arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 181 records · Page 10Linked to original sources

arXiv2002

A Spin Fluctuation Model for D-wave Superconductivity

In this review we demonstrate that superconducting pairing, mediated by the exchange of spin fluctuations, is a viable alternative to conventional phonon-mediated pairing. We discuss in detail the normal state properties, the spin fluctuation induced d-wave pairing and the superconducting behavior of a material near an antiferromagnetic instability, when the dominant interaction between quasiparticles is of electronic origin, and at energies much smaller than the fermionic bandwidth, can be viewed as being due to the emission and absorption of a collective, soft spin degree of freedom. We show that in the vicinity of an antiferromagnetic quantum critical point the system behavior is universal, at least when the effective spin fermion interaction is smaller than the fermionic bandwidth. We further argue that spin-fluctuation exchange yields an attraction and pairing in the $d_{x^{2}-y^{2}}$ channel in agreement with what nearly all researchers now believe is the pairing symmetry in the cuprates. We discuss "fingerprints" of a spin mediated pairing state, chiefly associated with the emergence of the resonance peak in the spin response in a d-wave superconductor and identify these fingerprints in spectroscopic experiments on optimally doped cuprate superconconductors.

cond-mat.str-el↗

arXiv2001

The differential sum rule for the relaxation rate in the cuprates

Motivated by recent experiments by Basov {\it et al}, we study the differential sum rule for the effective scattering rate $1/τ(ω)$. We show that in a dirty BCS superconductor, the area under $1/τ(ω)$ does not change between the normal and the superconducting states. For magnetically mediated pairing, similar result holds between $T<T_c$ and $T \geq T_c$, while in the pseudogap phase, $1/τ(ω)$ is just suppressed compared to $1/τ(ω)$ in the normal state. We argue that this violation of the differential sum rule is due to the fact that low-energy fermions in the pseudogap phase are still incoherent.

cond-mat.supr-con↗

arXiv2001

Quantum-critical theory of the spin-fermion model and its application to cuprates. Normal state analysis

We present the full analysis of the normal state of the spin-fermion model near the antiferromagnetic instability in two dimensions. This model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies - an effective spin-fermion interaction $\bar g$ and an energy $ω_{sf}$ below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction $λ^2 \propto {\bar g}/ω_{sf}$. We show that $λ$ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We developed a novel approach to the problem - the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavors - which allowed us to explicitly account for all terms which diverge as powers of $λ$, and treat the remaining, $O(λ)$ terms in the RG formalism. We applied this technique to study the properties of the spin-fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for cuprates, and argue that the spin-fermion model is capable to explain the anomalous normal state properties of high $T_c$ materials. We also discuss the non -applicability of the conventional $ϕ^4$ theory of the quantum-critical behavior in 2D.

cond-mat.supr-con↗

arXiv2001

Order from disorder in the double-exchange model

The magnetic excitations of the double exchange (DE) model are usually discussed in terms of an equivalent ferromagnetic Heisenberg model. However this equivalence is valid only at a quasi--classical level - we show that both quantum and thermal corrections to the magnetic properties of DE model differ from an effective Heisenberg model because its spin excitations interact only indirectly, through the exchange of charge fluctuations. We also find that the competition between ferromagnetic double exchange and an antiferromagnetic superexchange provides a new example of an "order from disorder" phenomenon - an intermediate spin configuration (either a canted or a spiral state) is selected by quantum and/or thermal fluctuations.

cond-mat.str-el↗

arXiv2001

Coherent vs incoherent pairing in 2D systems near magnetic instability

We study the superconductivity in 2D fermionic systems near antiferromagnetic instability, assuming that the pairing is mediated by spin fluctuations. This pairing involves fully incoherent fermions and diffusive spin excitations. We show that the competition between fermionic incoherence and strong pairing interaction yields the pairing instability temperature $T_{ins}$ which increases and saturates as the magnetic correlation length $ξ\to \infty$. We argue that in this quantum-critical regime the pairing problem is qualitatively different from the BCS one.

cond-mat.supr-con↗

arXiv2001

Singularities in the optical response of cuprates

We argue that the detailed analysis of the optical response in cuprate superconductors allows one to verify the magnetic scenario of superconductivity in cuprates, as for strong coupling charge carriers to antiferromagnetic spin fluctuations, the second derivative of optical conductivity should contain detectable singularities at $2Δ+Δ_{\rm spin}$, $4Δ$, and $2Δ+2Δ_{\rm spin}$, where $Δ$ is the amplitude of the superconducting gap, and $Δ_{s}$ is the resonance energy of spin fluctuations measured in neutron scattering. We argue that there is a good chance that these singularities have already been detected in the experiments on optimally doped $YBCO$.

cond-mat.supr-con↗

arXiv2001

Quantum-critical superconductivity in underdoped cuprates

We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermionic spectral function.

cond-mat.supr-con↗

arXiv2000

Dispersion of the neutron resonance in cuprate superconductors

We argue that recently measured downward dispersion of the neutron resonance peak in cuprate superconductors is naturally explained if the resonance is viewed as a spin-1 collective mode in a d-wave superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the d-wave superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnon-like, i.e., curve upwards from (pi,pi).

cond-mat.supr-con↗

arXiv2000

Fingerprints of spin-fermion pairing in cuprates

We demonstrate that the feedback effect from bosonic excitations on fermions, which in the past allowed one to verify the phononic mechanism of a conventional, $s-$wave superconductivity, may also allow one to experimentally detect the ``fingerprints'' of the pairing mechanism in cuprates. We argue that for spin-mediated $d-$wave superconductivity, the fermionic spectral function, the density of states, the tunneling conductance through an insulating junction, and the optical conductivity are affected by the interaction with collective spin excitations, which below $T_c$ are propagating, magnon-like quasiparticles with gap $Δ_s$. We show that the interaction with a propagating spin excitation gives rise to singularities at frequencies $Δ+ Δ_s$ for the spectral function and the density of states, and at $2Δ+ Δ_s$ for tunneling and optical conductivities, where $Δ$ is the maximum value of the $d-$wave gap. We further argue that recent optical measurements also allow one to detect subleading singularities at $4Δ$ and $2Δ+ 2Δ_s$. We consider the experimental detection of these singularities as a strong evidence in favor of the magnetic scenario for superconductivity in cuprates.

cond-mat.supr-con↗

arXiv2000

Spectral function and conductivity in the normal state of the cuprates: a spin fluctuation study

We study the spectral function $A_k (ω)$ and the optical conductivity $σ_1 (ω)$ for a system of fermions interacting with their collective spin fluctuations (the spin-fermion model), and apply the results to optimally doped cuprates in the normal state. We show that there is no qualitative distinction between hot and cold regions in the Brillouin zone - in both cases, there exists a wide range of frequencies where the width of the peak in $A_k (ω)$ scales linearly with $ω$. We demonstrate that $σ_1 (ω)$ is inversely linear in $ω$ up to very high frequencies. We argue that these results agree {\it quantitatively} with the photoemission and optical data for $Bi2212$.

cond-mat.supr-con↗

arXiv2000

Spin-fermion model near the quantum critical point: one-loop renormalization group results

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, N and present the results beyond previously studied $N = \infty $ limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from z=2 to z>2. To first order in 1/N we found $z = 2N/(N-2)$ which for a physical N=8 yields $z\approx 2.67$.

cond-mat.supr-con↗

arXiv2000

SIN and SIS tunneling in cuprates

We calculate the SIN and SIS tunneling conductances for the spin-fermion model. We argue that at strong spin-fermion coupling, relevant to cuprates, both conductances have dip features near the threshold frequencies when a tunneling electron begin emitting propagating spin excitation. We argue that the resonance spin frequency measured in neutron scattering can be inferred from the tunneling data by analyzing the derivatives of SIN and SIS conductances.

cond-mat.supr-con↗

arXiv1999

On the relative positions of the $2Δ$ peaks in Raman and tunneling spectra of d-wave superconductors

We study $B_{1g}$ Raman intensity $R(Ω)$ and the density of states $N(ω)$ in isotropic 2D d-wave superconductors. For an ideal gas, $R(Ω)$ and $N(ω)$ have sharp peaks at $Ω=2Δ$ and $ω=Δ$, respectively, where $Δ$ is the maximum value of the gap. We study how the peak positions are affected by the fermionic damping due to impurity scattering. We show that while the damping generally shifts the peak positions to larger frequencies, the peak in $R(Ω)$ still occurs at almost twice the peak position in $N(ω)$ and therefore cannot account for the experimentally observed downturn shift of the peak frequency in $R(Ω)$ in underdoped cuprates compared to twice that in $N(ω)$. We also discuss how the fermionic damping affects the dynamical spin susceptibility.

cond-mat.supr-con↗

arXiv1999

Condensation energy in the spin-fermion model for cuprates

We use the Scalapino-White relation between the condensation energy and the difference between the dynamical structure factor in the normal and the superconducting states to compute the condensation energy in the spin-fermion model. We show that at strong coupling, the extra low-frequency spectral weight associated with the resonance peak in the dynamical structure factor in a superconductor is compensated only at energies $\sim J$ which are much larger than the superconducting gap $Δ$. We argue that in this situation, the condensation energy is large and well accounts for the data for cuprates.

cond-mat.supr-con↗

arXiv1999

Electronic Raman Scattering in Superconducting Cuprates

We show that the novel features observed in Raman experiments on optimally doped and underdoped Bi-2212 compounds in $B_{1g}$ geometry can be explained by a strong fermionic self-energy due to the interaction with spin fluctuations. We compute the Raman intensity $R(ω)$ both above and below $T_c$, and show that in both cases $R(ω)$ progressively deviates, with decreasing doping, from that in a Fermi-gas due to increasing contribution from the fermionic self-energy. We also show that the final state interaction increases with decreasing doping and gradually transforms the $2Δ$ peak in the superconducting state into a pseudo resonance mode below $2Δ$. We argue that these results agree well with the experimental data for Bi-2212.

cond-mat↗

arXiv1999

A relation between the resonance neutron peak and ARPES data in cuprates

We argue that the resonant peak observed in neutron scattering experiments on superconducting cuprates and the peak/dip/hump features observed in ARPES measurements are byproducts of the same physical phenomenon. We argue that both are due to feedback effects on the damping of spin fluctuations in a $d-$wave superconductor. We consider the spin-fermion model at strong coupling, solve a set of coupled integral equations for fermionic and bosonic propagators and show that the dynamical spin susceptibility below $T_c$ possesses the resonance peak at $Ω_{res} \propto ξ^{-1}$. The scattering of these magnetic excitations by electrons gives rise to a peak/dip/hump behavior of the electronic spectral function, the peak-dip separation is exactly $Ω_{res}$.

cond-mat.supr-con↗

arXiv1998

Unconventional properties of superconducting cuprates

We present an explanation of the unusual peak/dip/hump features observed in photoemission experiments on Bi2212 at $T \ll T_c$. We argue that these features arise from the interaction of the fermionic quasi-particles with overdamped spin fluctuations. We show that the strong spin-fermion interaction combined with the feedback effect on the spin damping due to superconductivity yields a Fermi-liquid form of the fermionic spectral function for $ω< 2 Δ$ where $Δ$ is the maximum value of the superconducting gap, and a non-Fermi-liquid form for $ω> 2 Δ$. In the Fermi-liquid regime, the spectral function $A({\bf k}_F,ω)$ displays a quasiparticle peak at $ω= Δ$; in the non-Fermi-liquid regime it possesses a broad maximum (hump) at $ω\gg Δ$. In between the two regimes, the spectral function has a dip at $ω\sim 2 Δ$. We argue that our theory also explains the tunneling data for the superconducting density of states.

cond-mat.supr-con↗

arXiv1998

Evolution of the quasiparticle spectral function in cuprates

We analyzed photoemssion data for several doping levels of the Bi_2Sr_2CaCu_2O_{8+x} compounds, ranging from overdoped to underdoped. We show that the high frequency part of the spectra near (0,π) can be described by Fermi liquid theory in the overdoped regime, but exhibits a non-Fermi liquid behavior in the underdoped regime. We further demonstrate that this novel behavior fits reasonably well to a 1/\sqrtω behavior suggested for systems with strong spin fluctuations.

cond-mat.supr-con↗