Anomalous Scaling Relations & Pairing Mechanism of Fe-based SC

Transcription

1 Part III: SH jump & CE Anomalous Scaling Relations & Pairing Mechanism of Fe-based SC Yunkyu Bang (Chonnam National Univ., Kwangju, S Korea) G R Stewart (Univ. of Florida, Gainesville, USA) Refs: New J Phys, 18, (2016) arxiv:

2 We believe : IBS are Unconventional Superconductors

3 Common Phase diagram of unconventional SCs cuprate heavy fermion CeRhIn 5 Fe-122( BaFe2 As2)

4 Popular belief of paradigm : -- Strong correlation QCP (?) NFL normal state Un-conventional SC (perhaps high-t c ) Un-conventional pairing mechanism (non-bcs type?)

5 Thermodynamic Evidences for Unconventional Superconductivity of IBS.

6 Two anomalous (non-bcs) scaling behaviors in IBS : C vs. T c & E vs. T c indication of non-bcs pairing mechanism. T c (K) HH Wen et al, PRB 89, (2014) E» T 3:5 c Bud ko et al, PRB 79, (2009) C» T 3 c

7 BNC scaling: C ~ T c 3

8 BNC scaling Does it mean new physics (or at least Non-BCS pairing mechanism)? C=T c» Tc 2 or ( C» Tc 3 )» T 2 c BCS theory C=T c» 1:43

9 (1) Zaanen claimed (prb 80, (2009): C ~ T c3 is a reflection of C normal ~ T 3 QCP critical fluctuations is the main contribution to C(T) Hyperscaling assumption from 2 nd derivative of F s QCP therefore, C» T 3 if z = 1 for d = 3: Z=1 means dim( )=dim(q) : eg. AFM Spin wave No experimental evidence for ~ cq excitations over the whole doping range.

10 Some deviation exist, too. e.g. (Ba,K)Fe 2 As 2 Contrast between two hole doped Ba(K,Na)Fe 2 As 2 Na_ imp stronger than K_ imp

11 Our Theory of C : A hint from multi band theory C = N h (0) ³ d 2 dt h Tc + N e (0) ³ d 2 dt e Tc ±S-wave Two band SC mediated by V inter-band >> V intra-band

12 One band BCS theory ³ d C = N(0) 2 dt Tc 2 BCS (T) ¼ (3:06)2 T 2 c (1 T=T c ). C=T c» N 0 T c =! D exp[ 1 V N(0) ] Two band (BCS) model If V inter À V intra, N tot = N h + N e ; ¹ Nh;e = N h;e N tot

13 Our Model (1) Two band BCS SC + (2) Doping assumption N tot = N h +N e =const. N tot =const. can be relaxed.

14 (1) Minimal Two Band model => S gap solution Pairing interaction All repulsive V ab >0 V inter-band > V intra-band Coupled Gap Eq.

15 (2) Modeling of Doping» T 2 c undoped BaFe 2 As 2 : compensated metal hole carriers = electron carriers (N h N e )

16 (2) Modeling of Doping: Rigid band model Elec. doping N h < N e No doping N h N e hole doping N h > N e With doping, the FS size, N h,e (=N tot N e,h ) changes, but keeping N tot = N h +N e =const. h-band e-band x Co, Ni doping electron doping K, Na doping 2016 POSTECH hole doping Lectures Sato et al., PRL 103, (2009)

17 Results

18 Calculations of T c with varying N h Pairing interaction V eff varies strongly with doping. Simple model captures the Dome -shape T c phase diagram for whole doping range.

19 Calculation of C & T c with doping N h Results with V intra =0: Some deviation. How to cure?

20 Calculation of C including impurity: Gofryk et al. PRB Imp. Effects: Skalski et al., 136, A1500 (1957) (Non pair-breaking + pair-breaking) So, mainly q.p. damping

21 Results of C including impurity: Continuous evolution of the slope with imp. Strong deviation. (clean limit) (BaK)Fe 2 As 2 Perfect BNC scaling (non clean): (BaNa)Fe 2 2As 2, Ba(FeCo) 2As 2

22 Condensation E: E ~ T c 3.5

23 Condensation Energy : E = E n - E sc E» T 3:5 c T c (K) E BCS» T 2 c HH Wen et al, PRB 89, (2014) Evidence of the Non-BCS pairing mechanism?

24 Condensation Energy: E cond = E normal - E sc C/T T c T S(T) T

25 BCS calculations of E cond E =< H > s < H > n H = KE + P E (1) = X k;¾»(k)c y k;¾ c k;¾ + X k;l V k;l c y k;" cy k;# c l;#c l;" (2) BCS theory KE = [ 2 V 1 2 N(0) 2 ] > 0 1 E = PE = 2 N(0) 2 < 0 2 V < 0 using BCS ¼ T c. E BCS» T 2 c Subtle balance btw KE & PE HH Wen et al, PRB 89, (2014)

26 Condensation Energy of Two band BCS model with V he = V eh = V inter ; V ee = V hh = V intra E =< H > s < H > n 6= 1 2 N h 2 h 1 2 N e 2 e

27 Calculation with V intra =0 Calculations Experimental results Genuine two band model (V intra =0) follows E» T 3 c, but not» T 3:5 c

28 Effect of V intra 0 1. Attractive V intra (<0) makes E more BCS-like ( T c 2 ) 2. Repulsive V intra (>0) makes E steeper ( T c 3 )

29 General Trend of the Scaling relations of E vs T c 1. Ising or Heinsenberg magnet (MFT): E ~ T c ~ O(J) KE=0 and E= PE 2. BCS SC: E ~ T c 2 KE > 0, PE <0 and E= KE + PE KE = [ 2 V 1 2 N(0) 2 ] > 0 PE = 2 V < 0 Speculation: E ~ T c β (β > 2) if KE loss >> PE gain Indeed, this is the case for the multiband superconductor PE gain is not fully exploited.

30 = 2 Single band BCS : KE s > 0 PE s <0 > 2 (c) KE = KE s, PE < PE s (d) KE = KE s, PE << PE s (e) Reduces to a single band N channels of V inter N(N-1) channels of V intra

31 Impurity scattering makes E vs. T c steeper. because the imp effect suppresses more effectively h,e than T c.

32 Conclusions: 1. BCS theory of two band model straightforwardly reproduces the anomalous power laws of C vs. T c and E vs. T c. 2. It is almost impossible to invent any other theories to explain these two scaling behaviors simultaneously. 2. Strong Correlation Effects in Normal state do exist in Fe-based SC compounds. And it renormalizes : pairing interactions (V inter, V intra ), q.p. m *, N ren, etc 3. However, the SC transition itself seems to follow the conventional BCS pairing mechanism. 4. Shall we call them BCS SC?

33 Previous theories to explain C ~ T c 3 : Kogan, Zaanen, and Chubukov et al.

34 (1) Zaanen claimed (prb 80, (2009): C ~ T c3 is a reflection of C normal ~ T 3 QCP critical fluctuations is the main contribution to C(T) Hyperscaling assumption from 2 nd derivative of F s QCP therefore, C» T 3 if z = 1 for d = 3: Z=1 means dim( )=dim(q) : eg. AFM Spin wave No experimental evidence for ~ cq excitations over the whole doping range.

35 (2) Kogan PRB 81, (2010) : C ~ T c3 is a general behavior of very dirt limit superconductors if À T c However, we believe that this claim is based on the inconsistent approximation. In BCS, if << T c F / N(0) 4 Tc 2 2 BCS (T) ¼ T c 2 (1 T=T c ). Kogan s app, if >> T c F / N(0) BCS (T) ¼ T 2 c (1 T=T c ). C=T c 2» N(0) Correct app, for >> T c F / N(0) dirty (T) ¼ 2 (1 T=T c ). C=T c 2» N(0) 2 T 2 c

36 (3) Chubukov+coworkers (PRB 84, (2011)) focused only on SDW+SC region. Simply showed that when SDW order M develops, C steeply decreases. Solved coupled gap Eq with M AFM & sc Probably, not very wrong, but not much information

37 One band BCS theory ³ d C = N(0) 2 dt Tc 2 BCS (T) ¼ (3:06)2 T 2 c (1 T=T c ). C=T c» N 0 T c =! D exp[ 1 V N(0) ] Two band (BCS) model If V inter À V intra, C=T c ; T c can strongly vary even with N tot = const: N tot = N h + N e ; ¹ Nh;e = N h;e N tot