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Non-Fermi liquid and quantum-critical pairing in electron-doped cuprates

Andrey V. Chubukov Pavel Krotkov University of Wisconsin University of Maryland Hvar 05 October 1, 2005

Motivation

electron doped hole doped

Is there a niche for itinerant models in the cuprates? Itinerant = fermions + low-energy collective modes (no Mott physics)

Nd2-xCexCuO4

Steglish et al, Von Lohneysen et al, ….. Zimmers et al Electron-doped cuprates

Pr2-xCexCuO4

SDW Tc Mathur et al, similar in Ce2XIn5, Pagliuso et al

Sketch of experimental data AFM state = SDW state Hot spots are closer to zone diagonals than in hole-doped cuprates

• 1. Antiferromagnetic state

hole-doped electron-doped Armitage et al, Damascelli et al

• T. Sato et al

Onose et al, Zimmers et al

• 2. Mott physics

Mott gap, x=0 SDW gap, x ~0.1 Opt doping, x ~0.15 Mott physics seems to nearly disappear around

• ptimal electron doping

Rama n ARPES 3.1 D-wave (most likely), Δ scales with Tc

• 3. Superconducting state

Blumberg et al

3.2 Non-monotonic d-wave gap Rama n ARPES

• 3. Superconducting state

Blumberg et al T.Sato et al

At what geometry of the Fermi surface antiferromagnetism ends? RPA calculation QCP2 Antiferromagnetism ends when hot spots merge along zone diagonals Onufrieva, Pfety, Eremin, Zlatic t-t’ model

The model Near-diagonal fermions, interacting via the exchane of antiferromagnetic spin fluctuations

• low-energy fermions
• collective mode in the spin channel
• spin-fermion interaction (analog of U)

Two input parameters: coupling g Scalapino, Prelovsek, Zlatic, … Di Castro et al (spin-> charge)

• 1. Normal state:

System properties at QCP

• Fermi-liquid is broken for diagonal fermions:
• There is only one energy scale at QCP

Almost MFL QC behavior “High frequency”, but still QC behavior

Fermionic self- energy Dynamic spin susceptibility

N=2 numerics

Optical conductivity

ω> ω0 are relevant

Re and Im parts of Conductivity should generaly have different functional forms

Optical conductivity Results:

• C. Homes et al

Pr1.85Ce0.15CuO4

Similar results for Bi2212 van der Marel et al

B2G Raman scattering

T=0 part finite T part Blumberg et al Experiment

B2G Raman scattering

Theor y B2G Raman vertex Doesn’t change sign when k -> k + π, and approximately satisfies Ward identity

• 2. Superconductivity

hole-doped electron-doped What happens with Tc when hot spots merge along zone diagonal? Is d-wave gone? + A transition to s-wave? Yakovenko et al

interaction is larger than Still, attraction in a d-wave channel Small Small No other smallness Parameters: coupling g In the normal state, there was only one scale For the pairing problem: Yakovenko et al

Results:

• 1. Onset temperature of the pairing

flat region Tc ~ 0.0005 g, weakly depends on r Same parameters as in hole-doped materials: r ~ 0.08, Tc ~ 10K Prelovsek et al, Norman et al numerics analytics Abanov, AC, Finkelstein

r ~ 0.08 Tc ~ 10K

Some analytics/reasons for flattening Small r numerics

small r Tc =0.5 g r Actual Tc g = 1.7 eV Tc (K) r r Tc (K) actual Tc small r r

• 2. Momentum dependence of the gap

Frequency Momentum py Gap Pairing gap is non-monotonic even when hot spots are out

• 2. Momentum dependence of the gap

Pairing gap is non-monotonic even when hot spots are out

Conclusions

Problem: fermions near zone diagonals, interacting with collective AFM spin fluctuations

• non-FL in the normal state

“scaling” behavior of the conductivity flat B2G Raman intensity

• d-wave pairing by spin fluctuations

Tc ~10K (for the same coupling as for hole-doped) gap is highly non-monotonic Unsolved problems:

• self-energy and the pairing in SDW phase
• how Mott physics emerges at x->0

THANK YOU