Pressure effects on the superconducting properties of single-crystalline Co doped NaFeAs

Resistivity and magnetic susceptibility measurements under external pressure were performed on NaFe1−xCoxAs (x = 0, 0.01, 0.028, 0.075 and 0.109) single crystals. For both underdoped and optimally doped NaFe1−xCoxAs, the maximum Tc reached as high as 31 K under certain pressures. Meanwhile the overdoped sample with x = 0.075 also exhibits a positive pressure effect on Tc, and an enhancement of Tc by 13 K is achieved under a pressure of 2.3 GPa. All of these superconducting samples show large positive pressure coefficients on superconductivity, being distinct from those of Ba(Fe1−xCox)2As2. However, the superconductivity cannot be induced by pressure in heavily overdoped non-superconducting NaFe0.891Co0.109As. These studies reveal that the electronic structure is very different between superconducting and heavily overdoped non-superconducting NaFe1−xCoxAs, consistent with the observation of angle-resolved photoemission spectroscopy.


I. INTRODUCTION
Extensive experimental and theoretical efforts have been made to study the iron based superconductors since the discovery of superconductivity in F doped LaOFeAs. 1 Most of the parent compounds of the iron based superconductors undergo structural and spin density wave (SDW) transitions.With doping or applying high pressure, both the structural and SDW transitions are suppressed and superconductivity emerges.The so called "111"-type iron arsenide compound with the PbFCl structure, including LiFeAs 2 and NaFeAs 3 , has been regarded as a unique family which is superconducting without purposely doping or applying pressure.Although no long range antiferromagnetic order has been observed in LiFeAs 4 , NaFeAs is reported to undergo three successive phase transitions at around 52, 41, and 23 K, which correspond to structural, magnetic, and superconducting transition, respectively. 5Although the resistivity of NaFeAs drops to zero at about 10K, it has been pointed out that the superconductivity is filamentary rather than a bulk phenomenon. 6,7With substitution of Co on Fe site, both magnetism and the structural distortion are suppressed, and bulk superconductivity with zero resistivity up to 20 K can be achieved. 8,9Full shielding fraction and large specific heat jump can be observed in single-crystalline optimally doped NaFe 0.972 Co 0.028 As samples. 7pplying pressure has been proved to be an effective method to enhance the superconductivity transition temperature in many types of iron arsenide superconductors.It was revealed that the T c of F-doped LaOFeAs was enhanced up to 43 K soon after the discovery of superconductivity in this system. 10In tetragonal FeSe, T c increases from 8.5 K at ambient pressure to about 37 K under P = 8.9 GPa, which is the largest pressure effect reported in iron based superconductors so far. 11Pressure effects in electron doped 122-system Ba(Fe 1−x Co x ) 2 As 2 with different doping levels have been thoroughly studied.Applying pressure dramatically enhances T c in the underdoped regime, whereas, the effect of pressure on T c is rather small in the optimally doped and overdoped regimes. 12,13For the "111"-type Fe-pnictides, it is reported that the transition temperature of LiFeAs is suppressed linearly with pressure 14 , whereas, T c of Na 1−x FeAs polycrystal can be enhanced up to 31 K at about 3 GPa. 15This difference is attributed to the different ionic radius between Li and Na.However, in former high-pressure study the superconducting transition is rather broad due to the highly hygroscopic nature of polycrystalline NaFeAs sample.In order to study the intrinsic properties of this system, it is of great interest to investigate the combined effect of doping and pressure on superconducting properties of single-crystal samples.In this paper, we report the results of resistivity measurements under hydrostatic pressure for single-crystalline NaFe 1−x Co x As, tracking T c as a function of both pressure and doping level in different regions of the phase diagram.The initial slope of the pressure dependence of T c , (dT c /dP ) P=0 , is positive in the whole superconducting doping regime of phase diagram.The value of pressure coefficient is comparably large among Fe-pnictides, even in the overdoped region.For the nonsuperconducting extremely overdoped sample, the pressure effect is negligible.T offset c as high as 31 K, generally consistent with the maximum T c under pressure in polycrystalline NaFeAs, can be reached in both underdoped and optimally doped samples.The identical maximum T c under pressure in different doping regions indicates that there is a universal maximum transition temperature of about 31 K in electron-doped NaFeAs, which can be obtain by applying high pressure or combined effect of pressure and doping.

II. EXPERIMENTAL DETAILS
High-quality NaFe 1−x Co x As single crystals were grown by the conventional high temperature solution growth method using the NaAs self-flux technique.Details of the growth procedures were provided in our previous work. 7Electrical resistivity was measured using the ac four-probe method.Pressure was generated using a Be-Cu pressure cell with a Teflon cup which was filled with Daphene Oil 7373.The pressure applied in the resistivity measurement was determined by shift of the superconducting transition temperature of pure Sn. 16 The magnetic susceptibility was measured under pressure up to 6.1 GPa in a diamond anvil cell (DAC).The pressure transmitting medium was Daphene Oil 7373 and the pressure was measured at room temperature by ruby fluorescence spectroscopy.The resistivity measurements were performed using a Quantum Design physical properties measurement system (PPMS-9), and the magnetic susceptibility was measured using a superconducting quantum-interference device magnetometer (SQUID-MPMS-7T, Quantum Design).

III. RESULTS AND DISCUSSION
Fig. 1(a) shows the temperature dependence of resistivity for NaFeAs under different pressures.Two anomalies in the resistivity curve are observed at 51 K and 41 K under ambient pressure, which are consistent with previous reports. 5These anomalies have been proved by neutron scattering experiment to arise from the structural and SDW transition, respectively. 6With increasing pressure the anomalies corresponding to the SDW transition is gradually suppressed to lower temperature, whereas the structural transition quickly becomes undetectable.The suppression of the resistive anomalies can also be seen in the derivative of resistivity shown in Fig. 1(c).We use the same criteria to infer the structural and SDW transitions from the resistivity as described in Ref.17, which has been confirmed by specific heat and magnetic susceptibility measurements. 7As shown in Fig. 1(b), the superconducting transition is rather broad, and the three transitions take place in a narrow temperature range, thus it is difficult to define the T onset c .We use the criterion T offset c to describe the superconducting transition temperature in this paper, the definition of which is shown in Fig. 1(b).With the applied pressure increasing, T offset c firstly decreases slightly, then increases quickly with pressure higher than 1 GPa.The highest T offset c we can achieve is 11.9 K at P = 1.79 GPa.The data of NaFeAs under pressure are summarized in Fig. 1(d).The phase diagram T(P ) is similar to that of underdoped Ba(Fe 1−x Co x ) 2 As 2 12 , in which T SDW is suppressed gradually while superconductivity is enhanced by applied pressure.For the underdoped sample NaFe 0.99 Co 0.01 As with T offset c ∼16K, the kinks in resistivity curves associate with the structural and SDW transition are distinct at ambient pressure.Once the external pressure is applied, the kinks quickly become obscure and then indistinguishable, similar to the case in doped 122-system. 12As shown in Fig. 2(a), the low-temperature resistive upturn corresponding to the structural and/or magnetic transition are progressively suppressed, and ultimately vanished at P = 2.05 GPa, at which the highest superconducting transition temperature about 30.7 K is obtained.The criteria used to determine the onset and offset temperature of superconducting transition are shown in Fig 2(b).Since the onset temperature of superconductivity is ambiguous in NaFe 1−x Co x As, we write T c for T offset c for convenience hereafter.As reported in underdoped Ba(Fe 1−x Co x ) 2 As 2 , the critical pressure at which the high temperature transition disappears coincides rather well with the pressure at which T c is highest and the superconducting transition is narrowest. 13The pressure coefficient dT c /dP is 9.6 K/GPa below 1.28 GPa, and the pressure coefficient between ambient and the pressure at which T c reaches its maximum is 7.06 K/GPa, even larger than the pressure coefficient of FeSe (3.2 K GPa −1 ). 11The pressure effect coefficient based on the T onset c is about 4.7 K/GPa which is still relatively large in iron pnictides.In the phase diagram shown in figure 2(d), it is obvious that the superconducting transition width become narrower with increasing the pressure.The sharp superconducting transition observed at 2.05 GPa indicates that the pressure condition is still hydrostatic.For the optimally doped sample NaFe and comparable with 5 K/GPa in optimally doped LaFeAsO 1−x F x . 10In order to establish the complete superconducting dome in the phase diagram.We carried out the magnetic susceptibility measurement using the diamond anvil cell (DAC) technology.Pressures up to 6.1 GPa were applied on NaFe 0.972 Co 0.028 As single crystal.The T M c values under various pressures are determined from the beginning of deviation from the extrapolated line of the normal state M -T curve as shown in Fig. 3(c).Fig. 3(d) displays the T (P ) phase diagram based on the resistivity and magnetic susceptibility measurements.The T M c measured by DAC technology initially increases monotonously, and begins to decrease when pressure is higher than 2.3 GPa.The behavior of transition temperature obtained by resistivity and magnetic susceptibility are highly consistent with each other.The highest transition temperature obtained by our measurement is 31.0K, where the transition width is 0.5 K which is considerably sharp.The T c = 31.0K presented here is the highest in the 111 system up to now.The superconducting transition temperature of this overdoped sample is 11.5 K at ambient pressure.Similar to the case in optimally doped NaFe 0.972 Co 0.028 As, the T c increases monotonously up to 24.5 K with increasing the applied pressure to 2.32 GPa.Domelike shape of T c (P ) was revealed by magnetic susceptibility measurement, from which we can infer that the highest superconducting transition temperature in NaFe 0.925 Co 0.075 As is about 24.5 K with the uncertainty less than 1 K.A large enhancement of T c by 13 K, which is comparable to those in underdoped and optimally doped samples, is still exist in this overdoped composition.The pressure coefficient of NaFe 0.925 Co 0.075 As is 5.57 K/GPa, even higher than that of the optimally doped sample.The large pressure coefficient of overdoped NaFe 0.925 Co 0.075 As is obviously different from those in other iron-pnictide superconductors, which are rather small or change their sign from positive to negative in the overdoped regime in the phase diagram.When external pressure was applied on the extremely overdoped sample NaFe 0.891 Co 0.109 As which shows no superconductivity down to 2 K at ambient pressure, we cannot observe the pressure-induced superconductivity with applied pressure up to 2.32 GPa.Besides, both the magnitude and the behavior of the resistivity do not change much with the applied pressure.
The effect of applied pressure on the superconducting transition temperature of NaFe 1−x Co x As is illustrated in Fig. 6(a), where the maximum T c under pressure and T c at ambient pressure are plotted as a function of doping level x.Because the maximum transition temperature has not been reached in undoped NaFeAs, we use the maximum value reported by Zhang et al. for this composition. 15Large positive pressure coefficient dT c /dP is observed in all the superconducting compositions, even in the overdoped regime.The maximum tran- sition temperatures in NaFeAs, NaFe 0.99 Co 0.01 As and NaFe 0.972 Co 0.028 As are all around 31 K. T (P ) phase diagram of NaFe 1−x Co x As system for various x is shown in Fig. 6(b).It is obvious that the maximum transition temperature in undoped, underdoped and optimally doped sample is strikingly the same.These results indicate that there is a universal maximum transition temperature in NaFe 1−x Co x As of about 31 K, which can be achieved by applying a critical pressure of P = 2-3 GPa.
For the undoped and underdoped samples, applied external pressure suppresses the structural and SDW transitions, and enhances superconductivity simultaneously.This behavior is similar to the pressure effect in LaFeAsO 1−x F x 10 and 122-systems. 12,19,21,22Although the T c and normal state resistivity behavior evolve systematically with Co doping, the maximum transition temperature enhancement and corresponding critical pressure is nearly the same in all the superconducting samples.These properties are different from the case in most of the iron based superconductors that pressure effect is different in different regions of electronic phase diagram.An identical maximum T c of 31 K un-der doping as well as pressure has also been reported in BaFe 2 (As 1−x P x ) 2 . 23In the P doped Ba-122 system, phosphorous substitution could be regarded as chemical pressure, which changes Fe-Pn distance and causes similar effects on superconductivity to the physical pressure.Though the Co substitution in NaFeAs is referred to as electron doping, different from the replacement of As by P which is referred to as isovalent substitution, it is likely that the pressure-induced enhancement of T c in NaFe 1−x Co x As is also associated with the optimization of the structural parameters of FeAs layers, including the As-Fe-As bond angle and anion height. 24One possible reason for lower maximum transition temperature obtained in overdoped NaFe 0.925 Co 0.075 As single crystal is that the superconductivity is disturbed by the disorder or additional scattering induced by excess cobalt doping.This phenomenon is different from the case of overdoped LaFeAsO 1−x F x , in which the conducting layer is not affected by F doping and the highest transition temperature acquired in optimal and overdoped samples are almost the same. 10he overdoped superconducting sample NaFe 0.925 Co 0.075 As still has considerable positive pressure coefficient which is rare in Fe-pnictide superconductors.However, when the pressure is applied on the extremely overdoped non-superconducting sample, no superconductivity induced by pressure can be observed.It has also been reported that temperature linear dependent susceptibiltiy can be observed in high temperatures for all the superconducting samples and the breakdown of the temperature linear dependent susceptibility in the overdoped region coinciding with the disappearance of superconductivity. 7These phenomena indicate that there is a sudden change in the electronic structure between the superconducting compositions and the heavily overdoped non-superconducting phase.This conclusion is supported by the experimental results of STM investigations 25 and the angle-resolved photoemission spectroscopy (ARPES) studies. 26The STM study revealed that the high energy dI/dV spectra of superconducting NaFe 1−x Co x As remain nearly the same, whereas, the high energy spectrum suddenly started to shift to the lower energy substantially for the sample with x = 0.109.The direct measurements of the electronic structure of NaFe 1−x Co x As by ARPES revealed that all the superconducting NaFe 1−x Co x As compounds have similar band structures and small relative Fermi level shifts.However, the x = 0.109 compound in the heavily overdoped regime shows a large Fermi level shifts (about 100 meV) relative to the optimally doped compounds, and its band structure is significantly changed as the hole-like bands around the zone center disappears and an electron pocket appears instead, which means the consequent Fermi surface consists of electron pockets only in this sample.The drastic change in electronic structure for the heavily overdoped nonsuperconducting samples could explain the observed properties of pressure effect.

IV. SUMMARY
In conclusion, we have performed resistivity and magnetic susceptibility measurements under various pressure on NaFe 1−x Co x As (x=0, 0.01, 0.028, 0.075, 0.109) single crystals.In the undoped and underdoped compounds, structural and SDW transitions are gradually suppressed while superconductivity is enhanced by applied external pressure.A universal maximum transition temperature of about 31 K under external pressure is observed in underdoped and optimally doped NaFe 1−x Co x As.The superconducting transition temperature of NaFe 1−x Co x As is strongly enhanced in the whole superconducting regime of the phase diagram, and the pressure effect is considerably large compared to other iron pnictides.The large positive pressure coefficient in the optimally and overdoped region is different from that in Ba(Fe 1−x Co x ) 2 As 2 , and disappears simultaneously with the superconductivity in the phase diagram.These results could be explained as originated from the similarity of electron structures within the superconducting dome, and a drastic change of the electron structures between the superconducting overdoped regime and the non-superconducting heavily overdoped regime, which correspond to the conclusions of STM and ARPES measurements.

FIG. 1 :
FIG. 1: (color online).(a): Temperature dependence of in plane resistivity for NaFeAs under different pressures.Arrow indicates the direction of the increasing pressure.(b): Expanded plot of the temperature dependence of resistivity under various pressure around Tc. (c): The derivative of the in-plane resistivity dρ/dT and the criteria by which we infer Ts and TSDW.(d): TC and TSDW as a function of pressure for the parent compound NaFeAs.

FIG. 2 :
FIG. 2: (color online).(a): Temperature dependence of the resistivity under different pressures up to 2.05 GPa for NaFe0.99Co0.01As,normalized to the room temperature value.Each subsequent data set is shifted downward by 0.1 for clarity.(b): Enlargement of the low temperature resistivity and the criteria used to determine the onset and offset temperatures for the superconducting transitions.(c): TC as a function of pressure for the underdoped crystal NaFe0.99Co0.01As.

FIG. 3 :
FIG. 3: (color online).(a) Temperature dependence of in plane resistivity for NaFe0.972Co0.028Asunder various pressures.Data are shown normalized by room temperature resistivity, successive data sets are offset vertically by 0.1 for clarity.(b) The data in panel (a) is plotted in low temperature range for clarity.(c): The plot of Magnetic susceptibility as a function of temperature in zero-field cooled measurements up to 6.1 GPa.(d): Evolution of Tc determined by resistivity and susceptibility measurements with the applied pressure.

FIG. 4 :
FIG. 4: (color online).(a): Temperature dependence of in plane resistivity for NaFe0.925Co0.075Asunder various pressures, Successive data sets are offset vertically by 0.1 for clarity.(b): The same data shown in (a) around the superconducting transition.(c): Temperature dependence of magnetic susceptibility under different pressures for NaFe0.925Co0.075As.(d): The TC obtained from resistivity and susceptibility measurements as a function of pressure.

Fig. 4 (
Fig.4(a) and Fig.4(c) display the pressure dependence of the in-plane resistivity and magnetic susceptibility

FIG. 6 :
FIG. 6: (color online).(a): Comparison of Tc at ambient pressure and the maximum Tc achieved under applied pressure at various Co concentrations.The open square represent the T onset c reported by Zhang et al. 15 (b): T (P ) phase diagram of NaFe1−xCoxAs with different doping levels.Open and filled symbols represent data obtained from susceptibility and resistivity measurements, respectively.
0.972 Co 0.028 As, the anomalies associated with the structural or SDW transition are suppressed completely by Co doping.As shown in Fig.3(a), T c measured by in-plane resistivity increases monotonously from 20.4 K to 31.0K with increasing the applied pressure from zero to 2.28 GPa.The pressure coefficient is 4.67 K/GPa, much larger than 1 K/GPa in optimally doped Ba(Fe 1−x Co x ) 2 As 2 12 12,[18][19][20]