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

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History, Present, Future: Functional RG for unconventional superconductors Ronny Thomale Julius-Maximilians Universitt Wrzburg Topolectrics SPP 1458 SFB 1170 Functional Renormalization - from quantum gravity and dark energy to

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SLIDE 1

History, Present, Future: Functional RG for unconventional superconductors

Ronny Thomale

Julius-Maximilians Universität Würzburg

“Functional Renormalization - from quantum gravity and dark energy to ultracold atoms and condensed matter”

Topolectrics

SFB 1170 SPP 1458

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SLIDE 2

Unconventional superconductors

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SLIDE 3

Outline

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SLIDE 4

Outline

History

  • Timeline of materials studied through FRG
  • Recent methodological step: multi-band/orbital superconductivity

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SLIDE 5

Outline

Present

  • Pnictides: extended d-wave vs. extended s-wave
  • Sodium cobaltates: chiral d-wave?

History

  • Timeline of materials studied through FRG
  • Recent methodological step: multi-band/orbital superconductivity

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SLIDE 6

Outline

Present

  • Pnictides: extended d-wave vs. extended s-wave
  • Sodium cobaltates: chiral d-wave?

Future

  • SrPtAs: Weyl superconductors
  • LAO/STO heterostructures

History

  • Timeline of materials studied through FRG
  • Recent methodological step: multi-band/orbital superconductivity

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SLIDE 7

History

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SLIDE 8

‘84 Polchinski ’93 Wetterich ’94 Shankar

Timeline

Schulz ’99 Metzner ’00 ’01 Honerkamp, Salmhofer ’08 Fa Wang ’09 Thomale ’11 Qianghua Wang

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SLIDE 9

‘84 Polchinski ’93 Wetterich ’94 Shankar

Timeline

Schulz ’99 Metzner ’00 ’01 Honerkamp, Salmhofer ’08 Fa Wang ’09 Thomale ’11 Qianghua Wang

Platt, Hanke, Thomale Advances in Physics

  • Vol. 62, p. 453-562, 2014

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SLIDE 10

Harmonic composition of SC form factors

∆i,j ⇠ hc†

ic† ji

The favored real space pairing function transforms under irreducible point group representations

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SLIDE 11

Harmonic composition of SC form factors

∆i,j ⇠ hc†

ic† ji

The favored real space pairing function transforms under irreducible point group representations

s

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SLIDE 12

Harmonic composition of SC form factors

∆i,j ⇠ hc†

ic† ji

The favored real space pairing function transforms under irreducible point group representations

s dx2-y2

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SLIDE 13

Harmonic composition of SC form factors

∆i,j ⇠ hc†

ic† ji

The favored real space pairing function transforms under irreducible point group representations The point group representation does not fix the form of the superconducting gap function, even without further symmetry breaking

s dx2-y2

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SLIDE 14

∆dx2−y2(k) = coskx −cosky +α(cos2kx −cos2ky) ∆s(k) = 1+α(coskx +cosky)

Harmonic composition of SC form factors

∆i,j ⇠ hc†

ic† ji

The favored real space pairing function transforms under irreducible point group representations The point group representation does not fix the form of the superconducting gap function, even without further symmetry breaking

s dx2-y2

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SLIDE 15

Extended s-wave in the pnictides

h h e e

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SLIDE 16

Extended s-wave in the pnictides

+

  • +
  • h

h e e

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SLIDE 17

Thomale, Platt, Hanke, Bernevig, PRL 106, 187003 (2011)

LaFeAsO vs. LaFePO: s-wave anisotropy

Nodeless s+/- Nodal s+/-

LaFePO LaFeAsO

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Thomale, Platt, Hanke, Bernevig, PRL 106, 187003 (2011)

LaFeAsO vs. LaFePO: s-wave anisotropy

Nodeless s+/- Nodal s+/-

LaFePO LaFeAsO

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Prediction of extended d-wave in pnictides

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Prediction of extended d-wave in pnictides

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Present

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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)

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FRG: s to d-wave transition in K-doped Ba-122

Thomale, Platt, Hanke, Hu, Bernevig, PRL 107, 117001 (2011). hole doping Γ1 Γ2 M

x=0.4

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Evidence for d-wave: thermal transport

Taillefer group, Reid et al. PRL 2012

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Shik Shin group, Science 2012 I M O

Evidence against d-wave: Laser ARPES

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Raman: extended d-wave dominant subleading order

Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation.

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SLIDE 27

Raman: extended d-wave dominant subleading order

Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation.

Extended d-wave!

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Raman: extended d-wave dominant subleading order

Maiti et al., PRL 117, 257001 (2016); Böhm et al., in preparation.

To be submitted: Raman scattering confirms the prediction of extended d-wave as the dominant subleading d-wave instability in K-doped Ba-122.

Extended d-wave!

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ξk = cos(kx)+cos(ky) ∆k = cos(kx)−cos(ky)+isin(kx)sin(ky) = |∆k|eiϕk

Hd+id = ∑

k

(c†

k↑,c−k↓)

✓ ξk ∆k ∆∗

k

−ξk ◆ ck↑ c†

−k↓

!

ˆ ∆ = 1

Chiral d-wave superconductivity

1 −1 −i

i

π −π

i −i −1

−π π

Cd±id = 1 2π

I

∇kϕkdk = ±2

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SLIDE 30

Takada et al., Nature 422, 53-55 (2003)

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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)

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Cobaltate phase diagram

Ong group, PRB 2004 Aligia et al., PRL 2008 x=0.3 x=0.2 x=0.1

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Cobaltate phase diagram

Ong group, PRB 2004 Aligia et al., PRL 2008 x=0.3 x=0.2 x=0.1

Insulators

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Evidence at x=0.3: Singlet, close-to-nodal superconductor

Knight shift: Lin group, PRB 2006 Specific heat: Cava group, PRB 2008

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Hexagonal d-wave superconductivity

dx2-y2/dxy

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Hexagonal d-wave superconductivity

dx2-y2/dxy

The d-wave hexagonal point group representation is two-dimensional, implying a degeneracy at the instability level.

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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.

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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

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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

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T violation probed by Kerr angle

Kapitulnik group (unpublished)

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T violation probed by Kerr angle

Tc

metallic

Kapitulnik group (unpublished)

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T violation probed by Kerr angle

d-wave

Tc

metallic

Kapitulnik group (unpublished)

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T violation probed by Kerr angle

d-wave

Tc

metallic d+id-wave entropy-driven transition

Kapitulnik group (unpublished)

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Future

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SrPtAs - a Weyl superconductor?

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Bogoliubov spectrum

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SrPtAs: First prediction of a Weyl superconductor

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LAO/STO - tight binding setup

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LAO/STO - tight binding setup

New methodological step: Spin-orbit FRG with complete double group implementation.

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LAO/STO - s-wave vs. d-wave

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Research team

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