arXiv subjects

Artem Abanov

Publications and source records attributed to Artem Abanov.

At least 19 recordsLinked to original sources

arXiv2026

Does a pole in the self-energy imply a violation of the Luttinger theorem?

Luttinger theorem relates Fermi surface volume to electron density per spin $n$. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, originating from a self-energy $Σ(ω, \mathbf{k})$ with a pole, and a narrow residual quasiparticle band crossing $ω=0$, with a small residue $Z \ll 1$ (a residual Fermi liquid). We consider Model I, in which $Z$ also renormalizes quasiparticle bandwidth $W$ to $ZW$ and Model II, in which $W$ remains unrenormalized. The Green's function for such a system $G(ω, \mathbf{k})$ contains two zeros and three poles --- one from the quasiparticle band and two from the gapped bands. Yet, we show that in Model I, the Luttinger-Ward analysis is fully applicable for any $Z >0$, and the results are exactly the same as if the gapped bands did not exist. For Model II, the Luttinger-Ward analysis recovers once $Z$ exceeds some critical value, which depends on fermionic density.

cond-mat.str-el↗

arXiv2026

Limits of validity for Migdal-Eliashberg theory: role of polarons/bi-polarons

It is widely believed that in the adiabatic limit the Fermi liquid state of an electron-phonon system, described by Migdal-Eliashberg theory, remains stable until the dressed phonon softens. Our variational and analytic analysis of the prototypical Holstein model shows that, in a wide range of fillings both in 3D and 2D, a polaronic/bipolaronic state emerges before phonon softening; at small filling in 3D this happens already at weak coupling. We show that a polaronic/bipolaronic state emerges, upon increasing coupling, via an intermediate pseudogap-type mixed state, in which some fermions retain Fermi liquid behavior, yet Luttinger's theorem is violated. At even larger couplings the density of states gradually approaches its form in the atomic limit.

cond-mat.str-el↗

arXiv2026

Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons

The Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and for an interaction with an optical phonon breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option for this case---a collapse to a polaronic/bipolaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling $λ$, at which a Fermi-liquid state transforms into the bipolaron/polaron state. We show that at small and near-maximum densities, this happens well before a dressed phonon softens. This is true both in two- and three-dimensional systems; in the latter, the upper bound on $λ$ tends to zero in the limit of small or near-full density. We present analytical reasoning for this behavior based on hints extracted from exact diagrammatic treatment of the on-site Holstein model for the spin polarized case and argue that polarons are produced by fermions with energies comparable to the bandwidth; i.e., polaron formation is outside the realm of MET. Closer to half-filling, the leading instability upon increasing $λ$ is toward a charge-density-wave state (CDW), and there exists a strong coupling regime of MET near this instability, while the polaron/bipolaron state develops at larger $λ$ out of a CDW-ordered state and inherits a CDW order over some range of coupling.

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arXiv2026

Superconductivity Near a Quantum Critical Point: Bounds on the Transition Temperature in the $γ$-Model

Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS and Migdal-Eliashberg theories. We consider the problem of obtaining closed-form analytical lower and upper bounds on transition temperatures for such systems. We focus mainly on a class of models known as the gamma-model, a variation of the Eliashberg theory of superconductivity where the effective interaction potential scales as V(Omega) proportional to 1/|Omega|^gamma. Building on a recent reformulation of Migdal-Eliashberg theory expressed as a classical infinite spin chain with nonlocal interactions [1,2], and employing a linear algebra analysis of the Hessian matrix obtained from the free energy functional, we derive rigorous, closed-form expressions for upper and lower bounds on the superconducting transition temperature for any gamma > 0. The main result of the paper is to establish an analytical upper bound on the transition temperature in closed form. Our upper bound is significantly tighter than those currently available in the literature and demonstrates rapid convergence toward results from prior numerical studies. Also, by applying the singularity condition directly to the unbounded Hessian matrix, our independently performed calculations confirm the lower bounds previously established in the literature [3].

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arXiv2025

Kinetics of Bose-Einstein condensation of magnons in Yttrium Iron Garnet films

In this article, we explain the reason of the apparent contradiction between recent experiments [1] and [2] and earlier theoretical predictions [3] of strongly asymmetric condensate resulting in attractive interaction between the condensate magnons. We show that the relaxation time for equilibrium between two condensates at two minima of energy exceeds the time of experiment. Therefore, it should be described by Boltzmann kinetic equation. We develop the proper kinetic theory and find the relation between the critical pumping power and the effective temperature of over-condensate magnons.

cond-mat.mes-hall↗

arXiv2025

Three-Dimensional Domain-Wall Membranes

Three-dimensional magnetic textures, such as Hopfions, torons, and skyrmion tubes, possess rich geometric and topological structure, but their detailed energetics, deformation modes, and collective behavior are yet to be fully understood. In this work, we develop an effective geometric theory for general three-dimensional textures by representing them as embedded two-dimensional orientable domain-wall membranes. Using a local ansatz for the magnetization in terms of membrane coordinates, we integrate out the internal domain-wall profile to obtain a reduced two-dimensional energy functional. This functional captures the coupling between curvature, topology, and the interplay of micromagnetic energies, and is expressed in terms of a small set of soft-mode fields: the local wall thickness and in-plane magnetization angle. Additionally, we construct a local formula for the Hopf index which sheds light on the coupling between geometry and topology for nontrivial textures. We analyze the general properties of the theory and demonstrate its utility through the example of a flat membrane hosting a vortex as well as a toroidal Hopfion, obtaining analytic solutions for the wall thickness profile, associated energetics, and a confirmation of the Hopf index formula. The framework naturally extends to more complex geometries and can accommodate additional interactions such as Dzyaloshinskii-Moriya, Zeeman, and other anisotropies, making it a versatile tool for exploring the interplay between geometry, topology, and micromagnetics in three-dimensional spin systems.

cond-mat.mes-hall↗

arXiv2024

Non-BCS behavior of the pairing susceptibility near the onset of superconductivity in a quantum-critical metal

We analyze the dynamical pairing susceptibility $χ_{pp} (ω_m)$ at $T=0$ in a quantum-critical metal, where superconductivity emerges out of a non-Fermi liquid ground state once the pairing interaction exceeds a certain threshold. We obtain $χ_{pp} (ω_m)$ as the ratio of the fully dressed dynamical pairing vertex $Φ(ω_m)$ and the bare $Φ_0 (ω_m)$ (both infinitesimally small). For superconductivity out of a Fermi liquid, the pairing susceptibility is positive above $T_c$, diverges at $T_c$, and becomes negative below it. For superconductivity out of a non-Fermi liquid, the behavior of $χ_{pp} (ω_m)$ is different in two aspects: (i) it diverges at the onset of pairing at $T=0$ only for a certain subclass of bare $Φ_0 (ω_m)$ and remains non-singular for other $Φ_0 (ω_m)$, and (ii) below the instability, it becomes a non-unique function of a continuous parameter $ϕ$ for an arbitrary $Φ_0 (ω_m)$. The susceptibility is negative in some range of $ϕ$ and diverges at the boundary of this range. We argue that this behavior of the susceptibility reflects a multi-critical nature of a superconducting transition in a quantum-critical metal when immediately below the instability an infinite number of superconducting states emerges simultaneously with different amplitudes of the order parameter down to an infinitesimally small one.

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arXiv2024

Thickness-Driven Transitions Between Novel Magnetic States in Ferromagnetic Films

Magnetic materials hosting stable topological spin textures have demonstrated energy efficiency and potential as information carriers in novel logic and memory devices, offering an alternative to magnetic tunnel junction technology. While these structures are well understood in 2D, in 3D their stability, interactions, and topological transitions require further exploration. Here we present two thermodynamically stable topological states, termed the "hourglass" and "dome", in centrosymmetric magnetic films of varying thickness. Crucially, we observe thickness-dependent transitions between the two states, with regions of metastability where both configurations coexist. We construct a phase diagram detailing the parameter space for their existence and transitions, provide an effective description of the interactions that mediate the transition, and discuss the implications of this type of state switching.

cond-mat.mes-hall↗

arXiv2022

Superconductivity out of a non-Fermi liquid. Free energy analysis

In this paper, we present in-depth analysis of the condensation energy $E_c$ for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in a metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective $0+1$ dimensional model with the effective dynamical interaction $V(Ω_m) = {\bar g}^γ/|Ω_m|^γ$, where $γ$ is model-specific (the $γ$-model). In previous papers, we argued that the pairing in the $γ$ model is qualitatively different from that in a Fermi liquid, and the gap equation at $T=0$ has an infinite number of topologically distinct solutions, $Δ_n (ω_m)$, where an integer $n$, running between $0$ and infinity, is the number of zeros of $Δ_n (ω_m)$ on the positive Matsubara axis. This gives rise to the set of extrema of $E_c$ at $E_{c,n}$, of which $E_{c,0}$ is the global minimum. The spectrum $E_{c,n}$ is discrete for a generic $γ<2$, but becomes continuous at $γ= 2-0$. Here, we discuss in more detail the profile of the condensation energy near each $E_{c,n}$ and the transformation from a discrete to a continuous spectrum at $γ\to 2$. We also discuss the free energy and the specific heat of the $γ$-model in the normal state.

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arXiv2022

Odd frequency pairing in a quantum critical metal

We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(Ω_n)\sim 1/|Ω_n|^γ$ (the $γ$-model). This interaction gives rise to a non-Fermi liquid in the normal state and is attractive for pairing. The two trends compete with each other. We search for odd-frequency solutions for the pairing gap $Δ(ω_m)= -Δ(ω_m)$. We show that for $γ<1$, odd-frequency superconductivity looses the competition with a non-Fermi liquid and does not develop. We show that the pairing does develop in the extended model in which interaction in the pairing channel is larger than the one in the particle-hole channel. For $γ>1$, we argue that the original model is at the boundary towards odd-frequency pairing and analyze in detail how superconductivity is triggered by a small external perturbation. In addition, we show that for $γ>2$, the system gets frozen at the critical point towards pairing in a finite range in the parameter space. This give rise to highly unconventional phase diagrams with flat regions.

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arXiv2021

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. VI. The $γ$ model and its phase diagram at $2 < γ<3$

In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V(Ω_m) = {\bar g}^γ/|Ω_m|^γ$ (the $γ$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous Papers I-V we analyzed the $γ$ model for $γ\leq 2$ and argued that the ground state is an ordinary superconductor for $γ<1$, a peculiar one for $1<γ<2$, when the phase of the gap function winds up along real frequency axis due to emerging dynamical vortices in the upper half-plane of frequency, and that there is a quantum phase transition at $γ=2$, when the number of dynamical vortices becomes infinite. In this paper we consider larger $2< γ<3$ and address the issue what happens on the other side of this quantum transition. We argue that the system moves away from criticality in that the number of dynamical vortices becomes finite and decreases with increasing $γ$. The ground state is again a superconductor, however a highly unconventional one with a non-integrable singularity in the density of states at the lower edge of the continuum. This implies that the spectrum of excited states now contains a level with a macroscopic degeneracy, proportional to the total number of states in the system. We argue that the phase diagram in variables $(T,γ)$ contains two distinct superconducting phases for $γ<2$ and $γ>2$, and an intermediate pseudogap state of preformed pairs.

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arXiv2021

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal: V. The $γ$ model and its phase diagram. The case $γ=2$

This paper is a continuation and a partial summary of our analysis of the pairing at a quantum-critical point (QCP) in a metal for a set of quantum-critical systems, whose low-energy physics is described by an effective model with dynamical electron-electron interaction $V(Ω_m) = ({\bar g}/|Ω_m|)^γ$ (the $γ$-model). Examples include pairing at the onset of various spin and charge density-wave and nematic orders and pairing in SYK-type models. In previous papers, we analyzed the physics for $γ<2$. We have shown that the onset temperature for the pairing $T_p$ is finite, of order ${\bar g}$, yet the gap equation at $T=0$ has an infinite set of solutions within the same spatial symmetry. As the consequence, the condensation energy $E_c$ has an infinite number of minima. The spectrum of $E_c$ is discrete, but becomes more dense as $γ$ increases. Here we consider the case $γ=2$. The $γ=2$ model attracted special interest in the past as it describes the pairing by an Einstein phonon in the limit when the dressed phonon mass $ω_D$ vanishes. We show that for $γ=2$, the spectrum of $E_c$ becomes continuous. We argue that the associated gapless "longitudinal" fluctuations destroy superconducting phase coherence at a finite $T$, such that at $0<T< T_p$ the system displays pseudogap behavior. We show that for each gap function from the continuum spectrum, there is an infinite array of dynamical vortices in the upper half-plane of frequency. For the electron-phonon case, our results show that $T_p =0.1827 {\bar g}$, obtained in earlier studies, marks the onset of the pseudogap behavior of preformed pairs, while the actual superconducting $T_c$vanishes at $ω_D \to 0$.

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arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The $γ$ model and its phase diagram at $1<γ<2$

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 (QC) systems with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model). In previous papers we studied the cases $0<γ<1$ and $γ\approx 1$. We argued that the pairing by a gapless boson is fundamentally different from BCS/Eliashberg pairing by a massive boson as for the former there exists an infinite number of topologically distinct solutions for the gap function $Δ_n (ω_m)$ at $T=0$ ($n=0,1,2...$), each with its own condensation energy $E_{c,n}$. Here we extend the analysis to larger $1< γ<2$. We argue that the discrete set of solutions survives, and the spectrum of $E_{c,n}$ gets progressively denser as $γ$ approaches $2$ and eventually becomes continuous at $γ\to 2$. This increases the strength of "longitudinal" gap fluctuations, which tend to reduce the actual superconducting $T_c$ and give rise to a pseudogap region of preformed pairs. We also detect two features on the real axis for $γ>1$ which become critical at $γ\to 2$. First, the density of states evolves towards a set of discrete $δ-$functions. Second, an array of dynamical vortices emerges in the upper frequency half-plane. These two features come about because on a real axis, the real part of the interaction, $V' (Ω) \propto \cos(πγ/2)/|Ω|^γ$, becomes repulsive for $γ>1$, and the imaginary $V^{''} (Ω) \propto \sin(πγ/2)/|Ω|^γ$, gets progressively smaller at $γ\to 2$. The features on the real axis are consistent with the development of a continuum spectrum of $E_{c,n}$ obtained using $Δ_n (ω_m)$ on the Matsubara axis. We consider the case $γ=2$ separately in the next paper.

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arXiv2020

Pairing by a dynamical interaction in a metal

We consider pairing of itinerant fermions in a metal near a quantum-critical point (QCP) towards some form of particle-hole order (nematic, spin-density-wave, charge-density-wave, etc). At a QCP, the dominant interaction between fermions comes from exchanging massless fluctuations of a critical order parameter. At low energies, this physics can be described by an effective model with the dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$, up to some upper cutoff $Λ$. The case $γ=0$ corresponds to BCS theory, and can be solved by summing up geometric series of Cooper logarithms. We show that for a finite $γ$, the pairing problem is still marginal (i.e., perturbation series are logarithmic), but one needs to go beyond logarithmic approximation to find the pairing instability. We discuss specifics of the pairing at $γ>0$ in some detail and also analyze the marginal case $γ= 0+$, when $V(Ω_m) = λ\log{(Λ/|Ω_m|)}$. We show that in this case the summation of Cooper logarithms does yield the pairing instability at $λ\log^2{(Λ/T_c)} = O(1)$, but the logarithmic series are not geometrical. We reformulate the pairing problem in terms of a renormalization group (RG) flow of the coupling, and show that the RG equation is different in the cases $γ=0$, $γ= 0+$, and $γ>0$.

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arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $γ$-model and its phase diagram at $T=0$. The case $0 < γ<1$

We analyze a class of quantum-critical models, in which momentum integration and the selection of a particular pairing symmetry can be done explicitly, and the competition between non-Fermi liquid and pairing can be analyzed within an effective model with dynamical electron-electron interaction $V(Ω_m)\sim 1/|Ω_m|^γ$ (the $γ$-model). In this paper, the first in the series, we consider the case $T=0$ and $0<γ<1$. We argue that tendency to pairing is stronger, and the ground state is a superconductor. We argue, however, that superconducting state is highly non-trivial as there exists a discrete set of topologically distinct solutions for the pairing gap $Δ_n (ω_m)$ ($n = 0, 1, 2..., \infty$). All solutions have the same spatial pairing symmetry, but differ in the time domain: $Δ_n (ω_m)$ changes sign $n$ times as a function of Matsubara frequency $ω_m$. The $n =0$ solution $Δ_0 (ω_m)$ is sign-preserving and tends to a finite value at $ω_m =0$, like in BCS theory. The $n = \infty$ solution corresponds to an infinitesimally small $Δ(ω_m)$. As a proof, we obtain the exact solution of the linearized gap equation at $T=0$ on the entire frequency axis for all $0<γ<1$, and an approximate solution of the non-linear gap equation.We argue that the presence of an infinite set of solutions opens up a new channel of gap fluctuations. We extend the analysis to the case where the pairing component of the interaction has additional factor $1/N$ and show that there exists a critical $N_{cr} >1$, above which superconductivity disappears, and the ground state becomes a non-Fermi liquid.We show that all solutions develop simultaneously once $N$ gets smaller than $N_{cr}$.

cond-mat.str-el↗

arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. II. The $γ$-model at a finite $T$ for $0<γ<1$

In this paper we continue the analysis of the interplay between non-Fermi liquid and superconductivity for quantum-critical systems, the low-energy physics of which is described by an effective model with dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$ model). In paper I [A. Abanov and A. V. Chubukov, Phys Rev B. 102, 024524 (2020)] two of us analyzed the $γ$ model at $T=0$ for $0<γ<1$ and argued that there exist a discrete, infinite set of topologically distinct solutions for the superconducting gap, all with the same spatial symmetry. The gap function $Δ_n (ω_m)$ for the $n$th solution changes sign $n$ times as the function of Matsubara frequency. In this paper we analyze the linearized gap equation at a finite $T$. We show that there exist an infinite set of pairing instability temperatures, $T_{p,n}$, and the eigenfunction $Δ_n (ω_{m})$ changes sign $n$ times as a function of a Matsubara number $m$. We argue that $Δ_n (ω_{m})$ retains its functional form below $T_{p,n}$ and at $T=0$ coincides with the $n$th solution of the nonlinear gap equation. Like in paper I, we extend the model to the case when the interaction in the pairing channel has an additional factor $1/N$ compared to that in the particle-hole channel. We show that $T_{p,0}$ remains finite at large $N$ due to special properties of fermions with Matsubara frequencies $\pm πT$, but all other $T_{p,n}$ terminate at $N_{cr} = O(1)$. The gap function vanishes at $T \to 0$ for $N > N_{cr}$ and remains finite for $N < N_{cr}$. This is consistent with the $T =0$ analysis.

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arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. III: The $γ$ model and its phase diagram across $γ= 1$

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 $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-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 $0 < γ<1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions, $Δ_n (ω_m)$, all with the same spatial symmetry, and (ii) each $Δ_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper, we analyze how the system behavior changes between $γ<1$ and $γ>1$, both at $T=0$ and a finite $T$. The limit $γ\to 1$ is singular due to infra-red divergence of $\int d ω_m V(Ω_m)$, 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 $Δ_n (ω_m)$ gradually evolve through $γ=1$ both at $T=0$ and a finite $T$. For $N \neq 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $γ>1$. Namely, the form of $Δ_n (ω_m)$ 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 $γ>1$.

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arXiv2020

Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down

We analyze the validity of Eliashberg theory of phonon-mediated superconductivity in 2D systems in light of recent extensive Monte-Carlo studies of the Holstein model. Conventional wisdom says that Eliashberg theory is applicable as long as vertex corrections remain small. For small ratio of the phonon energy $Ω_0$ and the Fermi energy $E_F$, this condition is supposed to hold even when the dimensionless electron-phonon coupling $λ$ is larger than one, i.e., in the strong coupling regime. A comparison between various quantities computed in the Migdal approximation and those computed by Quantum Monte Carlo prove that this belief is wrong, and we identify analytically some of the ways in which this breakdown occurs for various "normal state" properties at $λ= λ_{cr}$, where $λ_{cr} = O(1)$. The breakdown occurs at temperatures high enough that neither superconducting nor charge-density wave correlations extend over any significant range of distances, so it cannot be associated with the onset of an instability toward any of the relevant ordered ground-states - rather it is associated with the local physics of classical bipolaron formation. Still, we show that certain properties, including the superconducting $T_c$ and the superconducting gap structure below $T_c$, can be accurately inferred from the strong-coupling limit of Eliashberg theory at $λ\leq λ_{cr}$.

cond-mat.supr-con↗