History, Present, Future: Functional RG for unconventional - PowerPoint PPT Presentation

History, Present, Future: Functional RG for unconventional superconductors Ronny Thomale Julius-Maximilians Universität Würzburg Topolectrics SPP 1458 SFB 1170 “Functional Renormalization - from quantum gravity and dark energy to ultracold atoms and condensed matter” Wednesday, March 8, 17

Unconventional superconductors Wednesday, March 8, 17

Outline Wednesday, March 8, 17

Outline History - Timeline of materials studied through FRG - Recent methodological step: multi-band/orbital superconductivity Wednesday, March 8, 17

Outline History - Timeline of materials studied through FRG - Recent methodological step: multi-band/orbital superconductivity Present - Pnictides: extended d-wave vs. extended s-wave - Sodium cobaltates: chiral d-wave? Wednesday, March 8, 17

Outline History - Timeline of materials studied through FRG - Recent methodological step: multi-band/orbital superconductivity Present - Pnictides: extended d-wave vs. extended s-wave - Sodium cobaltates: chiral d-wave? Future - SrPtAs: Weyl superconductors - LAO/STO heterostructures Wednesday, March 8, 17

History Wednesday, March 8, 17

Timeline Wetterich Schulz Honerkamp, Salmhofer Thomale ’93 ’99 ’01 ’09 ‘84 ’94 ’08 ’11 ’00 Polchinski Shankar Metzner Fa Wang Qianghua Wang Wednesday, March 8, 17

Timeline Wetterich Schulz Honerkamp, Salmhofer Thomale ’93 ’99 ’01 ’09 Platt, Hanke, Thomale ‘84 ’94 ’08 ’11 ’00 Advances in Physics Polchinski Shankar Metzner Fa Wang Qianghua Wang Vol. 62, p. 453-562, 2014 Wednesday, March 8, 17

Harmonic composition of SC form factors ∆ i,j ⇠ h c † i c † The favored real space pairing function j i transforms under irreducible point group representations Wednesday, March 8, 17

Harmonic composition of SC form factors ∆ i,j ⇠ h c † i c † The favored real space pairing function j i transforms under irreducible point group representations s Wednesday, March 8, 17

Harmonic composition of SC form factors ∆ i,j ⇠ h c † i c † The favored real space pairing function j i transforms under irreducible point group representations s d x2-y2 Wednesday, March 8, 17

Harmonic composition of SC form factors ∆ i,j ⇠ h c † i c † The favored real space pairing function j i transforms under irreducible point group representations s d x2-y2 The point group representation does not fix the form of the superconducting gap function, even without further symmetry breaking Wednesday, March 8, 17

Harmonic composition of SC form factors ∆ i,j ⇠ h c † i c † The favored real space pairing function j i transforms under irreducible point group representations s d x2-y2 The point group representation does not fix the form of the superconducting gap function, even without further symmetry breaking ∆ s ( k ) = 1 + α ( cos k x + cos k y ) ∆ d x 2 − y 2 ( k ) = cos k x − cos k y + α ( cos2 k x − cos2 k y ) Wednesday, March 8, 17

Extended s-wave in the pnictides h e h e Wednesday, March 8, 17

Extended s-wave in the pnictides h e - + - + h e Wednesday, March 8, 17

LaFeAsO vs. LaFePO: s-wave anisotropy Thomale, Platt, Hanke, Bernevig, PRL 106, 187003 (2011) LaFeAsO Nodeless s +/- LaFePO Nodal s +/- Wednesday, March 8, 17

LaFeAsO vs. LaFePO: s-wave anisotropy Thomale, Platt, Hanke, Bernevig, PRL 106, 187003 (2011) LaFeAsO Nodeless s +/- LaFePO Nodal s +/- Wednesday, March 8, 17

Prediction of extended d-wave in pnictides Wednesday, March 8, 17

Prediction of extended d-wave in pnictides Wednesday, March 8, 17

Present Wednesday, March 8, 17

D-wave in hole doped iron pnictides? l moderate hole doping: electron and hole pockets l strong hole doping: only hole pockets present Ding group (China) Wednesday, March 8, 17

FRG: s to d-wave transition in K-doped Ba-122 Thomale, Platt, Hanke, Hu, Bernevig, PRL 107, 117001 (2011). x=0.4 hole doping M Γ 1 Γ 2 Wednesday, March 8, 17

Evidence for d-wave: thermal transport Taillefer group, Reid et al. PRL 2012 Wednesday, March 8, 17

Evidence against d-wave: Laser ARPES Shik Shin group, Science 2012 O M I Wednesday, March 8, 17

Raman: extended d-wave dominant subleading order Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation. Wednesday, March 8, 17

Raman: extended d-wave dominant subleading order Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation. Extended d-wave! Wednesday, March 8, 17

Raman: extended d-wave dominant subleading order Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation. Extended d-wave! To be submitted: Raman scattering confirms the prediction of extended d-wave as the dominant subleading d-wave instability in K-doped Ba-122. Wednesday, March 8, 17

Chiral d-wave superconductivity ◆ ! π ✓ c k ↑ ξ k ∆ k H d + id = ∑ ( c † − 1 k ↑ , c − k ↓ ) ∆ ∗ − i i c † − ξ k k k − k ↓ ˆ ∆ = 1 0 1 ∆ k = cos ( k x ) − cos ( k y )+ i sin ( k x ) sin ( k y ) = | ∆ k | e i ϕ k i − i − 1 ξ k = cos ( k x )+ cos ( k y ) − π 0 π − π C d ± id = 1 I ∇ k ϕ k d k = ± 2 2 π Wednesday, March 8, 17

Takada et al., Nature 422, 53-55 (2003) Wednesday, March 8, 17

Cobaltate phase diagram The phase diagram hosts a plethora of phases interpolating between the parent insulating compound (x=0) and Na-doped insulating limit (x=1) P . Lemmens (Braunschweig) Wednesday, March 8, 17

Cobaltate phase diagram Ong group, PRB 2004 Aligia et al., PRL 2008 x=0.1 x=0.2 x=0.3 Wednesday, March 8, 17

Cobaltate phase diagram Ong group, PRB 2004 Aligia et al., PRL 2008 Insulators x=0.1 x=0.2 x=0.3 Wednesday, March 8, 17

Evidence at x=0.3: Singlet, close-to-nodal superconductor Knight shift: Lin group, PRB 2006 Specific heat: Cava group, PRB 2008 Wednesday, March 8, 17

Hexagonal d-wave superconductivity d x2-y2 /d xy Wednesday, March 8, 17

Hexagonal d-wave superconductivity d x2-y2 /d xy The d-wave hexagonal point group representation is two-dimensional, implying a degeneracy at the instability level. Wednesday, March 8, 17

FRG analysis: anisotropic d+id phase The multi-orbital Hubbard model at x ~ 0.3 yields a d+id-wave superconductor with a strongly anisotropic gap function. Wednesday, March 8, 17

FRG analysis: anisotropic d+id phase The multi-orbital Hubbard model at x ~ 0.3 yields a d+id-wave superconductor with a strongly anisotropic gap function. large gap Wednesday, March 8, 17

FRG analysis: anisotropic d+id phase The multi-orbital Hubbard model at x ~ 0.3 yields a d+id-wave superconductor with a strongly anisotropic gap function. large gap small gap Wednesday, March 8, 17

T violation probed by Kerr angle Kapitulnik group (unpublished) Wednesday, March 8, 17

T violation probed by Kerr angle Kapitulnik group (unpublished) metallic T c Wednesday, March 8, 17

T violation probed by Kerr angle Kapitulnik group (unpublished) d-wave metallic T c Wednesday, March 8, 17

T violation probed by Kerr angle Kapitulnik group (unpublished) d+id-wave d-wave metallic T c entropy-driven transition Wednesday, March 8, 17

Future Wednesday, March 8, 17

SrPtAs - a Weyl superconductor? Wednesday, March 8, 17

Bogoliubov spectrum Wednesday, March 8, 17

SrPtAs: First prediction of a Weyl superconductor Wednesday, March 8, 17

LAO/STO - tight binding setup Wednesday, March 8, 17

LAO/STO - tight binding setup New methodological step: Spin-orbit FRG with complete double group implementation. Wednesday, March 8, 17

LAO/STO - s-wave vs. d-wave Wednesday, March 8, 17

Research team Wednesday, March 8, 17