Individual molecule description of kappa-type organic charge transfer salts

Transcription

1 Individual molecule description of kappa-type organic charge transfer salts Daniel Guterding Institut für Theoretische Physik Goethe-Universität Frankfurt am Main Germany June 21, 2016 SFB/TR 49 1 / 21

2 Outline 1 Crystal structure, Electronic structure, Phase diagram 2 Cooling-rate dependent metal-insulator transition 3 Superconducting state 4 Ab-initio calculations 5 Modelling 6 Explanation for the cooling-rate dependent MIT 7 RPA calculations for the superconducting state 8 Conclusion 2 / 21

3 Crystal structure of organic charge transfer salts ET = BEDT-TTF = bis(ethylene-dithio)-tetrathiafulvalene is the electron donor X is the electron acceptor [e.g. Cu(NCS) 2 ] ET molecules can be packed in different patterns κ-phase often superconducting features (ET) 2 dimers that donate one electron to acceptor layer here we concentrate on κ-(et) 2 X Müller, ChemPhysChem 12, 1222 (2011) 3 / 21

4 Electronic structure of κ-(et)2 X two-dimensional electronic structure in the ET-plane anion layer has filled shells (e.g. Cu d10 ) bands at Fermi level only from organic molecules often modelled by 1/2-filled anisotropic triangular lattice of dimers Fermi surface is an ellipse larger than the first BZ E (ev) alternative is 3/4-filled individual molecule model on complicated lattice π 0.25 ky π M X Γ Y M Γ Z -π 0 kx π Ferber, Foyevtsova, Jeschke, Valentı, PRB 89, (2014) 4 / 21

5 Properties of κ-(et) 2 X AFI to SC transition with pressure or variation of X ( chemical pressure ) spin- 1 /2 smeared out over (ET) 2 dimer in AFI state almost perfect triangular lattice in κ-(et) 2 Cu 2 (CN) 3, quantum spin-liquid nature of the superconducting state? no phase sensitive probes as in cuprates, problems with sample preparation critical endpoint of the MIT line freezing of intramolecular degrees of freedom around 100 K Müller, ChemPhysChem 12, 1222 (2011); Kino, Fukuyama, JPSJ 65, 2158 (1996) 5 / 21

6 Cooling-rate dependent Metal-Insulator transition ground state can be tuned by deuteration ethylene end group orientations metastable: parallel (eclipsed) and canted (staggered) glass transition for ethylene endgroups metal-insulator transition can be studied in one sample without application of pressure Hartmann, Müller, Sasaki, PRB 90, (2014) 6 / 21

7 Experimental results for the SC order parameter experimentalists assume fourfold rotationally invariant order parameter all experiments subtract twofold rotationally invariant background almost all experiments agree on presence of nodes, try to determine locations both d xy and d x 2 y 2 exist in experiment have been concluded to multitude of disagreeing experiments top panel result from magnetocalorimetry, bottom panel results from thermal conductivity Malone, Taylor, Schlueter, Carrington, PRB 82, (2010); Izawa, Yamaguchi, Sasaki, Matsuda, PRL 88, (2002) 7 / 21

8 New results from scanning tunneling spectroscopy first time that clean surface was used more than one set of nodes in one sample consistent with both d xy and d x 2 y 2 phase separation? insulating patches in SC matrix known for κ-(et) 2 X proximity of d xy to AFI makes sense, square lattice physics how to explain d x 2 y 2 phase? Oka et al., JPSJ 84, (2015) 8 / 21

9 Ab-initio calculations for organic charge transfer salts all-electron full-potential DFT calculations (FPLO) more than 100 atoms per unit cell molecular orbital TB Hamiltonians from projective Wannier functions four hopping parameters sufficient t 2 /t 1 [0.538, 0.661], t 3 /t 1 [0.289, 0.404], t 4 /t 1 [0.099, 0.220] Guterding, Altmeyer, Jeschke, Valentí, arxiv: ; Ferber, Foyevtsova, Jeschke, Valentí, PRB 89, (2014) 9 / 21

10 Relation between Dimer and Molecule model original lattice structure encoded in molecule model traditionally dimer-approximated anisotropic triangular lattice is used one-band instead of four-band model averaging of t 2 and t 4 introduces C 4 -symmetric hopping BZ can be unfolded from two- to one-band model (a) t 1 t 2 t 3 t 4 (b) t t' dimer approx. t=( t 2 + t 4 )/2 t'= t 3 /2 y x Guterding, Altmeyer, Jeschke, Valentí, arxiv: / 21

11 Brillouin zones and superconducting order parameters physical BZ is that of four- or two-band model larger unfolded BZ and 45 deg. rotation in one-band model natural SC order parameter of square lattice is d x 2 y 2 becomes d xy in physical BZ we label SC states in physical BZ (a) k y k x (b) 2- and 4-band (c) 1-band physical small BZ model large BZ d xy d x 2 -y 2 (d) (e) d x d 2 -y 2 xy k k y k y x k x Guterding, Altmeyer, Jeschke, Valentí, arxiv: / 21

12 Phase diagram of the anisotropic triangular lattice model t /t controls frustration on-site interaction term H int = U i n i n i AFI, M, QSL and SC phases reproduced not all methods agree on phase boundaries and existence of SC top plot is PIRG, bottom plot is CDMFT (most extreme examples for disagreement) many studies find same SC order parameter as in cuprates (d xy ) are d x 2 y 2 experiments wrong? side note: intra-dimer charge ordering observed Morita, Watanabe, Imada, JPSJ 71, 2109 (2002); Kyung, Tremblay, PRL 97, (2006) 12 / 21

13 Phase diagram of the molecule model top panel HF, bottom panel FLEX HF reproduces important phases antiferromagnetic metal disappears for large dimerization SC order parameter changes as function of dimerization strength very few studies, no complete phase diagram influence of parameters aside from dimerization not studied Kino, Fukuyama, JPSJ 65, 2158 (1996); Kuroki, Kimura, Arita, Tanaka, Matsuda, PRB 65, (R) (2002) 13 / 21

14 Influence of molecular conformations on the electronic structure relax ethylene endgroups and adjacent sulfur atoms in DFT relaxed endgroups influence hopping amplitudes and Hubbard repulsion C t4 t1 staggered endgroups have larger t0 /t, U/t S H eclipsed analyze within dimer model relaxed fixed t2 0.9 t /t S 0.8 t3 staggered 0.7 t4 t1 E 0.6 S t2 S 0.5 κ-(et)2cu2(cn)3 κ -(ET)2Cu[N(CN)2]Cl κ-(et)2cu[n(cn)2]br κ-(et)2cu[n(cn)2]i, T=127 K κ-(et)2cu[n(cn)2]i, T=295 K S E 0.4 E E E S t U/t 7.5 Guterding, Valentı, Jeschke, PRB 92, (R) (2015) 14 / 21

15 Tight binding+rpa formalism in a nutshell χ pq st ( q) = 1 N H = H 0 + H int = ijσ k,µ,ν t ij (c iσ c jσ + h.c.) + U n iσ n i σ 2 a s µ( k)a p µ ( k)a q ν( k+ q)a t ν ( k+ q) f(e ν( k + q)) f(e µ ( k)) E ν ( k + q) E µ ( k) [ (χ RPA spin ) pq st [ 3 Γ pq st ( k, k ) = 2 U s χ RPA s Γ ij ( k, k ) = stpq ] 1 = [χ pq st ] 1 (U spin ) pq st ( k k ) U s U s 1 2 U c χ RPA ( k k )U c U c [ ] i ( k)ai s ( k)re Γ pq st ( k, k ) a p j ( k )a q j ( k ) a t c iσ ] tq ps j Cj dk 2π 1 4π v F ( k ) [ ] Γ ij ( k, k ) + Γ ij ( k, k ) g j ( k ) = λ i g i ( k) Graser, Maier, Hirschfeld, Scalapino, NJP 11, (2009) 15 / 21

16 Susceptibility and order parameter: connecting the molecule and dimer models at finite dimerization q2 q1 dimer model physics is reproduced in molecule model for t4 /t2 1 averaging of transfer integrals is crucial, not only dimerization strength additional set of nodes close to ky = 0 solution identified as s± + dx2 y2 main features are q1 and q2 Guterding, Altmeyer, Jeschke, Valentı, arxiv: / 21

17 Connection between susceptibility features and hopping parameters s 1 : cos k x + cos k y s 2 : cos k x cos k y d x 2 y 2: cos k x cos k y q 2 d xy : sin k x sin k y q 1 feature q 1 controlled by t 3 feature q 2 controlled by t 2 and t 4 increase of t 4 /t 2 makes q 2 more square-like, drives d xy q 2 s 2,d xy s 1,d x 2 -y 2 q 1 t 1 t 2 t 3 t 4 y x Guterding, Altmeyer, Jeschke, Valentí, arxiv: / 21

18 Pairing phase diagram of κ-(et) 2 X [1] κ-(et) 2 Ag(CF 3 ) 4 (TCE) [2] κ-(et) 2 I 3 [3] κ-(et) 2 Ag(CN) 2 H 2 O [4] κ-α 1 -(ET) 2 Ag(CF 3 ) 4 (TCE) phase transition from d xy to s ± + d x 2 y 2 dimerization plays only minor role competition between t 2, t 4 and t 3 controls phases many materials close to phase transition additional set of nodes appears there some experimental reports of d xy might have picked up those near-degeneracy of d xy and s ± + d x 2 y 2 in most materials (a) 0.5 t 3 / t (c) 0.5 t 3 / t 1 λ s ± +d x 2 -y 2 d xy 5 8 t 4 /t 1 = 0.10 (b) t 2 / t 1 7 t 4 /t 1 = 0.20 (d) [5] κ-(et) 2 Cu(NCS) 2 [6] κ-α 2 -(ET) 2 Ag(CF 3 ) 4 (TCE) [7] κ-(et) 2 Cu[N(CN) 2 ](CN) [8] κ-(et) 2 Cu[N(CN) 2 ]Br t 4 /t 1 = t 2 / t 1 3 t 4 /t 1 = 0.25 t 4 /t t 2 /t 1 =0.5 t 3 /t 1 =0.33 s ± +d x 2 y 2 d xy t 4 /t 2 Guterding, Altmeyer, Jeschke, Valentí, arxiv: / 21

19 Connection to experiment: scanning tunneling spectroscopy ( k) = 0 [c s1 (cos k x +cos k y )+c d1 (cos k x cos k y )+c s2 (cos k x cos k y )] ρ qp (E, Γ) k E + iγ Re (E + iγ) 2 ( k) 2 S(V) = 1 B(V)T(V) di(v) dv de [ρ qp(e)(1 x) + x] df(e+ev) dv simulate tunneling conductivity from quasiparticle DOS calculate QP DOS from Fermi surface approximation, FS not concentric circle introduce small broadening discriminates d x 2 y 2 and d xy Guterding et al., PRL 116, (2016) 19 / 21

20 Simulation of STS for the different SC states three different nodal states s ± + d x 2 y 2 with four nodes s ± + d x 2 y 2 with eight nodes close to phase transition d xy state in square-like regime QP DOS somewhat similar, but different slopes (mev) ρ qp (arb. units) (a) π k y -π 0 s ± +d x 2 -y 2, four nodes β node maxima -π 0 k x π 8 β t 3 = A B ϕ (deg.) B A E-E F (mev) A B (b) α s ± +d x 2 -y 2, eight nodes β nodes maxima C -π 0 k π x α β A B ϕ (deg.) A B t 3 =0.35 C B A E-E F (mev) C (c) δ γ δ nodes d xy maxima -π 0 k π x γ δ D E ϕ (deg.) D E t 3 =0.25 E D E-E F (mev) Guterding, Altmeyer, Jeschke, Valentí, arxiv: / (mev)

21 Summary κ-(et) 2 X materials offer extraordinary tunability we calculated kinetic part of models for many κ-type materials dimer model describes phase diagram to first approximation blocked further progress regarding SC state molecule model mostly unexplored (spin-liquid, influence of V on phase boundaries) References Guterding, Valentí, Jeschke, PRB 92, (R) (2015) Guterding et al., PRL 116, (2016) Guterding, Altmeyer, Jeschke, Valentí, arxiv: / 21

22 Electronic bandstructure for different ethylene endgroup configurations E [ev] E [ev] κ-(et) 2 Cu 2 (CN) 3 staggered eclipsed κ -(ET) 2 Cu[N(CN) 2 ]Cl staggered eclipsed -0.6 M Y Γ X M Γ Z T Y Γ Z T Γ X κ-(et) 2 Cu[N(CN) 2 ]Br κ-(et) 2 Cu[N(CN) 2 ]I 0.3 staggered staggered 0.15 eclipsed eclipsed M Z Γ X M Γ Y M Z Γ X M Γ Y Guterding, Valentí, Jeschke, PRB 92, (R) (2015) 22 / 21

23 STS data for κ-(et)2 [N(CN)2 ]Br tunneling parallel to conducting layers background DOS is modelled by Anderson-Hubbard model φ c c Guterding et al., PRL 116, (2016) 23 / 21

24 Alternative fits for STS data 1.1 s + d x 2 y 2 and s ± + d x 2 y2 equally good meaning of plain s-wave component? 1/[B(V)T(V)] di/dv (arb. units) K exp. s ± +d x 2 -y 2 s+d x 2 -y 2 s+d xy E-E F (mev) Guterding et al., PRL 116, (2016) 24 / 21

25 Calculating the quasiparticle DOS use gap calculated from RPA and TB bands or Fermi surface full calculation uses bandstructure and tetrahedron method quasiparticle calculation uses Fermi surface only excellent agreement in relevant energy window LDOS (arb. units) unbroadened e - broadened e - quasiparticle E-E F (mev) Guterding et al., PRL 116, (2016) 25 / 21