arXiv subjects

Ar. Abanov

Publications and source records attributed to Ar. Abanov.

At least 37 records · Page 2Linked to original sources

arXiv2009

Reduced effect of impurities on the universal pairing scale in the cuprates

We consider the effect of non-magnetic impurities on the onset temperature $T^*$ for the $d-$wave pairing in spin-fluctuation scenario for the cuprates. We analyze intermediate coupling regime when the magnetic correlation length $ξ/a >1$ and the dimensionless coupling $u$ is O(1). In the clean limit, $T^* \approx 0.02 v_f/a$ in this parameter range, and weakly depends on $ξ$ and $u$. We found numerically that this universal pairing scale is also quite robust with respect to impurities: the scattering rate $Γ_{cr}$ needed to bring $T^*$ down to zero is about 4 times larger than in weak coupling, in good quantitative agreement with experiments. We provide analytical reasoning for this result.

cond-mat.supr-con↗

arXiv2009

Multi-Cuts Solutions of Laplacian Growth

A new class of solutions to Laplacian growth with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hele-Shaw cells. Integrals of motion for the multi-cut Laplacian growth solutions in terms of singularities of the Schwarz function are found, and the dynamics of densities (jumps) on the cuts are derived. The subclass of these solutions with linear Cauchy densities on the cuts of the Schwarz function is of particular interest, because in this case the integral equation for the conformal map becomes linear. These solutions can also be of physical importance by representing oil/air interfaces, which form oil fjords with a constant opening angle, in accordance with recent experiments in a Hele-shaw cell.

nlin.SI↗

arXiv2009

Static and Dynamic properties of a Fermi-gas of cooled atoms near a wide Feshbach resonance

We introduce the Global Spin Model to study the static and dynamic properties of the ultracold fermionic gas near the broad Feshbach resonance. We show that the problem of molecular production, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in a wide range of parameters. We calculate the amplitude of the condensate as function of the initial detuning and the rate of the magnetic field sweep.

cond-mat.other↗

arXiv2008

Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates

We consider the evolution of d-wave pairing, mediated by nearly critical spin fluctuations, with the coupling strength. We show that the onset temperature for pairing, T*, smoothly evolves between weak and strong coupling, passing through a broad maximum at intermediate coupling. At strong coupling, T* is of order the magnetic exchange energy J. We argue that for all couplings, pairing is confined to the vicinity of the Fermi surface. We also find that thermal spin fluctuations only modestly reduce T*, even at criticality, but they substantially smooth the gap anisotropy. The latter evolves with coupling, being the largest at weak coupling.

cond-mat.supr-con↗

arXiv2007

Molecular production at a wide Feshbach resonance in Fermi-gas of cooled atoms

The problem of molecular production from degenerate gas of fermions at a wide Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in inverse process of the molecule dissociation.

cond-mat.other↗

arXiv2007

Anomalous Hall effect in a two-dimensional electron gas

The anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling is studied within the Kubo-Streda formalism in the presence of pointlike potential impurities. We find that all contributions to the anomalous Hall conductivity vanish to leading order in disorder strength when both chiral subbands are occupied. In the situation that only the majority subband is occupied, all terms are finite in the weak scattering limit and the total anomalous Hall conductivity is dominated by skew scattering. We compare our results to previous treatments and resolve some of the discrepancies present in the literature.

cond-mat.mtrl-sci↗

arXiv2006

Self-similarity in Laplacian Growth

We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the integral equation for the conformal map. It is shown that solutions to the integral equation obey also a second order differential equation which is the one dimensional Schroedinger equation with the sinh inverse square potential. The solutions, which are expressed through the Gauss hypergeometric function, characterize the geometry of self-similar patterns in a wedge. We also find the potential for the Coulomb gas representation of the self-similar Laplacian growth in a wedge and calculate the corresponding free energy.

nlin.SI↗

arXiv2004

Anomalous scaling at the quantum critical point

We show that Hertz $ϕ^4$ theory of quantum criticality is incomplete as it misses anomalous non-local contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent $z=2$. The upper critical dimension is still $d= 4-z =2$, however the number of marginal vertices at $d=2$ is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for $d<2$ the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains $z=2$.

cond-mat.str-el↗

arXiv2004

The spin resonance and high frequency optical properties of the cuprates

We argue that recently observed superconductivity-induced blue shift of the plasma frequency $δω_{pl}$ in $Bi_2Sr_2CaCu_2O_{8+δ}$ is related to the change in the integrated dynamical structure factor associated with the development of the spin resonance below $T_c$. We show that the magnitude of $δω_{pl}$ is consistent with the small integrated spectral weight of the resonance, and its temperature dependences closely follow that of the spin resonance peak.

cond-mat.supr-con↗

arXiv2003

Inelastic Tunneling Spectroscopy in a D-wave Superconductor

We propose a mechanism to use inelastic tunneling spectrosopy STM to detect a single spin in a d-wave superconductor and in a pseudogap state, based on a direct exchange coupling J between the surface electrons and the local spin S in a magnetic field. This coupling will produce a kink in a dI/dV characteristic at Zeeman energy of the spin ω_0. We find that for relevant values of parameters signal scales as dI^2/dV^2 \simeq (JN_0)^2 Θ(eV - ω_0) and could be in the range of 10^{-2} of the bare density of states where N_0 is the density of states for surface electrons. Scattering in superconductor with the coherence peak at gap maximum Δleads also to strong features at Δ+ ω_0. This suggests a new technique for a detection of a local spin excitation with STM. We also consider a detection of a local vibrational mode as a simple extension of the spin case.

cond-mat.str-el↗

arXiv2003

The differential sum rule for the relaxation rate in dirty superconductors

We consider the differential sum rule for the effective scattering rate $% 1/τ(ω)$ and optical conductivity $σ_{1}(ω) $ in a dirty BCS superconductor, for arbitrary ratio of the superconducting gap $% Δ$ and the normal state constant damping rate $1/τ$. We show that if $τ$ is independent of $T$, the area under $1/τ(ω)$ does not change between the normal and the superconducting states, i.e., there exists an exact differential sum rule for the scattering rate. For \textit{any} value of the dimensionless parameter $Δτ$, the sum rule is exhausted at frequencies controlled by $Δ$. %but the numerical convergence is weak. We show that in the dirty limit the convergence of the differential sum rule for the scattering rate is much faster then the convergence of the $f-$sum rule, but slower then the convergence of the differential sum rule for conductivity.

cond-mat.supr-con↗

arXiv2003

Low Frequency Spin Dynamics in the CeMIn_5 Materials

We measure the spin lattice relaxation of the In(1) nuclei in the CeMIn_5 materials, extract quantitative information about the low energy spin dynamics of the lattice of Ce moments in both CeRhIn_5 and CeCoIn_5, and identify a crossover in the normal state. Above a temperature T* the Ce lattice exhibits "Kondo gas" behavior characterized by local fluctuations of independently screened moments; below T* both systems exhibit a "Kondo liquid" regime in which interactions between the local moments contribute to the spin dynamics. Both the antiferromagnetic and superconducting ground states in these systems emerge from the "Kondo liquid" regime. Our analysis provides strong evidence for quantum criticality in CeCoIn_5.

cond-mat.str-el↗

arXiv2002

The neutron resonance in the cuprates and its effect on fermionic excitations

We argue that the exciton scenario for the magnetic resonance in the cuprate superconductors yields a small spectral weight of the resonance, in agreement with experiment. We show that the small weight is related to its concentration in a small region of momentum and energy. Despite this, we find that a large fermionic self-energy can indeed be generated by a resonance with such properties, i.e., the scattering from the resonance substantially affects the electronic properties of the cuprates below $T_c$.

cond-mat.supr-con↗

arXiv2002

ARPES in the normal state of the cuprates: comparing the marginal Fermi liquid and spin fluctuation scenarios

We address the issue whether ARPES measurements of the spectral function $A_k (ω)$ near the Fermi surface in the normal state of near optimally doped cuprates can distinguish between the marginal Fermi liquid scenario and the spin-fluctuation scenario. We argue that the data for momenta near the Fermi surface are equally well described by both theories, but this agreement is nearly meaningless as in both cases one has to add to $Σ^{\prime \prime} (ω)$ a large constant of yet unknown origin. We show that the data can be well fitted by keeping only this constant term in the self-energy. To distinguish between the two scenarios, one has to analyze the data away from the Fermi surface, when the intrinsic piece in $Σ(ω)$ becomes dominant.

cond-mat.supr-con↗

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

Berry phase for ferromagnet with fractional spin

We study the double exchange model on two lattice sites with one conduction electron in the limit of an infinite Hund's interaction. While this simple problem is exactly solvable, we present an approximate solution which is valid in the limit of large core spins. This solution is obtained by integrating out charge degrees of freedom. The effective action of two core spins obtained in the result of such an integration resembles the action of two fractional spins. We show that the action obtained via naive gradient expansion is inconsistent. However, a ``non-perturbative'' treatment leads to an extra term in the effective action which fixes this inconsistency. The obtained ``Berry phase term'' is geometric in nature. It arises from a geometric constraint on a target space imposed by an adiabatic approximation.

cond-mat↗

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

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↗