arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 19 recordsLinked to original sources

arXiv2026

Stoner transitions beyond mean-field in two-dimensional electronic systems: a diagrammatic Monte Carlo study

Stoner instabilities for fermions with repulsive interaction have been well studied within the mean-field (ladder) approximation. In this study, we consider two-dimensional electronic systems with one or two valleys and discuss a Stoner transition beyond the ladder approximation. At weak coupling, the corrections to the ladder approximation come predominantly from the renormalization of the particle-hole vertex in the particle-particle channel, and the lowest-order corrections are logarithmically singular in the low-density limit. To investigate the problem beyond the lowest order, we apply the diagrammatic Monte Carlo algorithm and treat ladder and non-ladder renormalizations on equal footing. We find that in a one-valley system, a Stoner transition to a ferromagnetism occurs at low density only if there is a cutoff on the momentum transfer carried by the interaction. In a two-valley system, the restriction is less severe. Here we find either a direct Stoner transition into a spin- and valley-polarized state, or a set of two Stoner transitions via an intermediate valley-polarized state. The pathway is controlled by the anisotropy of the fermionic dispersion.

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arXiv2026

Magnon-Mediated Superconductivity in a 2D Itinerant Ferromagnet with Weak Easy-plane Magnetic Anisotropy

Motivated by recent observations of superconductivity in a quarter-metal state of spin- and valley- polarized graphene multilayers, we investigate pairing within a ferromagnetic phase of a single-valley model of itinerant two-dimensional (2D) electrons with Hubbard-type interaction and no artificial high-energy cutoff. In 2D, the Stoner transition is first-order into a fully-polarized state wherein the only gapless collective excitations are transverse magnons. We find that in a spin-SU(2) symmetric model, this magnon-mediated pairing interaction between equal-spin fermions vanishes at $T=0$. We show that a small easy-plane magnetic anisotropy $Ω_0 \ll E_F$, where $E_F$ is the Fermi energy, breaks the SU(2) symmetry and generates an attractive interaction for equal-spin $p-$wave pairing. We explicitly derive the corresponding coupling constant $λ_p$ as the scaling function of both the relative strength of the easy-plane anisotropy, $Ω_0/E_F$, and the proximity to the ferromagnetic transition. While $λ_p$ is parametrically small in $Ω_0/E_F$ deep inside the ferromagnetic phase, it becomes enhanced near the ferromagnetic transition, reaching order unity regardless of how small $Ω_0/E_F$ is. This mechanism yields a sizable $T_c$, peaked near the onset of ferromagnetism.

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arXiv2026

Non-BCS Pairing by a Singular Dynamical Interaction

This review examines the theory of superconductivity in systems with {\em singular dynamical} electron-electron interaction and contrasts it with a conventional BCS superconductivity. Examples include metals near a Quantum Critical Point, quantum dots and system near a localization (Mott) transition. We show, that the singular interaction destroys the traditional separation of energy scales, invalidating the significance of Cooper logarithm, and, as the consequence, the whole BCS framework. We explore the universal model with dynamical interaction $Γ(Ω) \propto 1/|Ω|^γ$ (the $γ$-model) and analyze the competition/interplay between the tendency towards pairing and towards non-Fermi liquid behavior. We show that superconductivity still develops once the pairing interaction exceeds a certain threshold, but the origin of the pairing is qualitatively different from that in BCS theory. We show that the gap equation at $T=0$ has an infinite set of topologically distinct solutions. These solution disappear one by one once the pairing interaction becomes non-singular (massive). We review the physics underlying these phenomena and outline future directions.

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arXiv2026

Magnetic field induced transition from nodeless to nodal superconductivity in $β$-PdBi$_{2}$

Recent tunneling measurements on $β$-PdBi$_2$ reported a magnetic field induced phase transition from a fully gapped to a nodal superconducting state. We develop a microscopic theory of superconductivity in this multi-band material, taking into account spin-orbit coupling and Zeeman splitting. We show that there are two attractive pairing channels in this system: an s-wave and a p-wave. At zero magnetic field, s-wave superconductivity wins. At a finite field, this channel becomes less favorable because Fermi surfaces split, and the gap symmetry changes to p-wave. We show that at a higher field, the excitation spectrum of a p-wave multi-band superconductor becomes gapless, with nodal points located in between the split Fermi surfaces. We argue that this behavior accounts for the experimentally observed field-induced nodal superconductivity in $β$-PdBi$_2$.

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arXiv2026

Nematic Phase Transitions in Multilayer Graphene Systems

Recent experiments on graphene multilayers under displacement field have demonstrated a wide variety of electronically ordered phases, including valley and/or spin polarized phases as well as potentially unconventional superconducting phases. In addition, quantum oscillation measurements in Bernal bilayer graphene and rhombohedral trilayer graphene showed the presence of electronic nematic states. Here, we investigate the emergence of nematic order in these systems, with emphasis on Bernal bilayer graphene, within a self-consistent Hartree--Fock framework, using a realistic band structure with trigonal warping and a dual-gate screened Coulomb interaction. We compute the phase diagram as carrier density and displacement field are varied, and find a sequence of isospin (spin and valley) polarized states consistent with experiment, including partially polarized phases with a large Fermi pockets for isospin-majority carriers and smaller Fermi pockets for isospin-minority carriers. Within these partially isospin polarized states, we identify regions with three $C_3$-symmetric pockets for the minority carriers and regions with only one or two such pockets, implying that the system develops a spontaneous nematic order that breaks $C_3$ symmetry. We find numerically that nematicity emerges near the boundary between fully and partially polarized phases and is controlled by the strength of the screened interaction. We analytically derive a criterion for the nematic order, which agrees with our numerical results.

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arXiv2026

Topologically non-trivial gap function and topology-induced time-reversal symmetry breaking in a superconductor with singular dynamical interaction

In many strongly correlated electron systems, non-Fermi liquid behavior and unconventional superconductivity can be viewed as emerging from an effective 4-fermion interaction with a singular frequency dependence. A pairing instability in such a system is qualitatively different from that in a Fermi liquid and generally gives rise to multiple pairing states with topologically distinct gap functions. However, in the systems studied so far, a topologically trivial solution has the lowest energy. Here we show that a repulsive Hubbard-type interaction with a finite cutoff added to a model with a singular dynamical interaction selects, in some parameter range, the theretofore subleading, topologically nontrivial solution. We consider a minimal model that displays this behavior and show that the transformation between the topologically trivial and nontrivial gap functions necessarily occurs via an intermediate phase with topology-induced breaking of time-reversal symmetry.

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arXiv2026

Spatially resolved collective modes in d-wave superconductors

We analyze the dispersion of collective modes in a superconductor with $d-$wave symmetry of the order parameter in the presence of long-range Coulomb interaction. We use diagrammatic technique and quasiclassical theory in Keldysh-Nambu formalism to compute longitudinal and transverse pair susceptibilities and extract from them the dispersion of the longitudinal and transverse collective mode. We show that at T=0, the dispersion of the transverse (plasma) mode is the same as in an s-wave superconductor, but at a finite temperature it is softer and has a much larger decay rate due to the partial screening of the Coulomb potential by nodal quasiparticles. We show that the dispersion of the longitudinal mode depends on the direction of momentum with respect to the positions of the nodes of the d-wave gap, while the decay rate of this mode does not depend on momentum. We discuss experimental implications of our results.

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arXiv2025

Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal

We examine the spectral properties of collective excitations with finite angular momentum $l$ for a system of interacting fermions near a Pomeranchuk quantum critical point, both in the Fermi liquid and non-Fermi liquid regimes. Previous studies found that deep in the Fermi liquid regime, the spectral functions for even and odd $l$ behave differently - the latter is suppressed compared to the former because of kinematic constraints on scattering processes. The main focus of our paper is to understand how the spectral functions for even and odd $l$ evolve as the system enters the non-Fermi liquid regime. We obtain the full scaling function for the electron polarization bubble at arbitrary $l$, which interpolates between the Fermi liquid and non-Fermi liquid regimes. We show that collective excitations for all $l$ remain stable and causal throughout the crossover and right at the quantum critical point.

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arXiv2025

Pseudogap in electron-doped cuprates: thermal precursor to magnetism

We study pseudogap behavior in a metal near an antiferromagnetic instability and apply the results to electron-doped cuprates. We associate pseudogap behavior with thermal magnetic fluctuations and compute the fermionic self-energy along the Fermi surface beyond Eliashberg approximation. We analyze the spectral function as a function of frequency (energy distribution curves, EDC) and momentum (momentum distribution curves, MDC). We show that the EDC display pseudogap behavior with peaks at a finite frequency at all momenta. On the other hand, MDC peaks disperse within the pseudogap, ending at a gossamer Fermi surface. We analyze magnetically-mediated superconductivity and show that thermal fluctuations almost cancel out in the gap equation, even when the self-energy is obtained beyond the Eliashberg approximation. We favorably compare our results with recent ARPES study [K-J Xu et al, Nat. Phys. 19, 1834-1840 (2023)].

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arXiv2025

Stoner Transition at Finite Temperature in a 2D Isotropic Fermi Liquid

We present the results of a mean-field analysis of the temperature evolution of a ferromagnetic Stoner transition in a two-dimensional (2D) system with an isotropic dispersion $\varepsilon_k \propto k^{2α}$, which for $α>1$ models flat dispersions in various multi-layer graphene systems in a displacement field. This study is an extension to a finite $T$ of previous studies at $T=0$, which found both first-order and second-order Stoner transitions, depending on the value of $α$ and special behavior at $α=1$ and $α=2$. We find that the Stoner transition at a finite $T$ displays new features not seen at $T=0$. The most interesting one is the reentrant behavior, where the ordered state emerges as temperature is increased. This behavior develops at $α>1.4$ and the range where it holds increases with $α$. We conjecture that the reentrant behavior is the fundamental feature of the Stoner transition in 2D, not sensitive to the details of the electronic structure.

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arXiv2025

BCS-like formula for $T_c$ does not necessarily imply BCS pairing mechanism: the case of magnetically-mediated quantum-critical pairing

In the BCS theory of superconductivity, an instability towards pairing develops at arbitrary weak dimensionless coupling $λ$ due to a divergence of logarithmic perturbative series for the pairing susceptibility (Cooper logarithms) at $T_c \sim ω_0 e^{-1/λ}$, where $ω_0$ is an energy cutoff. On the contrary, in many models of superconductivity out of a non-Fermi liquid, Cooper logarithm is absent and superconductivity emerges only when $λ$ exceeds a certain threshold. We argue that there are situations when there is no threshold and at weak coupling the formula for $T_c$ is BCS-like, yet the origin of the pairing instability is fundamentally different from that in the BCS scenario. As an example, we revisit superconductivity in a metal at the onset of $(π,π)$ spin-density-wave order. Earlier studies of this problem found no threshold and a BCS-like expression for $T_c$ at weak coupling. We argue that, despite this, the pairing is not caused by the Cooper logarithm and in many respects is qualitatively similar to that in non-Fermi liquids.

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arXiv2025

Valley and Spin Polarized States in Bernal Bilayer Graphene

We present the results for the evolution of the Fermi surfaces under variation of number density and displacement field for spin and valley-polarized states in Bernal bilayer graphene (BBG) using a realistic form of the electronic dispersion with trigonal warping terms. Earlier studies without trigonal warping have found discrete half-metal and quarter-metal states with full spin and/or valley polarization and complete depletion of some of the Fermi surfaces. We show that when trigonal warping terms are included in the dispersion, partially polarized states with large but non-complete polarization and with both majority and minority carriers present, emerge at small doping, as seen in the experimental data. We show the results when the intervalley and intravalley interactions are equal as well as when they are unequal.

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arXiv2025

An unusual first order phase transition in a 2D superconductor

We consider a superconductor under external perturbation, which forces Cooper pairs to develop with a finite total momentum $q$. The condensation energy of such a state decreases with $q$ and vanishes at a critical $q_c$. We analyze how superconducting order evolves at $ q \approx q_c$. In 3D, the result is well-known: the pairing susceptibility diverges at $q = q_c +0$, and the gap amplitude $Δ(q)$ gradually increases as $q$ decreases below $q_c$ and reaches its largest value $Δ_0$ at $q=0$. In 2D, we find different behavior. Namely, for a parabolic dispersion, the pairing susceptibility also diverges at $q = q_c +0$, but at $q = q_c -0$, the gap amplitude jumps to the maximal $Δ_0$ and remains equal to it for all $q 1$ the transition becomes second-order, but the gap evolution is rather sharp, whereas for $α<1$ it becomes first-order, but $Δ(q)$ is non-monotonic. This is similar, but not identical, to the behavior of magnetization near a Stoner transition in 2D.

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arXiv2025

Time-reversal symmetry breaking, collective modes, and Raman spectrum in pair-density-wave states

Inspired by empirical evidence of the existence of pair-density-wave (PDW) order in certain underdoped cuprates, we investigate the collective modes in systems with unidirectional PDW order with momenta $\pm {Q}$ and a $d$-wave form-factor with special focus on the amplitude (Higgs) modes. In the pure PDW state, there are two overdamped Higgs modes. We show that a phase with co-existing PDW and uniform ($d$-wave) superconducting (SC) order, PDW/SC, spontaneously breaks time-reversal symmetry - and thus is distinct from a simpler phase, SC/CDW, with coexisting SC and charge-density-wave (CDW) order. The PDW/SC phase exhibits three Higgs modes, one of which is sharply peaked and is predominantly a PDW fluctuation, symmetric between ${Q}$ and -${Q}$, whose damping rate is strongly reduced by SC. This sharp mode should be visible in Raman experiments.

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arXiv2024

Fermi Liquid near a q=0 Charge Quantum Critical Point

We analyze the quasiparticle interaction function (the fully dressed and antisymmetrized interaction between fermions) for a two-dimensional Fermi liquid at zero temperature close to a q=0 charge quantum critical point (QCP) in the $s-$wave channel (the one leading to phase separation). By the Ward identities, this vertex function must be related to quasiparticle residue $Z$, which can be obtained independently from the fermionic self-energy. We show that to satisfy these Ward identities, one needs to go beyond the standard diagrammatic formulation of Fermi-liquid theory and include series of additional contributions to the vertex function. These contributions are not present in a conventional Fermi liquid, but do emerge near a QCP, where the effective 4-fermion interaction is mediated by a soft dynamical boson. We demonstrate explicitly that including these terms restores the Ward identity. Our analysis is built on previous studies of the vertex function near an antiferromagnetic QCP [Phys. Rev. B 89, 045108 (2014)] and a d-wave charge-nematic QCP [Phys. Rev. B 81, 045110 (2010)]. We show that for $s-$wave charge QCP the analysis is more straightforward and allows one to obtain the full quasiparticle interaction function (the Landau function) near a QCP. We show that all partial components of this function (Landau parameters) diverge near a QCP, in the same way as the effective mass $m^*$, except for the $s$-wave charge component, which approaches $-1$. Consequently, the susceptibilities in all channels, except for the critical one, remain finite at a QCP, as they should.

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arXiv2024

Hydride superconductivity: here to stay

The field of hydride superconductivity has recently been mired in a controversy that might divert attention from the question of central importance: do hydrides support genuine superconductivity or not? We examine some key papers from the field, and conclude that hydride superconductivity is real.

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arXiv2024

Two-dimensional Stoner transitions beyond mean-field

We have previously shown that the Stoner instability 2D has unconventional behavior: it is strongly first order but features a susceptibility which diverges at the transition point. Here, we analyze the Stoner transition for two-dimensional systems with spin and valley degrees of freedom, beyond mean field. At low density, we show that in one-valley and isotropic two-valley systems the leading effect beyond mean-field theory is suppression of the Stoner instability. In anisotropic two-valley systems, we show that, for larger anisotropy, the transition remains mean-field-like and retains its unconventional properties. We discuss applications to AlAs quantum wells.

cond-mat.str-el↗

arXiv2024

Quantum criticality and optical conductivity in a two-valley system

We demonstrate that the optical conductivity of a Fermi liquid (FL) in the absence of umklapp scattering is dramatically affected by the topology of the Fermi surface (FS). Specifically, electron-electron (ee) scattering leads to rapid current relaxation in systems with multiple, or multiply connected, FSs, provided the valleys have different effective masses. This effect results from intervalley drag. We microscopically derive the optical conductivity of a two-valley system, both within the FL regime and near a quantum critical point (QCP) of the Ising-nematic type. In the FL regime, intervalley drag restores the Gurzhi-like scaling of the conductivity, $\mathrm{Re} σ(ω) \sim ω^0$. This dependence contrasts sharply with the previously identified sub-leading contribution to the conductivity of a two-dimensional FL with a single convex FS, where $\mathrm{Re} σ(ω) \sim ω^2 \ln |ω|$. The vanishing of the leading term in the optical conductivity is a signature of geometric constraints on ee scattering channels, which are lifted for a multiply connected FS. A large differential response, $d \mathrm{Re} σ/d μ$ with $μ$ being the chemical potential, is predicted at the Lifshitz transition from a single-valley to a multi-valley FS, which should be observable within the experimentally accessible frequency range. Near a QCP, intervalley drag leads to a $|ω|^{-2/3}$ scaling of $\mathrm{Re} σ(ω)$ in 2D, thus providing a specific current-relaxing process for this long-standing conjecture.

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