We analyze the structure of an $s-$wave superconducting gap in systems with electron-phonon attraction and electron-electron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap, $Delta (omega_m)$,
necessarily changes sign along the Matsubara axis. We analyze the sign-changing gap function from a topological perspective using the knowledge that a nodal point of $Delta (omega_m)$ is the center of dynamical vortex. We consider two models with different cutoffs for the repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane upon changing the relative strength of the attractive and repulsive parts of the interaction. We discuss how the presence of dynamical vortices affects the gap structure along the real axis, detectable in ARPES experiments.
In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction $V(Omega_m) propto 1/|Omega_m|^gam
ma$ (the $gamma$-model). We analyze both the original model and its extension, in which we introduce an extra parameter $N$ to account for non-equal interactions in the particle-hole and particle-particle channel. In two previous papers(arXiv:2004.13220 and arXiv:2006.02968), we considered the case $0 < gamma <1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions, $Delta_n (omega_m)$, all with the same spatial symmetry, and (ii) each $Delta_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper, we analyze how the system behavior changes between $gamma <1$ and $gamma >1$, both at $T=0$ and a finite $T$. The limit $gamma to 1$ is singular due to infra-red divergence of $int d omega_m V(Omega_m)$, and the system behavior is highly sensitive to how this limit is taken. We show that for $N =1$, the divergencies in the gap equation cancel out, and $Delta_n (omega_m)$ gradually evolve through $gamma=1$ both at $T=0$ and a finite $T$. For $N eq 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $gamma >1$. Namely, the form of $Delta_n (omega_m)$ changes qualitatively, and the spectrum of condensation energies, $E_{c,n}$ becomes continuous at $T=0$. We introduce different extension of the model, which is free from singularities for $gamma >1$.
Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconducti
vity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.
We show that a two-dimensional (2D) isotropic Fermi liquid harbors two new types of collective modes, driven by quantum fluctuations, in addition to conventional zero sound: hidden and mirage modes. The hidden modes occur for relatively weak attracti
ve interaction both in the charge and spin channels with any angular momentum $l$. Instead of being conventional damped resonances within the particle-hole continuum, the hidden modes propagate at velocities larger than the Fermi velocity and have infinitesimally small damping in the clean limit, but are invisible to spectroscopic probes. The mirage modes are also propagating modes outside the particle-hole continuum that occur for sufficiently strong repulsion interaction in channels with $lgeq 1$. They do give rise to peaks in spectroscopic probes, but are not true poles of the dynamical susceptibility. We argue that both hidden and mirage modes occur due to a non-trivial topological structure of the Riemann surface, defined by the dynamical susceptibility. The hidden modes reside below a branch cut that glues two sheets of the Riemann surface, while the mirage modes reside on an unphysical sheet of the Riemann surface. We show that both types of modes give rise to distinct features in time dynamics of a 2D Fermi liquid that can be measured in pump-probe experiments.
We calculate the fermionic spectral function $A_k (omega)$ in the spiral spin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature $T$. The spiral SDW order $Delta (T)$ develops below $T = T_N
$ and has momentum ${ bf K} = (4pi/3,0)$. We pay special attention to fermions with momenta ${bf k}$, for which ${bf k}$ and ${bf k} + {bf K}$ are close to Fermi surface in the absence of SDW. At the mean field level, $A_k (omega)$ for such fermions has peaks at $omega = pm Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at $T > T_N$. We show that this behavior changes qualitatively beyond mean-field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a non-perturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that $A_k (omega)$ shows peak/dip/hump features at $T < T_N$, with the peak position at $Delta (T)$ and hump position at $Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p > T_N$, and in between $T_N$ and $T_p$ the spectral function displays the pseudogap behavior. We show that the difference between $T_p$ and $T_N$ is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, $T_p = T_N$, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.
We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry-points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism
. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either $120^{circ}$ triangular order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and non-magnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the Free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.
Iron-based superconductors were discovered seven years ago, in 2008. This short review summarizes what we learned about these materials over the last seven years, what are open questions, and what new physics we expect to extract from studies of this new class of high-temperature superconductors.
We argue that Raman study of Fe-pnictides is a way to unambiguously distinguish between various superconducting gaps proposed for these materials. We show that $A_{1g}$ Raman intensity has a true resonance peak below $2Delta$ for extended s-wave supe
rconducting gap, $Delta(mathbf{k}) = Delta (cos k_x + cos k_y)/2$ in the folded Brillouin zone. No such peak emerges for a pure s-wave gap, a d-wave gap, and another extended s-wave gap with $Delta(mathbf{k}) = Delta cos{frac{k_x}{2}} cos{frac{k_y}{2}}$ proposed by several groups.
