Direct evidence for a pressure-induced nodal

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Received 27 Apr 2015 | Accepted 12 Oct 2015 | Published 9 Nov 2015

Z. Guguchia1, A. Amato1, J. Kang2, H. Luetkens1, P.K. Biswas1, G. Prando3, F. von Rohr4, Z. Bukowski5,A. Shengelaya6, H. Keller4, E. Morenzoni1, Rafael M. Fernandes2 & R. Khasanov1

decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superuid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

1 Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen, Switzerland. 2 School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA. 3 Leibniz-Institut fr Festkrper- und Werkstoffforschung (IFW) Dresden, D-01171 Dresden, Germany. 4 Physik-Institut der Universitat Zrich, Winterthurerstrasse 190, CH-8057 Zrich, Switzerland. 5 Institute of Low Temperature and Structure Research, Polish Academy of Sciences, 50-422 Wroclaw, Poland. 6 Department of Physics, Tbilisi State University, Chavchavadze 3, GE-0128 Tbilisi, Georgia. Correspondence and requests for materials should be addressed to Z.G. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms9863 OPEN

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9863

After 6 years of intensive research on the Fe-based high-temperature superconductors (Fe-HTSs), no consensus on a universal gap structure has been reached.

There is evidence that small differences in electronic or structural properties can lead to a strong diversity in the superconducting (SC) gap structure. On the one hand, nodeless isotropic gap functions were observed in optimally doped Ba1 xKxFe2As2, Ba1 xRbxFe2As2 and BaFe2 xNixAs2 as well as

in BaFe2 xCoxAs2, KxFe2 ySe2 and FeTe1 xSex (refs 18).

On the other hand, signatures of nodal SC gaps were reported in LaOFeP, LiFeP, KFe2As2, BaFe2(As1 xPx)2, BaFe2 xRuxAs2,

FeSe as well as in overdoped Ba1 xKxFe2As2 and BaFe2 xNixAs2

(refs 7,917). Understanding what parameters of the systems control the different SC gap structures observed experimentally is paramount to elucidate the microscopic pairing mechanism in the Fe-HTSs and, more generally, to provide a deeper understanding of the phenomenon of high-temperature superconductivity. On the theoretical front, it has been proposed that both the s -wave and d-wave states are close competitors for the SC ground state1825. Although the former generally wins, it has been pointed out that a d-wave state may be realized on removing electron or hole pockets. On the experimental front, a sub-leading d-wave collective mode was observed by Raman experiments inside the fully gapped SC state of optimally doped Ba1 xKxFe2As2 (refs 26,27). In KFe2As2, a change of the SC

pairing symmetry by hydrostatic pressure has been recently proposed, based on the V-shaped pressure dependence of Tc (ref. 28). However, no direct experimental evidence for a pressure-induced change of either the SC gap symmetry or the SC gap structure in the Fe-HTSs has been reported until now.

Measurements of the magnetic penetration depth l, which is one of the fundamental parameters of a superconductor, since it is related to the superuid density ns via 1/l2 m0e2ns/m* (where

m* is the effective mass), are a sensitive tool to study multiband superconductivity. Most importantly, the temperature dependence of l is particularly sensitive to the presence of SC nodes: while in a fully gapped SC Dl 2(T) l 2(0) l 2(T)

vanishes exponentially at low T, in a nodal SC it vanishes as a power of T. The muon spin rotation (mSR) technique provides a powerful tool to measure l in type II super-conductors29. A mSR experiment in the vortex state of a type II superconductor allows the determination of l in the bulk of the sample, in contrast to many techniques that probe l only near the surface.

For the compound Ba0.65Rb0.35Fe2As2 investigated here, and

for the closely related system Ba1 xKxFe2As2, previous mSR

measurements of l(T) revealed a nodeless multi-gap SC state2,3, in agreement with angle-resolved photoemission spectroscopy (ARPES) measurements1,30,31. In this article, we report on mSR studies of l(0) and of the temperature dependence of Dl 2 in optimally doped Ba0.65Rb0.35Fe2As2 under hydrostatic pressures.

This system exhibits the highest TcC37 K among the extensively studied 122 family of Fe-HTSs. We observe that while Tc stays nearly constant on application of pressure, l(0) decreases substantially. In view of previous works in another 122 compound that reported a sharp peak of l(0) at a quantum critical point32, we interpret the observed suppression of l(0) as evidence that pressure moves the system away from a putative quantum critical point in Ba0.65Rb0.35Fe2As2. More importantly,

we nd a qualitative change in the low-temperature behaviour of Dl 2(T) as pressure is increased. While at p 0 an exponential

suppression characteristic of a nodeless superconductivity is observed, for p 2.25 GPa a clear power-law behaviour is found.

Because pressure does not affect the impurity concentration, which could promote power-law behaviour even for a nodeless

system33, our ndings are suggestive of a nodeless to nodal SC transition. Our ttings to microscopic models reveal that this behaviour is more compatible with a d-wave state rather than an s state with accidental nodes, suggesting that pressure promotes a change in the pairing symmetry.

ResultsProbing the vortex state as a function of pressure. Figure 1a,b exhibit the transverse-eld mSR time spectra for Ba0.65Rb0.35-

Fe2As2, measured at ambient p 0 GPa and maximum applied

pressure p 2.25 GPa, respectively. The spectra above (45 K) and

below (1.7 K) the SC transition temperature Tc are shown. Above Tc the oscillations show a small relaxation due to the random local elds from the nuclear magnetic moments. Below Tc the relaxation rate strongly increases with decreasing temperature due to the presence of a non-uniform local magnetic eld distribution as a result of the formation of a ux-line lattice in the SC state. Figure 1c,d show the Fourier transforms of the mSR time spectra shown in Fig. 1a,b, respectively. At T 5 K the narrow

signal around m0Hext 50 mT (Fig. 1c,d) originates from the

pressure cell, while the broad signal with a rst moment m0Hintom0Hext, marked by the solid arrow in Fig. 1c, arises from the SC sample.

Below Tc a large diamagnetic shift of m0Hint experienced by the muons is observed at all applied pressures. This is evident in Fig. 2a, where we plot the temperature dependence of the diamagnetic shift DBdia m0[H

int,SC

Hint,NS] for Ba0.65Rb0.35-

Fe2As2 at various pressures, where m0Hint,SC denotes the internal eld measured in the SC state and m0Hint,NS the internal eld measured in the normal state at 45 K. Note that m0Hint,NS is

temperature independent. This diamagnetic shift indicates the bulk character of superconductivity and excludes the possibility of eld-induced magnetism34 in Ba0.65Rb0.35Fe2As2 at all applied

pressures. The SC transition temperature Tc is determined from the intercept of the linearly extrapolated DBdia curve to its zero line (we used the same criterium for determination of Tc from DBdia(T) as from the susceptibility data wm(T), presented in Supplementary Fig. 1a). It is found to be Tc 36.9(7) K and

35.9(5) K for p 0 and 2.25 GPa, respectively. The ambient

pressure value of Tc is in perfect agreement with Tc 36.8(5) K

obtained from susceptibility and specic heat measurements (Supplementary Note 1 and Supplementary Figs 1a,b and 2). At the highest pressure of p 2.25 GPa applied, Tc decreases only by

C1 K, indicating only a small pressure effect on Tc in

Ba0.65Rb0.35Fe2As2. The temperature dependence of the muon

spin depolarization rate ssc of Ba0.65Rb0.35Fe2As2 in the SC state

at selected pressures is shown in Fig. 2b; note that ssc is

proportional to the second moment of the eld distribution, which was extracted using the equations described in the Method section. At all applied pressures, below Tc the relaxation rate ssc starts to increase from zero with decreasing temperature due to the formation of the ux-line lattice (we note that no pressure-induced magnetism is observed in Ba0.65Rb0.35Fe2As2, as shown in

Supplementary Note 2 and Supplementary Figs 3a,b and 4). It is interesting that the low-temperature value ssc(5 K) increases substantially under pressure (Fig. 2b): ssc(5 K) increases about 30% from p 0 to 2.25 GPa. Interestingly, the form of the

temperature dependence of ssc, which reects the topology of the SC gap, changes as a function of pressure. The most striking change is in the low-temperature behaviour of ssc(T). At ambient

pressure ssc(T) shows a at behaviour below T/TcC0.4, whereas the high-pressure data exhibit a steeper (linear) temperature dependence of ssc(T) below T/TcC0.4. We show in the following how these behaviours indicate the appearance of nodes in the gap function.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9863 ARTICLE

p = 0 GPa p = 2.25 GPa

0.3

5 K45 K

0.2

0.1

A (t)

0.0

0.1

0.2

0.3

0 1 2 3

t (s) t (s)

5 K

45 K

1.6

p = 0 GPa 5 K

45 K Narrow Broad Sum

p = 2.25 GPa

5 K45 K

FT amplitude (a.u.)

1.2

0.8

0.4

0.0 30 40 50 60 70

30 40 50 60 70

0H (mT)

Figure 1 | lSR time spectra and the corresponding Fourier transforms. The spectra for Ba0.65Rb0.35Fe2As2 are obtained above (45 K) and below (5 K) Tc (after eld cooling the sample from above Tc): (a,c) p 0 GPa and (b,d) p 2.25 GPa. Error bars are the s.e.m. in about 106 events. The error of each bin

count n is given by the s.d. of n. The errors of each bin in A(t) are then calculated by s.e. propagation. The solid lines in a and b represent ts to the data by means of equation (3). The solid lines in c and d are the Fourier transforms of the tted time spectra. The dashed and solid arrows indicate the rst moments for the signals of the pressure cell and the sample, respectively.

1.5

Pressure-dependent magnetic penetration depth. To investigate a possible change of the symmetry of the SC gap, we note that l(T) is related to the relaxation rate ssc(T) by the equation35:

ssc T

0:06091 F0

l2 T

0.0

0.0 0 10 20 30 40 50

; 1

where gm is the gyromagnetic ratio of the muon and F0 is the magnetic-ux quantum. Thus, the at T dependence of ssc

observed at p 0 for low temperatures (Fig. 2b) is consistent with

a nodeless superconductor, in which l 2(T) reaches its zero-temperature value exponentially. On the other hand, the linear T dependence of ssc observed at p 2.25 GPa (Fig. 2b) indicates

that l 2(T) reaches l 2(0) linearly, which is characteristic of line nodes. This is the main result of this communication: pressure in an optimally doped Fe-HTS can tune a nodeless gap into a nodal gap. Although this qualitative analysis is robust, and independent of any tting models for the gap function, it does not elucidate whether these nodes arise due to a nodal s state or a d-wave state.

To proceed with a quantitative analysis, we consider the local (London) approximation (lcx, where x is the coherence length)

and rst employ the empirical a-model. The latter, widely used in previous investigations of the penetration depth of multiband superconductors3,3641, assumes that the gaps occurring in different bands, besides a common Tc, are independent of each other. Then, the superuid density is calculated for each component separately3 and added together with a weighting factor. For our purposes a two-band model sufces yielding:

l 2 T

l 2 0

o1 l 2 T; D0;1

l 2 0; D0;1

0.5

0 GPa1.17 GPa2.22 GPa

B dia (mT)

1.0

2.5

2.0

1 )

1.5

sc (s

1.0

0 GPa1.17 GPa2.22 GPa

0.5

T (K)

Figure 2 | Diamagnetic shift and the relaxation rate. The temperature dependence of the diamagnetic shift DBdia m0[H

int,SC

Hint,NS] (a) and the

muon spin relaxation rate ssc (b) for Ba0.65Rb0.35Fe2As2, measured in a

magnetic eld of m0H 50 mT. The dashed vertical lines denote Tc for p 0

and 2.22 GPa. The error bars represent the s.d. of the t parameters.

l 2 T; D0;2

l 2 0; D0;2

; 2

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9863

where l(0) is the penetration depth at zero temperature, D0,i is the

value of the i-th SC gap (i 1, 2) at T 0 K and oi is the

weighting factor, which measures their relative contributions to l 2 (that is, o1 o2 1).

The results of this analysis are presented in Fig. 3af, where the temperature dependence of l 2 for Ba0.65Rb0.35Fe2As2 is plotted at various pressures. We consider two different possibilities for the gap functions: either a constant gap, D0,i Di, or an angle-

dependent gap of the form D0,i Di cos2j, where j is the polar

angle around the Fermi surface. The resulting functions l(T) are shown in the Methods section. The data at p 0 GPa are

described remarkably well by two constant gaps, D1 2.7(5) meV

and D2 8.4(3) meV. These values are in perfect agreement with

our previous results3 and also with ARPES experiments30, pointing out that most Fe-HTSs exhibit two-gap behaviour, characterized by one large gap with 2D2/kBTc 7(2) and one

small gap with 2D1/kBTc 2.5(1.5). In contrast to the case

p 0 GPa, for all applied pressures l 2(T) is better described by

one constant gap and one angle-dependent gap, consistent with the presence of gap nodes, as inferred from our qualitative analysis. Note that a tting to two angle-dependent gaps is inconsistent with the data.

To understand the implications of the tting to a constant and an angle-dependent gap for nite pressures, we analyse the two different scenarios in which nodes can emerge: a nodal s state (with gap functions of different signs in the hole and in the electron pockets) and a d-wave state. In the former, the position of the nodes are accidental, that is, not enforced by symmetry, while in the latter the nodes are enforced by symmetry to be on the Brillouin zone diagonals. Schematic representations of both scenarios are shown in Fig. 4, where a density plot of the gap functions is superimposed to the typical Fermi surface of the iron pnictides, consisting of one or more hole pockets at the centre of the Brillouin zone, and electron pockets at the border of the Brillouin zone. In this gure, we set the accidental nodes of the s state to be on the electron pockets, as observed by ARPES in the related compound BaFe2(As1 xPx)2 (ref. 17). Note that in the

d-wave state, while nodes appear in the hole pockets, the electron

pockets have nearly uniform gaps. Thus, the fact that the tting to the a-model gives a constant and an angle-dependent gap is consistent with a d-wave state.

To contrast the scenarios of a nodal s gap and a d-wave gap, we consider a microscopic model (Supplementary Note 3)

that goes beyond the simplications of independent gap functions of the a-model discussed above. In this microscopic model, the fully coupled nonlinear gap equations are solved for a hole pocket h and two electron pockets e1,2, and the penetration depth is calculated at all temperatures (Supplementary Fig. 5). The free parameters are then the density of states of the pockets, the amplitude of the pairing interaction and the gap functions themselves (Supplementary Note 3). For simplicity, the anisotropies of the electron pockets are neglected, the Fermi velocities of the pockets are assumed to be nearly the same and the gaps are expanded in their leading harmonics. Thus, for the nodal s

state we have Dh Dh,0 and Dei De;0 r cos2je

, whereas for

the d-wave state it follows that Dh Dh,0 cos2jh and

Dei De;0. Note the difference in the position of the nodes

in each case: while for the d-wave case they are always at jh

p/4, for the nodal s the nodes exist only when ro1 at

arbitrary positions je 12 arccos r. The results of the ttings

for the pressures p 1.57 and 2.25 GPa imposing a nodal s

state are shown in Fig 3c,f (Supplementary Fig. 6ac). Remarkably, we nd in both cases that the best t gives r-0. This extreme case is, within our model, indistinguishable from the tting to the d-wave state, since in both cases the nodes are at j p/4 (albeit in different Fermi pockets). We note that from

the ts one cannot completely rule out the possibility of small but non-vanishing values of r. Therefore, at least within our model, a nodal s state is compatible with the data only if the accidental nodes are ne tuned to lie either at or very close to the diagonals of the electron pockets for a broad pressure range. Since the position of the accidental nodes is expected to be sensitive to the topology of the Fermi surface, and consequently to pressure, it seems more plausible that the gap state is d-wave, since in that case the position of the gaps is enforced by symmetry to be along the diagonals of the

a b c

p = 0 GPa s + s

p = 1.17 GPa d

p = 1.57 GPa d

Microscopic model

2 ( m2 )

d e f

p = 2.22 GPa d

p = 2.25 GPadMicroscopic model

2 ( m2 )

0 0 10 20 30 40 50

T (K)

p = 1.83 GPa d

T (K)

Figure 3 | Inverse-squared magnetic penetration depth. The temperature dependence of l 2 measured at various applied hydrostatic pressures for Ba0.65Rb0.35Fe2As2. The solid line for p 0 GPa corresponds to a two-gap s-wave model (a) and the solid lines for nite pressure represent a ts to the data

using a multiband d-wave model (bf). The dashed lines in c and f represent ts to the data using the microscopic model. The error bars are calculated as the s.e.m.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9863 ARTICLE

260

240

(nm)

2 ( m2 )

220

k y

200

1, 2 (0) (meV)

0.30

Weight of the small gap ( 2)

0.25

0.20

0.15

0.10

p (GPa)

Figure 4 | Schematic representation of the nodal s and d-wave states. In both gures, a density plot of the gap function is superimposed to a representative Fermi surface consisting of a hole pocket (h) at the centre and an electron pocket (e) at the borders of the Brillouin zone. In the nodal s states (a) the nodes are not enforced by symmetry (here they are located at the electron pockets). In the d-wave state (b) the nodes are enforced by symmetry to be on the diagonals of the Brillouin zone, and therefore can only cross the hole pockets.

0.05 0.0 0.5 1.0 1.5 2.0 2.5

Figure 5 | Pressure dependence of various quantities. The magnetic penetration depth l(0) and l 2(0) (a), the zero-temperature gap values

D1,2(0) (b) as well as the relative weight o2 of the small gap to the superuid density (c) are plotted for Ba0.65Rb0.35Fe2As2 as a function of

pressure. The error bars represent the s.d. of the t parameters. The dashed lines are guides to the eyes and the solid lines represent linear ts to the data.

hole pockets regardless of the value of the pressure (Supplementary Fig. 7a,b).

The pressure dependence of all the parameters extracted from the data analysis within the a-model are plotted in Fig. 5ac.

From Fig. 5a a substantial decrease of l(0) with pressure is evident. At the maximum applied pressure of p 2.25 GPa the

reduction of l(0) is B15% compared with the value at p 0 GPa.

Both D1 and D2 show a small reduction on increasing the pressure from p 0 to 1.17 GPa, while above p 1.17 GPa the gaps values

stay constant. On the other hand, the relative contribution o2 of

the small gap to the superuid density increases by approximately factor of 2 for the maximum applied pressure of p 2.25 GPa

(Fig. 5c), indicating a spectral weight shift to the smaller gap. The parameters extracted from the microscopic model are discussed in Supplementary Note 3.

DiscussionThe main nding of our paper is the observation that pressure promotes a nodal SC gap in Ba0.65Rb0.35Fe2As2. This conclusion is

model independent, as it relies on the qualitative change in the low-temperature behaviour of Dl 2 from exponential to linear in T on applied pressure. To our knowledge this is the rst direct experimental demonstration of a plausible pressure-induced change in the SC gap structure in a Fe-HTS. Two possible gap structures could be realized at nite pressures: a nodal s state

and a d-wave state. In the rst case, the change from nodeless s to nodal s is a crossover rather than a phase transition42,43, whereas in the latter it is an actual phase transition that could harbour exotic pairing states, such as s id (refs 21,23,24) or s d (ref. 44).

Additional results provide important clues of how pressure may induce either a nodal s or a d-wave state. In the closely related optimally doped compound Ba0.6K0.4Fe2As2, Raman

spectroscopy27, as well as theoretical calculations21,20, reveal a subdominant d-wave state close in energy to the dominant s

state. Pressure may affect this intricate balance, and tip the balance in favour of the d-wave state. On the other hand, theoretical calculations have shown that the pnictogen height is an important factor in determining the structure of the s SC order parameter18,45. A systematic comparison of the quasiparticle excitations in the 1111, 122 and 111 families of Fe-HTSs showed that the nodal s state is favoured when the pnictogen height decreases below a threshold value of C1.33 (ref. 46). Hydrostatic pressure may indeed shorten the pnictogen height and consequently modify the s gap structure from nodeless to nodal. Although our tting of the penetration depth data to both a microscopic model and an effective a-model suggest that the d-wave state is more likely to be realized than the nodal s state, further quantitative calculations of the pressure effect are desirable to completely discard a nodal s state.

Besides the appearance of nodes with pressure, another interesting observation is the reduction of l(0) under pressure, despite the fact that Tc remains nearly unchanged. Interestingly,

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in the compound BaFe2As2 xPx, a sharp enhancement of l(0) is

observed as optimal doping is approached from the overdoped side32, which has been interpreted in terms of a putative quantum critical point (QCP) inside the SC dome4749. In Ba0.65Rb0.35Fe2As2, if such a putative QCP is also present,

pressure is likely to move the system away from the putative QCP, which, according to the results of BaFe2As2 xPx, would

explain the observed suppression of the penetration depth at T 0. This scenario does not explain why Tc stays nearly constant

under pressure, but this could be due to the intrinsic atness of Tc around optimal doping in Ba1 xRbxFe2As2. Note that a similar

behaviour for l(0) and Tc with pressure has been recently observed in LaFeAsO1 xFx (ref. 50), but interpreted in terms of

the interplay between impurity scattering and pressure. To distinguish between these two scenarios, pressure-dependent studies of the quasiparticle mass in Ba0.65Rb0.35Fe2As2 are

desirable to probe whether a putative QCP is present or not in this compound.

In conclusion, the zero-temperature magnetic penetration depth l(0) and the temperature dependence of l 2 were studied in optimally doped Ba0.65Rb0.35Fe2As2 by means of mSR

experiments as a function of pressure up to p 2:25 GPa. The

SC transition temperature stays nearly constant under pressure, whereas a strong reduction of l(0) is observed, possibly related to the presence of a putative quantum critical point. Our main result is the observation of a qualitative change in the low-temperature behaviour of Dl 2(T) from exponential to linear in the investigated Fe-based superconductor as pressure is increased.

This most likely indicates that a nodal SC gap is promoted by hydrostatic pressure. Model calculations favour a d-wave over a nodal s -wave pairing as the origin for the nodal gap. The present results offer important benchmarks for the elucidation of the complex microscopic mechanism responsible for the observed non-universaltiy of the SC gap structure and of high-temperature superconductivity in the Fe-HTSs in general.

Methods

Sample preparation. Polycrystalline samples of Ba0.65Rb0.35Fe2As2 were prepared in evacuated quartz ampoules by a solid-state reaction method. Fe2As, BaAs and RbAs were obtained by reacting high-purity As (99.999 %), Fe (99.9%), Ba (99.9%) and Rb (99.95%) at 800, 650 and 500 C, respectively. Using stoichiometric amounts of BaAs or RbAs and Fe2As, the terminal compounds BaFe2As2 and

RbFe2As2 were synthesized at 950 and 650 C, respectively. Finally, samples of Ba1 xRbxFe2As2 with x 0.35 were prepared from appropriate amounts of single-

phase BaFe2As2 and RbFe2As2. The components were mixed, pressed into pellets, placed into alumina crucibles and annealed for 100 h under vacuum at 650 C with one intermittent grinding. Powder X-ray diffraction analysis revealed that the synthesized samples are single-phase materials.

Method for creation and measurement of high pressures. Pressures up to2.4 GPa were generated in a double-wall piston-cylinder type of cell made of MP35N material, especially designed to perform mSR experiments under pressure51,52. As a pressure-transmitting medium Daphne oil was used. The pressure was measured by tracking the SC transition of a very small indium plate by a.c. susceptibility. The lling factor of the pressure cell was maximized. The fraction of the muons stopping in the sample was B40%.

lSR experiment. Zero-eld and transverse-eld (TF) mSR experiments at ambient and under various applied pressures were performed at the mE1 beamline of the Paul Scherrer Institute, Switzerland, using the dedicated general purpose decay channel instrument (GPD) spectrometer, where an intense high-energy (pm 100

MeVc 1) beam of muons is implanted in the sample through the pressure cell. A gas-ow 4He (base temperature B4 K) and a VARIOX cryostat (base temperature B1.3 K) were used. High-energy muons (pm 100 MeVc 1) were implanted in the

sample. Forward and backward positron detectors with respect to the initial muon spin polarization were used for the measurements of the mSR asymmetry time spectrum A(t). The typical statistics for both forward and backward detectors were 6 millions. All zero-eld and transverse-eld mSR experiments were performed by stabilizing the temperature in before recording the mSR time spectra. Note that a precise calibration of the GPD results was carried out at the pM3 beamline using

the low-background GPS. The mSR time spectra were analysed using the free software package MUSRFIT36.

In a mSR experiment nearly 100% spin-polarized muons m are implanted into the sample one at a time. The positively charged m thermalize at interstitial lattice sites, where they act as magnetic microprobes. In a magnetic material the muon spin precesses in the local eld Bm at the muon site with the Larmor frequency nm gm/(2p)Bm (muon gyromagnetic ratio gm/(2p) 135.5 MHz T 1). By means of

mSR important length scale of superconductor can be measured, namely the magnetic penetration depth l. When a type II superconductor is cooled below Tc in an applied magnetic eld ranging between the lower (Hc1) and the upper (Hc2) critical eld, a vortex lattice is formed, which in general is incommensurate with the crystal lattice, and the vortex cores will be separated by much larger distances than those of the unit cell. Because the implanted muons stop at given crystallographic sites, they will randomly probe the eld distribution of the vortex lattice. Such measurements need to be performed in a eld applied perpendicular to the initial muon spin polarization (so called transverse-eld conguration).

Analysis of transverse-eld-lSR data. Our zero-eld mSR experiments (Supplementary Note 2) reveal a pressure-independent magnetic fraction of about 10% in the sample, caused by the presence of diluted Fe moments as discussed in previous mSR studies. The signal from the magnetically ordered parts vanishes within the rst 0.2 ms. Thus, the ts of transverse-eld data were restricted to times t40.2 ms for all temperatures.

The transverse-eld mSR data were analysed by using the following functional form36:

P t

Asexp s s

h i

cos gmBint;st j

Apcexp s t2

t 2

Apc denote the initial assymmetries of the sample and the pressure cell, respectively. g=2p 135:5 MHz T 1 is the muon gyromagnetic ratio, j is the

initial phase of the muon spin ensemble and Bint represents the internal magnetic eld at the muon site. The relaxation rates ssc and snm characterize the damping due to the formation of the vortex lattice in the SC state and of the nuclear magnetic dipolar contribution, respectively. In the analysis snm was assumed to be constant over the entire temperature range and was xed to the value obtained above Tc, where only nuclear magnetic moments contribute to the muon relaxation rate s. The Gaussian relaxation rate spc reects the depolarization due to the nuclear magnetism of the pressure cell. It can be seen from the Fourier transforms shown in Fig. 1c,d that the width of the pressure cell signal increases below Tc. As shown previously53, this is due to the inuence of the diamagnetic moment of the SC sample on the pressure cell, leading to a temperature-dependent spc below Tc.

To consider this inuence, we assume a linear coupling between spc and the eld shift of the internal magnetic eld in the SC state: spc(T) spc(T4Tc) C(T)

(m0Hint,NS m0H

int,SC), where spc(T4Tc) 0.35 ms 1 is the temperature-

independent Gaussian relaxation rate. m0Hint,NS and m0Hint,SC are the internal magnetic elds measured in the normal and in the SC state, respectively. As indicated by the solid lines in Fig. 1ad, the mSR data are well described by equation (1). The solid lines in Fig. 1c,d are the Fourier transforms of the tted curves shown in Fig. 1a,b. The model used describes the data rather well.

Analysis of k(T). As pointed out in the manuscript, for polycrystalline samples the temperature dependence of the London magnetic penetration depth l(T) is related to the muon spin depolarization rate ssc(T) by equation (1) (see the main text). Equation (1) is valid when the separation between the vortices is smaller than l and the applied eld small with respect to the second critical eld Bc2. In this case according to the London model ssc is eld independent35. Field-dependent measurements of ssc at ambient pressure was reported previously3. It was observed that rst ssc strongly increases with increasing magnetic eld until reaching a maximum at m0HC0.03 T and then above 0.03 T stays nearly constant up to the highest eld (0.64 T) investigated. Such a behaviour is expected within the London model and is typical for polycrystalline HTSs54.

l(T) was calculated within the local (London) approximation l x

by the

following expression36,37:

l 2 T; D0;i

l 2 0; D0;i

h i

cos gmBint;pct j ;

1 p

Z2p

@f @E

EdEdj

; 4

where f [1 exp(E/kBT)] 1 is the Fermi function, j is the angle along the Fermi

surface and Di(T, j) D0,iG(T/Tc)g(j) (D0,i is the maximum gap value at T 0).

The temperature dependence of the gap is approximated by the expressions G(T/Tc) tanh{1.82[1.018(Tc/T 1)]0.51} (ref. 38), while g(j) describes the

angular dependence of the gap and it is replaced by 1 for both an s-wave and an s s-wave gap, and |cos(2j)| for a d-wave gap39. The tting of the T dependence of

the penetration depth with a-model was performed using the library BMW36.

E2 Di T; j

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9863 ARTICLE

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Acknowledgements

Experimental work was performed at the Swiss Muon Source (SmS) Paul Scherrer Institute, Villigen, Switzerland. Z.G. acknowledges the support by the Swiss National Science Foundation. R.M.F. and J.K. were supported by the U.S. Department of Energy, Ofce of Science, Basic Energy Sciences, under award number DE-SC0012336. A.S. acknowledges support from the SCOPES grant No. IZ73Z0_128242. G.P. is supported by the Humboldt Research Fellowship for Postdoctoral Researchers.

Author contributions

Project planning: Z.G.; sample growth: Z.B.; mSR experiments: Z.G., R.K., A.A., H.L., P.K.B., E.M., A.S., G.P., H.K. and F.v.R.; magnetization experiment: Z.G. and F.v.R.; mSR data analysis: Z.G.; analysis of the penetration depth data with a-model: Z.G.; analysis of the penetration depth data with the microscopic model: J.K. and R.M.F.; data interpretation: Z.G., R.M.F. and R.K.; draft writing: Z.G. with contributions and/or comments from all authors.

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How to cite this article: Guguchia, Z. et al. Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor. Nat. Commun. 6:8863 doi: 10.1038/ncomms9863 (2015).

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The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. In contrast to other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba_0.65 Rb_0.35 Fe₂ As₂ . Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

Details

Title

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor

Author

Guguchia, Z; Amato, A; Kang, J; Luetkens, H; Biswas, P K; Prando, G; Von Rohr, F; Bukowski, Z; Shengelaya, A; Keller, H; Morenzoni, E; Fernandes, Rafael M; Khasanov, R

Pages

8863

Publication year

2015

Publication date

Nov 2015

Publisher

Nature Publishing Group

e-ISSN

20411723

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1038/ncomms9863

ProQuest document ID

1731793846

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor

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