arXiv subjects
Publications and source records attributed to Artem Abanov.
We discuss several results in electrostatics: Onsager's inequality, an extension of Earnshaw's theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible, we try to provide a brief historical context and references.
Near a quantum-critical point, a metal reveals two competing tendencies: destruction of fermionic coherence and attraction in one or more pairing channels. We analyze the competition within Eliashberg theory for a class of quantum-critical models with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model) for $0 < γ<1$. We argue that the two tendencies are comparable in strength, yet the one towards pairing is stronger, and the ground state is a superconductor. We show, however, that there exist two distinct regimes of system behavior below the onset temperature of the pairing $T_p$. In the range $T_{cr} < T < T_p$ fermions remain incoherent and the density of states $N(ω)$ displays "gap filling" behavior in which the position of the maximum in $N(ω)$ is set by temperature rather than the pairing gap. At lower $T < T_{cr}$, fermions acquire coherence, and $N(ω)$ displays a conventional "gap closing" behavior. We argue that the existence of the two regimes comes about because of special behavior of fermions with frequencies $ω= \pm πT$ along the Matsubara axis. Specifically, for these fermions, the component of the self-energy, which competes with the pairing, vanishes in the normal state. We further argue that the crossover at $T \sim T_{cr}$ comes about because Eliashberg equations allow an infinite number of topologically distinct solutions for the onset temperature of the pairing within the same gap symmetry. Only one solution, with the highest $T_p$, actually emerges, but other solutions are generated and modify the form of the gap function at $T \leq T_{cr}$. Finally, we argue that the actual $T_c$ is comparable to $T_{cr}$, while at $T_{cr} < T < T_{p}$ phase fluctuations destroy superconducting long-range order, and the system displays pseudogap behavior.
Near a quantum-critical point in a metal a strong fermion-fermion interaction, mediated by a soft boson, destroys fermionic coherence and also gives rise to superconductivity. In a class of large $N$ models, one would naively expect an incoherent (non-Fermi liquid) normal state behavior to persist down to $T=0$. However, this is not the case for quantum-critical systems described by Eliashberg theory, where non-Fermi liquid part of the self-energy $Σ(ω_m)$ is large for a generic Matsubara frequency $ω_m = πT(2m+1)$, but vanishes at $ω_m = \pm πT$, while the pairing interaction between fermions with these two frequencies remains strong. This peculiarity gives rise to a non-zero $T_c$ even at large $N$[Y. Wang et al PRL 117, 157001 (2016)]. We consider the system behavior below $T_c$ and contrast the two cases when $ω_m = \pm πT$ are either special or not. We obtain the solution of the non-linear gap equations in real frequency axis and obtain the spectral function $A(ω)$ and the density of states $N(ω)$. In a conventional BCS-type superconductor $A(ω)$ and $N(ω)$ are peaked at the gap value $Δ(T)$, and the peak position shifts to a smaller $ω$ as temperature increases, i.e. the gap "closes in". However when superconductivity is induced by fermions with $ω_m = \pm πT$, the peak in $N(ω)$ remains at a finite frequency even at $T =T_c-0$, the gap just "fills in". The spectral function $A(ω)$ either shows almost the same "gap filling" behavior, or its peak position shifts to zero frequency already at a finite $Δ$ ("emergent Fermi arc" behavior), depending on the strength of the thermal contribution. We compare our results with the data for the cuprates and argue that "gap filling" behavior holds in the antinodal region, while the "emergent Fermi arc" behavior holds in the nodal region.
We consider a quantum-critical metal with interaction mediated by fluctuations of a critical order parameter. This interaction gives rise to two competing tendencies -- pairing and non-Fermi liquid behavior. Due to competition, the pairing develops below a finite $T_p $, however its prominent feedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At $T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor -- the density of states (DOS) and the spectral function (SF) have sharp gaps which close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip, which {\it fills in} with increasing $T$. The SF in this region shows either the same behavior as the DOS, or has a peak at $ω=0$ (the Fermi arc), depending on the position on the Fermi surface. We argue that phase fluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$, while $T_p$ marks the onset of pseugogap behavior. We compare our theory with the behavior of optimally doped cuprates.
We compute the ratio of the pairing gap $Δ$ at $T=0$ and $T_c$ for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility $χ(Ω) \propto 1/|Ω|^γ$ (the $γ$ model). The limit $γ= 0+$ ($χ(Ω) =\log {|Ω|}$) describes color superconductivity, and models with $γ>0$ describe superconductivity in a metal at the onset of charge or spin order. The ratio $2Δ/T_c$ has been recently computed numerically for $0<γ<2$ within Eliashberg theory and was found to increase with increasing $γ$ [T-H Lee et al, arXiv:1805.10280]. We argue that the origin of the increase is the divergence of $2Δ/T_c$ at $γ=3$. We obtain an approximate analytical formula for $2Δ/T_c$ for $γ\leq 3$ and show that it agrees well with the numerics. We also consider in detail the opposite limit of small $γ$. Here we obtain the explicit expressions for $T_c$ and $Δ$, including numerical prefactors. We show that these prefactors depend on fermionic self-energy in a rather non-trivial way. The ratio $2Δ/T_c$ approaches the BCS value $3.53$ at $γ\to 0$.
We predict the electrical generation and injection of domain walls into a ferromagnetic nano-wire without the need of an assisting magnetic field. Our analytical and numerical results show that above a critical current $j_{c}$ domain walls are injected into the nano-wire with a period $T \sim (j-j_{c})^{-1/2}$. Importantly, domain walls can be produced periodically even in a simple exchange ferromagnet with uniaxial anisotropy, without requiring any standard "twisting" interaction like Dzyaloshinskii-Moriya or dipole-dipole interactions. We show analytically that this process and the period exponents are universal and do not depend on the peculiarities of the microscopic Hamiltonian. Finally we give a specific proposal for an experimental realization.
In this paper, we propose a practical way to stabilize half-hydrogenated graphene (graphone). We show that the dipole moments induced by an hexagonal-boron nitride (h-BN) substrate on graphene stabilize the hydrogen atoms on one sublattice of the graphene layer and suppress the migration of the absorbed hydrogen atoms. Based upon first principle spin polarized density of states (DOS) calculations, we show that the half hydrogenated graphene (graphone) obtained in different graphene-h-BN heterostructures exhibits a half metallic state. We propose to use this new exotic material for spin valve and other spintronics devices and applications.
We analyze the properties of Neel and Bloch domain walls as a function of film thickness h, for systems where, in addition to exchange, the dipole-dipole interaction must be included. The Neel to Bloch phase transition is found to be a second order transition at hc, mediated by a single unstable mode that corresponds to oscillatory motion of the domain wall center. A uniform out-of-plane rf-field couples strongly to this critical mode only in the Neel phase. An analytical Landau theory shows that the critical mode frequency varies as the square root of (hc - h) just below the transition, as found numerically.