Type-I superconductivity in PdTe 2 probed by μ SR
Huaqian Leng, Jean-Christophe Orain, Alex Amato, Yingkai Huang, Anne de Visser
TType-I superconductivity in PdTe probed by µ SR H. Leng, ∗ J.-C. Orain, A. Amato, Y. K. Huang, and A. de Visser † Van der Waals - Zeeman Institute, University of Amsterdam,Science Park 904, 1098 XH Amsterdam, The Netherlands Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland (Dated: October 17, 2019)The Dirac semimetal PdTe was recently reported to be a type-I superconductor with T c =1 .
64 K and a critical field µ H c = 13 . N , the intermediate state forms in applied fields (1 − N ) H c < H a < H c . We have carriedout transverse field muon spin rotation measurements on a thin disk-like crystal with the fieldperpendicular to ( N ⊥ = 0 .
86) and in the plane ( N (cid:107) = 0 .
08) of the disk. By analysing the µ SR signalwe find that the volume fraction of the normal domains grows quasi-linearly with applied field atthe expense of the Meissner domain fraction. This then provides solid evidence for the intermediatestate and type-I superconductivity in the bulk of PdTe . I. INTRODUCTION
The large family of layered transition metal dichalco-genides is extensively studied because of their fascinatingelectronic properties. One of the modern-day researchinterests is a non-trivial nature of the electronic bandstructure, which may result in topology driven quan-tum states. Density functional calculations show, forinstance, that selected transition metal dichalcogenideshost generic three-dimensional type-II Dirac fermionstates . In a type-II Dirac semimetal the Dirac cone,which embodies the linear energy dispersion, is tilted,and the Hamiltonian breaks Lorentz invariance . Herewe focus on the exemplary material PdTe . Extensiveelectronic structure calculations combined with angle re-solved photoemmission spectroscopy (ARPES) demon-strate a type-II Dirac semimetallic state with the Diracpoint at ∼ . . Anotherinteresting property of PdTe is that it superconductsbelow T c = 1 . . In a type-II Dirac semimetal theDirac point is the touching point of the electron and holepockets and a nearly flat band may form near the Fermilevel. This could promote superconductivity, which inturn prompts the question whether superconductivityhas a topological nature .In a recent paper Leng et al. reported a magneticand transport study on single crystalline PdTe and con-cluded superconductivity shows type-I behavior. Thisresult is surprising, because binary compounds when su-perconducting exhibit in general type-II behavior. Untiltoday this rare phenomenon has been documented con-vincingly for about a dozen binary or ternary compoundsonly (see Ref. 11). In the case of PdTe evidence for type-I behavior is provided by ( i ) the dc-magnetization curvesas function of the applied field, M ( H a ), that show thepresence of the intermediate state between (1 − N ) H c 2, the boundaryvalue for type-I and type-II behavior. The supercon-ducting phase has further been characterized by heat ca-pacity , scannning tunneling microscopy/spectroscopy(STM/STS) , and magnetic penetration depth mea-surements . The specific heat data confirm conven-tional weak-coupling Bardeen-Cooper- Schrieffer super-conductivity with a ratio ∆ c/γT c ≈ . 52, which is closeto the weak-coupling value 1.43. Here ∆ c is the size ofthe step in the specific heat at T c and γ the Sommerfeldcoefficient. The STM/STS spectra taken in zero mag-netic field point to a fully-gapped superconducting state,without any in-gap states. Finally, the magnetic pene-tration depth, λ ( T ), shows an exponential temperaturevariation for T /T c < . . First of all,ac-susceptibility measurements in a small driving fieldhave revealed large screening signals in applied dc-fields H a > H c (Ref. 10) (here H a is directed along the a -axis). This has been attributed to superconductivity ofthe surface sheath . Screening persists up to the criticalfield µ H Sc ( T → 0) = 34 . H c = 2 . × κH c (Ref. 17).In fact when κ < . H c < H c and Saint-James -de Gennes surface superconductivity should not occur.This opens up the possibility that superconductivity ofthe surface layer has a different nature and originatesfrom the topological surface states that were detectedby ARPES . Another striking feature is that elec-trical resistance measurements reveal superconductivityto survive up to fields that are much higher, typically µ H Rc (0) = 0 . (cid:29) µ H Sc (0) > µ H c (0) (Ref.10). The a r X i v : . [ c ond - m a t . s t r- e l ] O c t resulting complex phase diagram in the H − T planeshows some similarities with the diagrams reported forthe superconductors LaRhSi and ZrB . However,in these cases the unusual diagram is attributed to a field-induced change from type-I to type-II superconductivitybelow a conversion temperature T ∗ < T c . These ma-terials are called type-II/1 superconductors, and have a κ -value close to 1/ √ et al. have in-vestigated the closure of the gap for a field along the c -axis at T /T c = 0 . 23 and find that the superconduct-ing gap predominantly is suppressed at a critical field µ H c (0) ≈ 25 mT. However, they also find regions onthe surface of the crystal where significantly larger fieldsare required to suppress superconductivity, typically inthe range 1-4 T. These STM/STS results were taken astep further by Sirohi et al. who reported a distinctbehavior in the spectra taken in the low and high H c regions. They concluded that the observed spatial distri-bution of critical fields is due to mixed type-I and type-II superconducting behavior, which in turn stems fromelectronic inhomogeneities visible in the spectra in thenormal state. A third STM/STS characterization wascarried out by Clark et al . Since these authors observea vortex core in a field of 7 mT they claim PdTe is atype-II superconductor, and report an upper field criticalfield µ H c = 20 mT. We remark, that in the STM/STSwork reported so far, evidence of an Abrikosov vortexlattice has not been produced. More recently, mechani-cal and soft point contact spectroscopy (PCS) data werealso taken as evidence for mixed type-I and type-I su-perconductivity on the surface . A possible issue in allthese experiments is that the applied field was directedperpendicular to a flat crystal, which involves a largedemagnetization factor and the formation of the field-induced intermediate state. This possibility has not beenaddressed in the aforementioned STM/STS papers.These conflicting results warrant the investigation ofthe superconducting phase of PdTe on the microscopicscale. For this the µ SR technique is extremely well suited,because it is a local probe which permits to determinewhether regions with distinct magnetic properties arepresent in the crystal . µ SR is also a well-establishedtechnique to measure the penetration depth of type-II su-perconductors . In the transverse field configuration theprecession of the muon ( µ + ) spin is damped by the localfield distribution of the vortex lattice. From the resultingGaussian damping rate, σ ( T ), the magnetic penetrationdepth, λ ( T ), can be derived. In a type-I superconduc-tor in the Meissner phase, the application of a transversefield will not give rise to precession of the µ + spin becausethe magnetic induction in the crystal is zero. However,for applied fields larger than (1 − N ) H c the intermediatestate is generated and a macroscopic phase separation oc-curs in Meissner and normal state domains. The field inthe normal regions is equal to the critical field H c . Con-sequently, µ + spin precession will occur in the normal- phase fraction of the crystal. By fitting the µ SR signalwith the appropriate muon depolarization function, onecan determine the Meissner and normal phase fractionsin the crystal.Although a powerful technique, µ SR on type-I super-conductors has not been explored in much detail. Stud-ies of the intermediate state in elemental superconduc-tors are scarce and concise . The most recent workby Karl et al. (Ref. 31), however, presents a compre-hensive review of the technique and an in-depth anal-ysis of the µ SR signal in the intermediate phase ofa β -Sn sample. Binary and ternary compounds thathave been scrutinized for type-I superconductivity in-clude LaNiSn , LaRhSi , LaIrSi , LaPdSi , andvery recently AuBe .Here we report transverse field muon spin rotationmeasurements in the superconducting phase of PdTe .Experiments were performed on a thin disk-like crystalin two configurations: ( i ) with the field perpendicularto the plane of the disk ( N ⊥ = 0 . 86) and ( ii ) with thefield in the plane of the disk ( N (cid:107) = 0 . µ SR signal we find that the nor-mal phase volume fraction grows quasi-linearly with ap-plied field at the expense of the Meissner phase fraction.This provides solid evidence for the intermediate stateand type-I superconductivity in the bulk of our PdTe crystal. II. EXPERIMENT The PdTe crystal used for the µ SR experiment wastaken from a single-crystalline boule prepared by themodified Bridgman technique . Its single-crystalline na-ture was checked by Laue backscattering. Powder X-raydiffraction confirmed the trigonal CdI structure (space-group P ¯3 m . TheMeissner volume fraction for a bar-shaped crystal cutalong the a -axis, and H a (cid:107) a , amounts to 93% after cor-recting for demagnetization effects . The crystal usedin the present experiment is cut from the same regionof the single-crystalline boule and has a disk-like shape,with the c -axis perpendicular to the plane of the disk. Itsthickness equals 0.65 mm and the diameter is 10.0 mm.However, a small piece was removed and cut from thedisk along the a -axis, which reduced the size in the per-pendicular a ∗ -direction ( ⊥ a ) to 6.8 mm. This causesadditional field inhomogeneities near the edges of thesample, notably for the configuration with the field inthe plane of the disk. It also thwarts a precise calcu-lation of the demagnetization factors. With appropriateapproximations of the sample shape the estimated valuesare N ⊥ = 0 . ± . 02 and N (cid:107) = 0 . ± . . Thesevalues have been calculated for a completely diamagneticstate, χ = − µ SR spectra were taken in thetemperature range T = 0 . − ∼ 55 mm .Muon spin rotation ( µ SR) experiments were carriedout with the Multi Purpose Surface Muon InstrumentDOLLY installed at the π E1 beamline at the S µ S facilityof the Paul Scherrer Institute. The technique employsthe decay probability of spin-polarized muons that areimplanted in the crystal. In the case of PdTe (den-sity 8.3 g/cm ) the muons typically penetrate over adistance of 133 ± µ m, and thus probe the bulk ofthe crystal. In the presence of a local or applied fieldat the muon stopping site the muon spin will precessaround the field direction with an angular frequency ω µ = γ µ B loc , where γ µ is the muon gyromagnetic ra-tio ( γ µ / π = 135 . .The parameter of interest is the muon spin asymme-try function, A ( t ), which is determined by calculating A ( t ) = ( N ( t ) − αN ( t )) / ( N ( t ) + αN ( t )), where N ( t )and N ( t ) are the positron counts of the two oppositedetectors, and α is a calibration constant. In our case α is close to 1.Transverse field (TF) experiments were performedwith the magnetic field applied parallel and perpendic-ular to the crystal plane. In the first configuration themuon spin is along the beam direction, the field in thehorizontal plane at right angles to the beam (and in theplane of the disk, N = N (cid:107) ), and the decay positrons aredetected in the backward and forward counters. In thesecond case the beam-line is operated in the muon spin-rotated mode, the applied field is along the beam direc-tion (perpendicular to the plane of the disk, N = N ⊥ ),and the decay positrons are collected in the left and rightcounters. In the spin-rotated mode the muon spin is di-rected ∼ ◦ out of the horizontal plane. This results isa reduced asymmetry function ( A ≈ . 18) with respectto the full asymmetry ( A ≈ . 23) in the non-spin-rotatedmode. The µ SR time spectra were analysed with thesoftware packages WIMDA and MUSRFIT . III. RESULTS AND ANALYSIS In order to investigate the presence of the interme-diate state we have scanned the superconducting phasediagram as depicted in Fig. 1. In Fig. 1(a) we show the F C , N = 0 . 0 8 I n t e r m e d ia t e s t a t e T ( K ) T c H c ( 0 ) 5 m T M e i s s n e r s t a t e H a | | a * 10 mm ( b ) H c S ( T ) H c ( 0 ) Z F C , N = 0 . 8 6 P d T e I n t e r m e d i a t e s t a t e m H (mT) T ( K ) T c H a | | c ( a ) FIG. 1. Field and temperature scan procedure of the super-conducting phase diagram of PdTe reported in Ref. 10. Theblue colored area indicates the intermediate phase, and theyellow area the Meissner phase. (a) After zero field cooling(ZFC) down to T = 0 . 26 K, spectra were recorded by increas-ing the field H a (cid:107) c step-wise at values denoted by the up-triangles. (b) After cooling down to 0.26 K in a field H a (cid:107) a ∗ of 5 mT, spectra were recorded at the temperatures indicatedby the side triangles. In the upper part of (a) and (b) thesample and field geometry are sketched. The solid green linein (a) indicates the region below which surface superconduc-tivity is observed . Note the vertical scale is different in (a)and (b). case where the sample is slowly cooled in zero field (ZFC)after which the field, directed perpendicular to the planeof the disk, is increased in eight steps to a value H a > H c .In this case the intermediate state covers a large region ofthe phase diagram. In Fig.1(b) we show the case wherethe sample is cooled in 5 mT (FC), applied in the plane ofthe disk, after which the temperature is raised in elevensteps to T > T c (at 5 mT). In this case the intermediatestate region is expected to be small. A. Field perpendicular to the plane of the disk In Fig. 2 we show three typical TF µ SR spectra at T = 0 . 26 K recorded during step-wise increasing thefield to 15 mT. In panel (a) no field is applied and muonspin precession is absent, the muons probe the Meissnerphase. In panel (b) the applied field is raised to 9 mT.Now a clear spin precession is visible, but with a reducedasymmetry. The superconducting volume has shrunk.The spin precession frequency corresponds to a local field B loc = 13 . µ H c at 0.26 K. Thisshows the sample is in the intermediate state. Lastly,in panel (c) the field is raised to 15 mT > µ H c andall muons show a precession frequency corresponding to B a = B loc = 15 mT, as expected in the normal state.The µ SR response A ( t ) = AP ( t ), where P ( t ) is themuon depolarization function, in panel (a) of Fig. 2 iswell described by a Gaussian Kubo-Toyabe function A KG ( t ) = A [ 13 + 23 (1 − σ KG t exp( − σ KG t ))] (1)Here A is the initial asymmetry and σ KG the depo-larization rate. The fit is shown in panel (a) by thesolid blue line. The fit parameters are A = 17 . σ KG = 0 . µ s − . The small depolarization rate is at-tributed to a Gaussian distribution of static nuclear mo-ments. In the normal phase, panel (c), the µ SR responseis best fitted with the function (solid black line): A N ( t ) = A exp( − σ N t ) cos( γ µ B a t + φ N ) (2)where σ N is a Gaussian damping rate, B a the appliedfield and φ N a phase factor. The fit parameters are A =17.4 and σ N = 0 . µ s − . The small damping rate isattributed to the field distribution of nuclear momentsas well, which is considered to be static in the µ SR timewindow.In an applied field in the superconducting phase, panel(b), best fits are obtained with a three component func-tion (in the following we use B a and B c for the appliedand critical field rather than H a and H c ) A ( t ) = A [ f S ( 13 + 23 (1 − σ KG t exp( − σ KG t ))+ f N exp( − σ N t ) cos( γ µ B c t + φ N )+ f bg exp( − σ bg t ) cos( γ µ B a t + φ bg )] (3)The third term, which we give the label ' background ' forthe moment, is small and accounts for muons that precessin the applied field at the angular frequency ω = γ µ B a ,and σ bg and φ bg are the related damping and phasefactor, respectively. f S = A S /A , f N = A N /A and f bg = A bg /A are the volume fractions related to the su-perconducting domains, normal domains, and the back-ground term, respectively. A = A S + A N + A bg is thefull experimental asymmetry, and was kept constant inthe fitting procedure. The fit parameters at 9 mT (panel(b)) are: f S = 0 . 34 (solid blue line), f N = 0 . 56 and σ N = 0 . µ s − (solid green line), and f bg = 0 . 10 and σ bg = 0 . µ s − (solid pink line). Here we have fixed σ KG = 0 . µ s − . We remark that the Gaussian damp-ing in the normal domains, σ N = 0 . µ s − , is larger thanthe value extracted from the normal state fit, see panel(c). This is not unexpected given the complicated do-main patterns that can arise in the intermediate state .We will address the background term in the Discussionsection.In order to follow the evolution of the intermediatestate with increasing magnetic field it is illustrative toinspect the Fast Fourier Transforms (FFT) of the µ SRtime spectra. The FFT amplitudes are shown in a three-dimensional (3D) plot in Fig. 3. The magnetic field dis-tributions have a sharp peak at B = 0, which is due to - 2 0- 1 001 02 0- 2 0- 1 001 02 0 0 1 2 3 4 5 6 7 8 9- 2 0- 1 001 02 0 ( a ) M e i s s n e r p h a s eZ F C m H a = 0 m T Asymmetry T = 0 . 2 6 K ( b ) Asymmetry n o r m a l d o m a i n ss u p e r c o n d u c t i n g d o m a i n s m H a = 9 m T b a c k g r o u n d ( c ) Asymmetry T i m e ( m s ) m H a = 1 5 m T FIG. 2. µ SR spectra collected at T = 0 . 26 K in ZF and inapplied fields of 9 mT and 15 mT directed perpendicular tothe sample plane. (a) Zero-field. The solid blue line is a fit tothe Guassian Kubo-Toyabe function Eq. 1. (b) TF = 9 mT.The black line is a fit to the three component function Eq. 3.The different components, due to superconducting domains,normal domains and background, are shown by the solid blue,green and pink lines, respectively. (c) TF = 15 mT. The blacksolid line is a fit to the depolarization function Eq. 2. See textfor fit details. the superconducting volume fraction. For B a = 5 mT asecond peak appears at a field B = B c > B a . This mag-netic intensity is due to the normal domains. It shows thecrystal is phase separated in normal and superconduct-ing domains, as expected for the intermediate state. Byfurther increasing the field, the peak at B c grows, whilethe peak at B = 0 decreases in intensity and vanishes at B a = B c . Eventually, for B a = 15 mT > B c = 13 . µ SR spectra in applied fields to Eq. 3, as illustratedin Fig. 2(b). In Fig. 4 we trace the fit parameters f S , f N and f bg . In the Landau scenario the inter-mediate state is predicted to occur in the field range(1 − N ) H c < H a < H c and its volume fraction growslinearly f N ( H a ) = ( H a − (1 − N ) H c ) /N H c (Ref. 44).Overall, our results comply with the simple model, butfor small fields the quasi-linear behavior does not extendall the way to H a = (1 − N ) H c . This points to a complexflux penetration process in weak fields. To conclude thissection we remark that the value of H c at T = 0 . 26 Kobtained by µ SR for H a (cid:107) c , is close to the value for H a (cid:107) a (Ref. 10). Fourier Amplitude P d T e T = 0 . 2 6 K N = 0 . 8 6 I n t e r n a l F i e l d ( m T ) FIG. 3. Magnetic field distribution in the PdTe crystal at T = 0 . 26 K obtained by FFT for fields applied perpendicularto the sample plane. The field values are given in blue colorednumbers. In the intermediate state two peaks are present at B = 0 and at B = B c > B a . The weak intensity at B = B a signals the background contribution. f b g f N H c Fractions f S, f N, f bg P d T e N = 0 . 8 6 Z F C T = 0 . 2 6 K m H a ( m T ) ( 1 - N ) H c f S FIG. 4. Field variation of the superconducting f S (blue sym-bols), normal f N (green symbols) and background f bg (pinksymbols) volume fractions obtained by fitting the µ SR spec-tra. The open symbols are ZFC at B = 0. The verticaldashed lines at (1 − N ) H c and H c bound the region in whichthe intermediate state is expected for N ⊥ = 0 . 86. The dashedblue and green lines show the expected linear field variationof the superconducting and normal volume fractions. Thetemperature is 0.26 K. B. Field in the plane of the disk A second set of spectra was taken after field coolingin 5 mT to a base temperature of 0.26 K, followed bystepwise heating the crystal to above T c , as indicatedin Fig. 1(b). Here the field was applied in the plane ofthe disk. It is instructive to first inspect the 3D graphwith the FFT’s shown in Fig. 5. The large peaks at B = 0 signal the superconducting volume fraction. Sur-prisingly, after field cooling a tiny fraction of the crys-tal is in the intermediate state already, as validated bythe weak magnetic intensity at B = B c = 13 . > B a . Upon increasing the temperature thisfraction remains small up to 1.1 K. For higher tempera-tures the magnetic intensity at B c grows rapidly, whilethe peak at B = 0 shows the opposite behavior. This P d T e m H a = 5 m T N = 0 . 0 8 I n t e r n a l F i e l d ( m T ) Fourier Amplitude FIG. 5. Magnetic field distribution in the PdTe crystal afterFC in B a = 5 mT directed in the plane of the disk at differenttemperatures as indicated. The large peak at B = 0 corre-sponds to the superconducting volume fraction. The weakintensity at B c ( T ) is due to a tiny part of the crystal that isalready in the intermediate state at the lowest temperature(0.26 K). Upon approaching T c the whole crystal convertsto the intermediate phase. The small peak that remains at B = B a signals the background contribution. shows the bulk of the crystal converts to the intermediatestate. The temperature variation of B c follows the stan-dard quadratic expression B c ( T ) = B c (0)[1 − ( T /T c ) ],here B c (0) = 13 . T c = 1 . 53 K. These values ob-tained for H a (cid:107) a ∗ are a few percent smaller than thosereported in Ref. 10 for H a (cid:107) a . The low-intensity humpat B a = 5 mT below T c is attributed to the backgroundterm. For T > T c the FFT peak at 5 mT is large andcharacterizes the paramagnetic normal-state volume ofthe crystal.In Fig. 6 we show three typical µ SR spectra fromthe temperature run in 5 mT together with the fit re-sults using Eq. 2 and 3. Here the total experimen-tal asymmetry A = 23 . 3. At 0.26 K, panel (a), thesolid blue line describes the large Meissner volume, with σ KG = 0 . µ s − . A tiny volume fraction with normaldomains ( B c = 13 . σ N = 0 . µ s − .At 1.5 K, panel (c), the crystal is the normal state. Thedata are well fitted by Eq. 2 with the small relaxationrate σ N = 0 . µ s − (black solid line).In Fig. 7 we trace the different volume fractions asa function of temperature obtained by fitting all thespectra. Clearly, during field cooling some flux remainstrapped in the crystal, resulting in a superconducting vol-ume fraction f S (cid:39) . 90. The tiny volume fraction withnormal domains (internal field B c ) does not vary withtemperature below ∼ . f N (cid:39) . 02. Thisimplies that the Meissner fraction in this bulky sampleoccupies ∼ 90% of its volume, which may be compared - 2 002 0- 2 002 0 0 1 2 3 4 5 6- 2 002 0 m H a = 5 m Tb a c k g r o u n dn o r m a l d o m a i n s s u p e r c o n d u c t i n g d o m a i n s ( a ) Asymmetry T = 0 . 2 6 K F C ( b ) Asymmetry n o r m a l d o m a i n ss u p e r c o n d u c t i n g d o m a i n s T = 1 . 2 K b a c k g r o u n d T i m e ( m s ) ( c ) Asymmetry T = 1 . 5 K FIG. 6. µ SR spectra collected in a field H a = 5 mT directed inthe plane of the sample at 0.26 K, 1.2 K and 1.5 K. The sampleis field cooled. In (a) and (b) the black line is a fit to the threecomponent function Eq. 3. The different components, due tosuperconducting domains, normal domains and background,are shown by the solid blue, green and pink lines, respectively.In (c) the black solid line is a fit to the muon depolarizationfunction Eq. 2. See text for fit details. with the value of 93% obtained for a small crystal mea-sured via dc-magnetization . The presence of a tinyintermediate state fraction is most likely related to theedges of the crystal that may result locally in a large de-magnetization factor. Upon raising the temperature thebulk of the crystal transforms to the intermediate stateabove ∼ . f N grows steeply, f S decreases. InFig. 7 we have indicated the borders of the intermedi-ate phase by the vertical dashed lines at T IM = 1 . 14 Kand T c = 1 . 25 K. The temperature at which the trans-formation starts is lower than can be expected on thebasis of the demagnetization factor N = 0 . 08. This in-dicates a larger, effective demagnetization factor N eff .With T IM = 1 . 14 K, we calculate N eff = 0 . IV. DISCUSSION The most important conclusion that can be drawnfrom our µ SR experiments is that the bulk of our PdTe crystal exhibits type-I superconductivity. Solid evidencefor this is provided by the detection of the intermedi-ate phase. Here we use the muon as a local probe ofthe bulk on the microscopic level. It is of interest toprovide a lower bound of the crystal volume that is oc-cupied by type-I superconductivity. It cannot simply betaken equal to the ZFC Meissner volume, f S = 1, de-duced from Fig. 2(a), because muons stopping in a (tiny)non-superconducting part of the crystal will experience asimilar Gaussian Kubo-Toyabe depolarization as muons T c f b g f N T I M Fractions f S, f N, f bg P d T e N = 0 . 0 8 Z F C B a = 5 m T T ( K ) f S FIG. 7. Temperature variation of the superconducting f S (blue symbols), normal f N (green symbols) and background f bg (pink symbols) volume fractions obtained by fitting the µ SR spectra using Eq. 3 (FC 5 mT directed in the plane ofthe disk). The vertical dashed lines at T IM and T c boundthe region in which the intermediate state in the bulk of thecrystal is found. in the superconducting part, and thus cannot be distin-guished. However, an estimate can be made by consid-ering the intermediate phase fraction, f IM = f S + f N .From the data in Fig. 4 a lower bound for f IM can beobtained by linearly extrapolating f N ( H a ) to H c , where f S = 0. We find f N = f IM = 0 . 92. On the same grounds, f S = f IM = 0 . 94 at the start of the linear growth of f N .This tells us type-I superconductivity occupies at least92% of the crystal’s volume.Next we address the background term, that resultsin the remaining volume fraction (5-10%) due to thethird component in Eq. 3, i.e. muons that precess atthe frequency of the applied field. Since the muonsand decay positrons events are collected in the so-calledVETO mode, the contribution from positrons arisingfrom muons that do not stop in the sample will be small.Besides, the damping rate ( e.g. σ bg = 0 . µ s − forthe spectrum in Fig. 2(b)) is too large to stem from theusual background components, such as the sample holderand cryostat, and indicates a local broad field distribu-tion. This hints at an intrinsic source of inhomogeneitiesrelated to type-I superconductivity. In general the pene-tration or expulsion of flux in a type-I superconductor is acomplicated process, and the domain pattern in the inter-mediate state can be diverse and complex . Moreover,the demagnetization factor in the crystal is not uniform,especially near the edges. This brings about additionalinternal field inhomogeneities, as illustrated by the tinyintermediate state fraction observed with the field in theplane of the disk.Another aspect is that the superconducting and nor-mal domains in the intermediate state are separated bydomain walls. The width of the domain wall is ofthe order δ ∼ ξ − λ ≈ . µ m . In the ideal case ofa laminar domain pattern an estimate for the volumefraction of the domain walls is f DW = 2 δ/a , where theperiodicity length a = ( dδ/f (˜ h )) / , see Ref. 43. Here d = 0 . 65 mm is the sample thickness and f (˜ h ) a nu-merical function with ˜ h = H a /H c . For an applied fieldof typically 5 mT (Fig. 6), ˜ h = 0 . 38 and f (˜ h ) = 0 . f DW ≈ f bg measured, becausethe domain patterns in our crystal will be complex, andconcurrently the domain walls broad. We therefore arguethat muons stopping in domain walls can largely accountfor the background term. Besides, muons stopping in re-gions where the magnetic field is pinned or trapped at de-fects during flux penetration or expulsion will contributeas well. Considering that the background term can beaccounted for by these sources of µ + -spin depolarization,the data do not rule out that the type-I superconductingfraction in our crystal is close to 100%.On the other hand, the possibility that a minute frac-tion of the crystal exhibits type-II superconductivity can-not be completely dismissed. In a type-II superconductorthe local field in the vortex phase is close to the appliedfield and thus its field distribution could contribute to f bg . Local type-II behavior could possibly originate froma pronounced deviation of the 1:2 stoichiometry. We re-call, however, that the EDX spectra show a uniform 1:2composition within the experimental resolution of 0.5%.A mixed type-I and type-II behavior has been evoked toexplain the STM/STS and PCS spectra, measured at thesurface of PdTe . Here it is proposed that the elec-tron mean free path, (cid:96) , is locally reduced, which resultsin κ > / √ 2. We remark, evidence for flux quantizationand a vortex lattice required for type-II superconduc-tivity has not been produced. STM/STS and PCS aresurface sensitive probes, and thus possibly the mixed be-havior is a property of the crystal’s surface only. Butthis in turn is difficult to reconcile with the resultingfield of the vortex that has to penetrate the bulk. It istempting to speculate that these unusual surface effects,as well as the superconductivity of the surface sheath ,are related to the Dirac type-II character that involvestopological surface states. This warrants a continuinginvestigation of PdTe . Superconductivity of the surfacesheath has been detected by magnetic susceptibility in small ac-driving fields only, and could not be probed inthe present µ SR experiments, which employs dc-fields.In order to obtain access to the surface properties LowEnergy Muons (LEM) form an excellent tool. Here theenergy of the muons can be tuned such that they local-ize in the surface layer of the crystal. However, at themoment this µ SR technique is restricted to temperaturesabove 2 K only. V. SUMMARY We have investigated the superconducting phase ofPdTe ( T c = 1 . µ SR spectra were taken on a thindisk-like crystal in two configurations: with the field per-pendicular to the plane of the disk ( N ⊥ = 0 . 86) andwith the field in the plane of the disk ( N (cid:107) = 0 . H − T phase diagram was scanned as a function of tem-perature and applied field. The µ SR spectra have beenanalysed with a three component muon depolarizationfunction, accounting for the superconducting domains,the normal domains and a background term. In the su-perconducting phase normal domains are found in whichthe local field is always equal to B c and larger than theapplied field. This is the hall mark of the intermedi-ate phase in a type-I superconductor. The backgroundterm is predominantly attributed to muons stopping inthe superconducting-normal domain walls. In conclusion,our µ SR study provides solid evidence for type-I behaviorin the bulk of the PdTe crystal. VI. 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