TY - JOUR

T1 - Quantum-critical pairing with varying exponents

AU - Moon, Eun Gook

AU - Chubukov, Andrey

PY - 2010/10/1

Y1 - 2010/10/1

N2 - We analyze the onset temperature T p for the pairing in cuprate superconductors at small doping, when tendency towards antiferromagnetism is strong. We consider the model of Moon and Sachdev (MS), which assumes that electron and hole pockets survive in a paramagnetic phase. Within this model, the pairing between fermions is mediated by a gauge boson, whose propagator remains massless in a paramagnet. We relate the MS model to a generic γ-model of quantum-critical pairing with the pairing kernel λ(Ωn) α 1/Ωγ/n. We show that, over some range of parameters, the MS model is equivalent to γ=1/3-model (λ(Ω) α Ω -1/3). We find, however, that the parameter range where this analogy works is bounded on both ends. At larger deviations from a magnetic phase, the MS model becomes equivalent to γ model with varying γ>1/3, whose value depends on the distance to a magnetic transition and approaches γ=1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to γ model with varying γ<1/3. Right at the magnetic QCP, the MS model is equivalent to the model with λ(Ω n ) α log∈Ω n, which is the model for color superconductivity. Using this analogy, we verify the formula for T c derived for color superconductivity.

AB - We analyze the onset temperature T p for the pairing in cuprate superconductors at small doping, when tendency towards antiferromagnetism is strong. We consider the model of Moon and Sachdev (MS), which assumes that electron and hole pockets survive in a paramagnetic phase. Within this model, the pairing between fermions is mediated by a gauge boson, whose propagator remains massless in a paramagnet. We relate the MS model to a generic γ-model of quantum-critical pairing with the pairing kernel λ(Ωn) α 1/Ωγ/n. We show that, over some range of parameters, the MS model is equivalent to γ=1/3-model (λ(Ω) α Ω -1/3). We find, however, that the parameter range where this analogy works is bounded on both ends. At larger deviations from a magnetic phase, the MS model becomes equivalent to γ model with varying γ>1/3, whose value depends on the distance to a magnetic transition and approaches γ=1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to γ model with varying γ<1/3. Right at the magnetic QCP, the MS model is equivalent to the model with λ(Ω n ) α log∈Ω n, which is the model for color superconductivity. Using this analogy, we verify the formula for T c derived for color superconductivity.

KW - Non-Fermi liquid

KW - Quantum phase transitions

KW - Superconductivity

UR - http://www.scopus.com/inward/record.url?scp=77957822731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957822731&partnerID=8YFLogxK

U2 - 10.1007/s10909-010-0199-y

DO - 10.1007/s10909-010-0199-y

M3 - Article

AN - SCOPUS:77957822731

VL - 161

SP - 263

EP - 281

JO - Journal of Low Temperature Physics

JF - Journal of Low Temperature Physics

SN - 0022-2291

IS - 1-2

ER -