurity levelKaidanov1985 .

II.5 Debate on topological superconductivity

At higher indium content (¿10%), superconductivity emerges in Pb1-xSnxTe samples, with a typical superconducting transition temperature in the range of 3 to 5 K. There are intriguing questions about the nature of the superconductivity: is it conventional BCS superconductivity, or unconventional topological superconductivity? Topological superconductors are accompanied by gapless states at the edge or surface, which characterize the nontrivial topology of the bulk state and they may be composed of Majorana fermions Qi2009 ; Qi2010 .

The first plausible example of TSC (associated with TI or TCI compounds) was CuxBi2Se3Fu2010odd . Experimental evidence from point-contact spectroscopySasaki2011 ; Kirzhner2012 showing zero-bias conductance peaks coexisting with a superconducting gap may be indicative of the unconventional superconductivity, which is necessary (but not sufficient) for TSC in inversion symmetric, time-reversal-invariant superconductors. Similarly, results for In-doped SnTe from both point-contact spectroscopy and high-resolution ARPES studies have been interpreted as evidence for odd-parity pairing and topological superconductivity Sasaki2012 ; Sato2013 .

A markedly different conclusion was drawn, however, in an STM study on Cu0.2Bi2Se3Levy2013 , which reported a superconducting gap without any zero bias anomalies. Later studies on the optimally doped TCI system SIT using thermal conductivityHe2013 , magnetization and muon-spin rotation ($\mu$SR) measurementsSaghir2014 also supported the conclusion that SIT has a ful superconducting gap in the bulk, and is more likely to be a conventional $s$-wave superconductor. Similarly, STM measurementsDu2015 of the superconducting state as well as the superconducting energy gap in (Pb0.5Sn0.5)0.7In0.3Te on the high-symmetry (001) surface lead to the same conclusion, that the superconducting sample seems to be fully gapped without any in-gap states, contrary to the expectations for a topological superconductor.

These controversies may be due to the complexity of the junctions in point contact measurements, since the spectra that are indicative of an unconventional superconductor can also be interpreted by other mechanismsKirzhner2012 ; Du2015 . On the other hand, the observed fully-gapped tunneling spectra in STM measurements on CuxBi2Se3 and SIT can be also explained by the results of exotic pairing states with additional parametersLevy2013 . In addition, in TCI compounds where the exotic surface states only exist on certain high-symmetry planes guaranteed by the mirror symmetry, the possibility of topological superconductivity feature cannot be ruled out from studies of the (001) plane alone Du2015 . Besides, due to the poor cleavability cubic (Pb1-xSnx)1-yInyTe, it might be tricky to expose the desired surface for surface-sensitive measurements.

The debate on topological superconductivity has recently been reinvigorated by a nuclear magnetic resonance study of Cu0.3Bi2Se3 Matano2016 . There the authors find clear evidence for a breaking of the spin-rotation symmetry in the superconducting state, consistent with spin-triplet pairing. This will surely motivated further investigations.

III Discussion

In recent years, In-doped SnTe and Pb1-xSnxTe have been studied extensively both as examples of topological crystalline insulators and potentially-interesting superconductors. Our study of a broad range of compositions in the PSIT system shows that indium doping has a nonmonotonic effect on the electronic properties, which can be explained from the standpoint of the relative location of the indium-induced impurity band and the bulk band structure. In this article we have presented a summary which recaps our findings and conclusions, which can be instructive for future work on this system.

In the effort of looking for a new topological superconductor, Tl5Te3 has been found to be tunable between superconducting and topological surface states by Sn-substitutionArpino2014 ; Arpino2015 , which is quite similar to the In-substitution effect on the Pb1-xSnxTe system. These facts may imply that the topological surface states and the bulk superconductivity are two competing parameters. The goal of mixing the superconducting and topological characters remains a challenge.

A plausible strategy of looking for Majorana fermions is to artificially construct topological insulator/conventional superconductor heterostructures and make of use the superconducting proximity effectFu2008 ; Wang2012 ; Wang2013 ; Xu2014 ; Li2014 ; Xu2015 . Both SIT and PSIT would be perfect platforms for this purpose, since these systems undergo a continuous change from a TCI to a (likely conventional) superconductor. More specifically, the large bulk resistivity shows up in (Pb1-xSnx)1-yInyTe with $x=0.25$–0.5, a $p$-type matrix can be realized in series the with $x=0.35$–1.0, and superconductivity can also be realized in the latter compounds, which makes this system quite promising for exploitation in heterostructures.

IV Experimental Section

IV.1 Sample preparation.

In the Pb-Sn-In-Te alloy system, several elemental metals or compounds are found to be superconducting near liquid-helium temperatures, as indicated in Fig. 7. To investigate the indium substitution effect on the (Pb,Sn)Te system, compounds with the composition in the area of the red triangle have been grown and carefully studied in this work. Single crystal samples with nominal composition, (Pb1-xSnx)1-yInyTe ($x_{norm}$=0.2-0.5, 1.0, $y_{norm}$=0-0.5), were prepared via the vertical Bridgman method. Stoichiometric mixtures of high-purity (99.999%) elements were sealed in double-walled evacuated quartz ampoules. The ampoules were set in a vertical position, heated at 950∘C in a three-zone vertical box furnace, with rocking to achieve homogeneous mixing of the ingredients. The crystal growth took place via slow cooling from 950 to 760 ∘C at the rate of 1.5 ∘C/hr, and then the samples were gradually cooled down to room temperature over another 3 daysZhong2013 . Figure 8a shows examples of the resulting crystals (before removal from the quartz tubes).

For a few compositions, where we needed large crystals for ARPES measurements, we used the modified floating-zone method. In the normal traveling-solvent floating-zone (TSFZ) method, a polycrystalline rod is prepared as feed rod and seed rod, fixed at the upper or lower shaft of the furnace. During the growth, the molten zone is not in contact with any container. However, elements such as indium and tin easily evaporate and are reactive when heated to high temperature. Therefore, we used the modified TSFZ method, as explained in detail in our earlier publicationZhong2014 , where the starting material, prepared in the vertical Bridgman method, was sealed in a long quartz tube ($\sim$15 cm) and mounted at the bottom shaft in the floating zone furnace. The space inside the large glass chamber surrounding the quartz tube was filled with high-purity Ar at 1 bar to avoid oxygen diffusion through the quartz. During the growth the rotating shaft kept moving downwards at a velocity of 0.5-1 $mm/hr$, so that the new crystal gradually grew from the bottom of the starting ingot, resulting in a sample such as that shown in Fig. 8b.

For each sample used in the magnetization, transport and other measurements, the chemical composition was characterized using energy-dispersive X-ray spectroscopy (EDS). In this article, chemical composition values $x$ and $y$ correspond to the measured concentrations.

IV.2 Sample characterizations.

To identify the room-temperature crystal structure, each sample was characterized by X-ray powder diffraction (XRD) measured with Cu $K\alpha$ radiation from a model Rigaku Miniflex II. Microstructure and chemical composition of the samples were carefully investigated by an analytical high-resolution scanning electron microscope (SEM) equipped for EDS, model JEOL 7600F, located at the Center for Functional Nanomaterials (CFN) at Brookhaven National Laboratory. For each crystal piece, EDS was measured at 10 positions and the mean value was taken to characterize the sample. These measured $x$ and $y$ values agreed within the measurement uncertainty ($\pm$0.02), and the measured values are used throughout this article. Typical microstructure pictures of the PSIT cleaved surfaces were taken by optical microscope.

To study the effect of indium substitution on the magnetic properties, dc magnetic susceptibility measurements were performed using a commercial superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design), for temperatures down to 1.75 K. The sample pieces were cut into an approximately cubic shape, typically weighing 0.1 g.

For transport measurements, thin bar-like samples with typical dimensions of $4\times 1.5\times 0.5$ mm3 were cut from the bulk crystal and then polished. Electrical resistance was measured in the standard four-probe configuration, using gold wires and room-temperature-cured, fast-drying silver paint for the ohmic contacts on top side, and performed with a Keithley digital multimeter (model 2001), using the MPMS for temperature control. Measurement errors due to the contact geometry are estimated to be less than 10%.

Acknowledgements.

Work at Brookhaven National Laboratory is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-SC0012704; use of facilities at the Center for Functional Nanomaterials was supported by the Office of Basic Energy Sciences, Division of Scientific User Facilities. W. K. acknowledges support from National Natural Science Foundation of China #11674220 and 11447601, and Ministry of Science and Technology #2016YFA0300500 and 2016YFA0300501..