Signatures of non-monotonic d-wave gap in electron-doped cuprates

We address the issue whether the data on optical conductivity and Raman scattering in electron-doped cuprates below $T_c$ support the idea that the $d-$wave gap in these materials is non-monotonic along the Fermi surface. We calculate the conductivity and Raman intensity for elastic scattering, and find that a non-monotonic gap gives rise to several specific features in optical and Raman response functions. We argue that all these features are present in the experimental data on Nd$_{2-x}$Ce$_{x}$CuO$_4$ and Pr$_{2-x}$Ce$_{x}$CuO$_4$ compounds.Comment: 7 pages, 6 figure

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 $z\approx 2.67$.Comment: 5 pages, 2 figure

Quasiparticle interaction function in a 2D Fermi liquid near an antiferromagnetic critical point

We present the expression for the quasiparticle vertex function $\Gamma^{\omega }(K_{F},P_{F})$ (proportional to the Landau function) in a 2D Fermi liquid (FL) near a $T=0$ instability towards antiferromagnetism. Previous studies have found that near an instability, the system enters into a critical FL regime, in which the fermionic self-energy is large near hot spots (points on the Fermi surface connected by the antiferromagnetic ordering vector $q_\pi=(\pi,\pi)$) and has much stronger dependence on frequency than on momentum. We show that to properly calculate the vertex function in this regime one has to sum up an infinite series of terms which were explicitly excluded in the conventional treatment. Besides, we show that, to properly describe the spin component of $\Gamma^{\omega }(K_{F},P_{F})$ even in an ordinary FL, one has to include Aslamazov-Larkin terms. We show that the total $\Gamma^{\omega }(K_{F},P_{F})$ is larger in a critical FL than in an ordinary FL, roughly by an extra power of magnetic correlation length $\xi$. However, the enhancement of $\Gamma ^{\omega }(K_{F},P_{F})$ is highly non-uniform: It holds only when, for one of the two momentum variables, the distance from a hot spot along the Fermi surface is much larger than for the other one. We show that the charge and spin components of the total vertex function satisfy the universal relations following from the Ward identities related to the conservation of the particle number and the total spin. We find that the charge and spin components of $\Gamma^{\omega }(K_{F},P_{F})$ are identical to leading order in the magnetic correlation length. We derive the Landau parameters, the density of states $N_F$, and the uniform ($q=0$) charge and spin susceptibilities $\chi ^{l=0}_{c} = \chi^{l=0}_s$. We show that the susceptibilities remain finite at $\xi = \infty$ despite that $N_F$ diverges as $\log \xi$.Comment: 63 pages, 21 figures. A typo in Fig. 9 is correcte

Quantum Phase Transition in the Yukawa-SYK Model

We study the quantum phase transition upon variation of the fermionic density $\nu$ in a solvable model with random Yukawa interactions between $N$ bosons and $M$ fermions, dubbed the Yukawa-SYK model. We show that there are two distinct phases in the model: an incompressible state with gapped excitations and an exotic quantum-critical, non-Fermi liquid state with exponents varying with $\nu$. We show analytically and numerically that the quantum phase transition between these two states is first-order, as for some range of $\nu$ the NFL state has a negative compressibility. In the limit $N/M\to \infty$ the first-order transition gets weaker and asymptotically becomes second-order, with an exotic quantum-critical behavior. We show that fermions and bosons display highly unconventional spectral behavior in the transition region.Comment: 14 pages, 5 figures; published versio