The underdoped cuprates as fractionalized Fermi liquids (FL*)

Transcription

1 The underdoped cuprates as fractionalized Fermi liquids (FL*) R. K. Kaul, A. Kolezhuk, M. Levin, S. Sachdev, and T. Senthil, Physical Review B 75, (2007) R. K. Kaul, Y. B. Kim, S. Sachdev, and T. Senthil, Nature Physics 4, 28 (2008) S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu, Physical Review B 80, (2009) Y. Qi and S. Sachdev, Physical Review B 81, (2010) E.G. Moon and S. Sachdev, arxiv:1010.xxxx Talk online: sachdev.physics.harvard.edu HARVARD

2 Quantum criticality of the onset of antiferromagnetism in a metal ncreasing ϕ =0SDW ϕ =0 Metal with electron and hole pockets Metal with large Fermi surface s

3 SU(2) gauge theory: separating Fermi surface change from SDW order ncreasing SDW (A) (C) (B) (D) Leads to a FL* state: has Fermi pockets without translations symmetry breaking S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu, Physical Review B 80, (2009)

4 Kondo lattice model Kondo exchange J K Conduction k electrons ε k c kα c kα i<j J H (i, j) S i S j

5 Kondo lattice model Kondo exchange J K Conduction k electrons ε k c kα c kα J H (i, j) S i S j Large i<j Fermi surface Fermi liquid (FL)

6 Kondo lattice model Kondo exchange J K i<j J H (i, j) S i S j Conduction k electrons ε k c kα c kα Fractionalized Fermi liquid (FL*) T. Senthil, S. Sachdev, and M. Vojta, Phys. Rev. Lett. 90, (2003). T. Senthil, M. Vojta, and S. Sachdev, Phys. Rev. B 69, (2004).

7 Kondo lattice model Kondo exchange J K i<j J H (i, j) S i S j Conduction DMFT version: k electrons ε k c kα c kα Orbitally Selective Fractionalized Mott Transition (OSMT): gauge fields of FL* Fermi liquid (FL*) are missing T. Senthil, S. Sachdev, and M. Vojta, Phys. Rev. Lett. 90, (2003). T. Senthil, M. Vojta, and S. Sachdev, Phys. Rev. B 69, (2004).

8 FL* from a one-band model of cuprates Begin with SDW ordered state, and rotate to a frame polarized along the local orientation of the SDW order ˆϕ c ψ+ = R ; R ˆϕ σ R = σ z ; R R =1 c ψ With R = z z z z or ˆϕ = z α σ αβ z β we obtain a gauge theory of bosonic neutral spinons z α, spinless, charged fermions ψ ±, and an emergent gauge field. These particles can bind into two species of gauge neutral, electron-like quasiparticles: F iα z iα ψ i+, G iα ε αβ z iβψ i. This species doubling H. J. Schulz, is a key Physical characteristic Review Letters 65, of 2462 the (1990) topological order B. I. Shraiman and E. D. Siggia, Physical Review Letters 61, 467 (1988). of the underlying U(1) spin liquid. J. R. Schrieffer, Journal of Superconductivity 17, 539 (2004)

9 FL* from a one-band model of cuprates Begin with SDW ordered state, and rotate to a frame polarized along the local orientation of the SDW order ˆϕ c ψ+ = R ; R ˆϕ σ R = σ z ; R R =1 c ψ With R = z z z z or ˆϕ = z α σ αβ z β we obtain a gauge theory of bosonic neutral spinons z α, spinless, charged fermions ψ ±, and an emergent gauge field. These particles can bind into two species of gauge neutral, electron-like quasiparticles: F iα z iα ψ i+, G iα ε αβ z iβψ i. This species doubling is a key characteristic of the topological order of the underlying U(1) spin liquid.

10 FL* from a one-band model of cuprates Begin with SDW ordered state, and rotate to a frame polarized along the local orientation of the SDW order ˆϕ c ψ+ = R ; R ˆϕ σ R = σ z ; R R =1 c ψ With R = z z z z or ˆϕ = z α σ αβ z β we obtain a gauge theory of bosonic neutral spinons z α, spinless, charged fermions ψ ±, and an emergent gauge field. These particles can bind into two species of gauge neutral, electron-like quasiparticles: F iα z iα ψ i+, G iα ε αβ z iβψ i. This species doubling is a key characteristic of the topological order of the underlying U(1) spin liquid.

11 FL* from a one-band model of cuprates Use symmetry and physical arguments to constrain the effective Hamiltonian for the F α and G α H eff = ij t ij (F iα F jα + G iα G jα) + λ i ( 1) i x+i y (F iα F iα G iα G iα) i<j t ij (F iα G jα + G iα F jα) + (cos k x cos k y ) pairing in the superconductor

12 FL* from a one-band model of cuprates Use symmetry and physical arguments to constrain the effective Hamiltonian for the F α and G α H eff = ij t ij (F iα F jα + G iα G jα) + λ i Underlying band structure ( 1) i x+i y (F iα F iα G iα G iα) i<j t ij (F iα G jα + G iα F jα) + (cos k x cos k y ) pairing in the superconductor

13 FL* from a one-band model of cuprates Use symmetry and physical arguments to constrain the effective Hamiltonian for the F α and G α H eff = ij + λ i t ij (F iα F jα + G iα G jα) Potential from local antiferromagnetism ( 1) i x+i y (F iα F iα G iα G iα) i<j t ij (F iα G jα + G iα F jα) + (cos k x cos k y ) pairing in the superconductor

14 FL* from a one-band model of cuprates Use symmetry and physical arguments to constrain the effective Hamiltonian for the F α and G α H eff = ij t ij (F iα F jα + G iα G jα) Mixing between 2 species: descends from the + λ i Shraiman-Siggia term ( 1) i x+i y (F iα F iα G iα G iα) i<j t ij (F iα G jα + G iα F jα) + (cos k x cos k y ) pairing in the superconductor

15 Weaker local antiferromagnetism (a) (b) ky 0 Normal state electron spectrum (c) 0.4 (d) k x Angular dependence of electronic gap in normal state and in superconductor

16 Stronger local antiferromagnetism (a) (b) ky 0 Normal state electron spectrum (c) (d) 0 k x Angular dependence of electronic gap in normal state and in superconductor

17 Normal state with electron pockets