arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 37 records · Page 2Linked to original sources

arXiv2024

Pairing at a single Van Hove point

We show that an interacting electronic system with a single ordinary or extended Van Hove point, which crosses the Fermi energy, is unstable against triplet superconductivity. The pairing mechanism is unconventional. There is no Cooper instability. Instead, pairing is due to the divergence of the density of states at a Van Hove point, leading to a superconducting quantum critical point at a finite detuning from the Van Hove point. The transition temperature is universally determined by the exponent governing the divergence of the density of states. Enhancing this exponent drastically increases $T_c$. The Cooper pair wave function has a non-monotonic momentum dependence with a steep slope near the gap nodes. In the absence of spin-orbit coupling, pairing fluctuations suppress a $2e$ spin-triplet state, but allow pairs of triplets to condense into a charge-$4e$ singlet state at a temperature of similar order as our result.

cond-mat.supr-con↗

arXiv2024

Unconventional discontinuous transitions in isospin systems

We show that two-dimensional fermions with dispersion $k^2$ or $k^4$ undergo a first-order Stoner transition to a fully spin-polarized state despite that the spin susceptibility diverges at the critical point. We extend our analysis to systems with dispersion $k^{2α}$ and spin and valley isospin and show that there is a cascade of instabilities into fractional-metal states with some electron bands fully depleted; narrow intermediate ranges of partially-depleted bands exist for $α<1$ or $α> 2$. The susceptibility becomes large near each transition. We discuss applications to biased bilayer and tri-layer graphene and moiré systems.

cond-mat.str-el↗

arXiv2024

Unconventional discontinuous transitions in a 2D system with spin and valley degrees of freedom

We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly unconventional: the associated susceptibility diverges (or almost diverges) at the transition, yet immediately below it the system jumps discontinuously into a fully polarized state. We analyze the dispersion of the longitudinal and transverse collective modes in different parameter regimes above and below the transition. Additionally, we consider ordering in a system with full $\mathrm{SU(4)}$ symmetry and show that there is a cascade of discontinuous transitions into a set of states, which includes a quarter-metal, a half-metal and a three-quarter metal. We compare our results with the data for biased bilayer and tri-layer graphene.

cond-mat.str-el↗

arXiv2024

Applicability of Eliashberg theory for systems with electron-phonon and electron-electron interaction: a comparative analysis

We present a comparative analysis of the validity of Eliashberg theory for the cases of fermions interacting with an Einstein phonon and with soft nematic fluctuations near an Ising-nematic/Ising-ferromagnetic quantum-critical point (QCP). In both cases, Eliashberg theory is obtained by neglecting vertex corrections. For the phonon case, the reasoning to neglect vertex corrections is the Migdal ``fast electron/slow boson'' argument because the phonon velocity is much smaller than the Fermi velocity, $v_F$. The same argument allows one to compute the fermionic self-energy within Eliashberg theory perturbatively rather than self-consistently. For the nematic case, the velocity of a collective boson is comparable to $v_F$ and this argument apparently does not work. Nonetheless, we argue that while two-loop vertex corrections near a nematic QCP are not small parametrically, they are small numerically. At the same time, perturbative calculation of the fermionic self-energy can be rigorously justified when the fermion-boson coupling is small compared to the Fermi energy. Furthermore, we argue that for the electron-phonon case Eliashberg theory breaks down at some distance from where the dressed Debye frequency would vanish, while for the nematic case it holds all the way to a QCP. From this perspective, Eliashberg theory for the nematic case actually works better than for the electron-phonon case.

cond-mat.str-el↗

arXiv2024

Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point

We analyze optical conductivity of a clean two-dimensional electron system in a Fermi liquid regime near a $T=0$ Ising-nematic quantum critical point (QCP), and extrapolate the results to a QCP. We employ direct perturbation theory up to the two-loop order to elucidate how the Fermi surface's geometry (convex vs. concave) and fermionic dispersion (parabolic vs. non-parabolic) affect the scaling of the optical conductivity, $σ(ω)$, with frequency $ω$ and correlation length $ξ$. We find that for a convex Fermi surface the leading terms in the optical conductivity cancel out, leaving a sub-leading contribution $σ(ω) \propto ω^2 ξ^4 \mathcal{L}$, where $\mathcal{L} = \mathrm{const}$ for a parabolic dispersion and $\mathcal{L} \propto \log{ωξ^3}$ in a generic case. For a concave Fermi surface, the leading terms do not cancel, and $σ(ω) \propto ξ^2$. We extrapolate these results to a QCP and obtain $σ(ω) \propto ω^{2/3}$ for a convex Fermi surface and $σ(ω) \propto 1/ω^{2/3}$ for a concave Fermi surface.

cond-mat.str-el↗

arXiv2024

The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis

We investigate the crossover from an ordinary van Hove singularity (OVHS) to a higher order van Hove singularity (HOVHS) in a model applicable to Bernal bilayer graphene and rhombohedral trilayer graphene in a displacement field. At small doping, these systems possess three spin-degenerate Fermi pockets near each Dirac point $K$ and $K'$; at larger doping, the three pockets merge into a single one. The transition is of Lifshitz type and includes van Hove singularities. Depending on system parameters, there are either 3 separate OVHS or a single HOVHS. We model this behavior by a one-parameter dispersion relation, which interpolates between OVHS and HOVHS. In each case, the diverging density of states triggers various electronic orders (superconductivity, pair density wave, valley polarization, ferromagnetism, spin and charge density wave). We apply the parquet renormalization group (pRG) technique and analyze how the ordering tendencies evolve between OVHS and HOVHS. We report rich system behavior caused by disappearance/reemergence and pair production/annihilation of the fixed points of the pRG flow.

cond-mat.str-el↗

arXiv2023

Superfluid stiffness within Eliashberg theory: the role of vertex corrections

In this work we consider the superfluid stiffness of a generically non-Galilean invariant interacting system and investigate under what conditions the stiffness may nonetheless approach the Galilean-invariant value $n/m$. Within Eliashberg theory we find that the renormalized stiffness is approximately given by $n/m$ in the case when the $l=0$ and $l=1$ components of the effective Fermi-surface projected interaction are approximately equal over a range of frequencies. This holds, in particular, when the interaction is peaked at zero momentum transfer. We examine this result through three complementary lenses: the $δ(ω)$ term in the conductivity, the phase dependence of the Luttinger-Ward free energy, and the coupling of the amplitude and phase sectors in the Hubbard-Stratonovich collective mode action. From these considerations we show that the value of the stiffness is determined by the strength of renormalization of the current vertex and that the latter can be interpreted as the shift of the self-consistent solution due to flow of the condensate, or alternatively as coupling of the phase mode to $l=1$ fluctuations of the order parameter. We highlight that even though the superfluid stiffness in some non-Galilean systems approaches the Galilean value, this is not enforced by symmetry, and in general the stiffness may be strongly suppressed from its BCS value. As a corollary we obtain the generic form of the phase action within Eliashberg theory and charge and spin Ward identities for a superconductor with frequency dependent gap function.

cond-mat.supr-con↗

arXiv2023

Nonanalytic Corrections to the Landau Diamagnetic Susceptibility

We analyze potential non-analytic terms in the Landau diamagnetic susceptibility, $χ_{dia}$, at a finite temperature $T$ and/or in-plane magnetic field $H$ in a two-dimensional (2D) Fermi liquid. To do this, we express the diamagnetic susceptibility as $χ_{dia} = (e/c)^2 \lim_{Q\rightarrow0} Π^{JJ}_\perp (Q)/Q^2$, where $Π^{JJ}_\perp$ is the transverse component of the static current-current correlator, and evaluate $Π^{JJ}_\perp (Q)$ for a system of fermions with Hubbard interaction to second order in Hubbard $U$ by combining self energy, Maki-Thompson, and Aslamazov-Larkin diagrams. We find that at $T=H=0$, the expansion of $Π^{JJ}_\perp (Q)/Q^2$ in $U$ is regular, but at a finite $T$ and/or $H$, it contains $U^2 T$ and/or $U^2 |H|$ terms. Similar terms have been previously found for the paramagnetic Pauli susceptibility. We obtain the full expression for the non-analytic $δχ_{dia} (H,T)$ when both $T$ and $H$ are finite, and show that the $H/T$ dependence is similar to that for the Pauli susceptibility.

cond-mat.str-el↗

arXiv2023

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

It is generally believed that in a 2D metal, whose ground state is antiferromagnetically ordered with ${\bf Q} = (π,π)$, thermal (static) magnetic fluctuations give rise to precursor behavior above $T_N$, in which the spectral function of a hot fermion (the one for which ${\bf k}$ and ${\bf k} + {\bf Q}$ are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of $T >T_N$ and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following [Y.M. Vilk and A.-M. S. Tremblay, J. Phys. I France ${\bf 7}$ 1309 (1997)] that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion, but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, like, e.g., Eliashberg theory for magnetically-mediated superconductivity. We also analyze the potential pseudogap behavior at $T=0$. We argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.

cond-mat.str-el↗

arXiv2023

Superconductivity near spin and valley orders in graphene multilayers: a systematic study

Spin excitations that soften near the onset of magnetic order have long been known to act as `paramagnon' pairing glue that can drive spin-triplet superconductivity. Recent findings of superconductivity in graphene bilayers and trilayers, occurring in the proximity of different itinerant ordered phases polarized in isospin (spin and valley), have motivated us to conduct a comprehensive investigation of an isospin extension of the paramagnon pairing mechanism in the vicinity of spin/isospin orders. In each case, we identify a soft mode, associated with the order parameter fluctuations, that mediates pairing interaction. We develop an approach that relates the soft mode described through summation of the contributions most strongly divergent at the onset of spin/valley isospin orders. This interaction is not always attractive, but if it is, it gives rise to an enhancement of superconducting $T_c$ in an appropriate pairing channel. In the cases when the pairing interaction is attractive, it leads to the formation of a superconducting state which can be either spin-triplet and valley-singlet or vice versa, depending on the specific isospin order type. These findings demonstrate that the occurrence of superconductivity in the vicinity of an itinerant magnetic phase is a generic phenomenon, closely mirroring experimental observations.

cond-mat.supr-con↗

arXiv2023

Density of states and spectral function of a superconductor out of a quantum-critical metal

We analyze the validity of a quasiparticle description of a superconducting state at a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-s-wave gap symmetry, and at a first glance, should restore a coherent quasiparticle behavior. We argue that this does not necessarily hold as in some cases the fermionic self-energy remains singular slightly above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to broadening and eventual vanishing of the quasiparticle peak in the spectral function. We analyze the set of quantum-critical models with an effective dynamical 4-fermion interaction, mediated by a gapless boson at a QCP, $V(Ω) \propto 1/Ω^γ$. We show that coherent quasiparticle behavior in a superconducting state holds for $γ<1/2$, but breaks down for larger $γ$. We discuss signatures of quasiparticle breakdown and compare our results with the data.

cond-mat.supr-con↗

arXiv2023

Following the Higgs mode across the BCS-BEC crossover in two dimensions

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the longitudinal (Higgs) susceptibility in the lower half-plane of complex frequency. We analyze the behavior of the Higgs mode in a 2D neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $μ$ changes sign from positive to negative. For $μ>0$, we find a pole in the Higgs susceptibility in the lower half-plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $μ<0$, the pole still exists, but is "hidden," not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

cond-mat.supr-con↗

arXiv2023

Free energy and specific heat near a quantum critical point of a metal

We analyze free energy and specific heat for fermions interacting with gapless bosons at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes contributions from bosons, fermions, and their interaction, all expressed via fully dressed fermionic and bosonic propagators. The sum of the last two contributions is the free energy $F_γ$ of an effective low-energy model of fermions with boson-mediated dynamical 4-fermion interaction $V (Ω_m) \propto 1/|Ω_m|^γ$ (the $γ-$model). This purely electronic model has been used to analyze the interplay between non-Fermi liquid (non-FL) behavior and pairing near a QCP, which are both independent of the upper energy cutoff $Λ$. However, the specific heat $C_γ(T)$, obtained from $F_γ$, does depend on $Λ$. We argue that this dependence is spurious and cancels out, once we include the contribution from bosons. We compare our $C(T)$ with the one obtained within the $γ-$model using recently proposed regularization of $F_γ$. We argue that for $γ<1$, the full $C(T)$ and the regularized $C_γ(T)$ differ by a $γ-$dependent prefactor, while for $γ>1$, the full $C(T)$ is the sum of $ C_γ(T)$ and the specific heat of free bosons with fully dressed mass. For these $γ$, $C_γ(T)$ is negative. The authors of Ref. [1] argued that a negative $ C_γ(T)$ implies that the normal state becomes unstable at some distance to a QCP. In our calculation, both terms in $C(T)$ come from the same source, and $ C_γ(T)$ is smaller as long as vertex corrections can be safely neglected. We then argue that the normal state remains stable even at a QCP.

cond-mat.str-el↗

arXiv2022

Cascade of transitions in twisted and non-twisted graphene layers within the van Hove scenario

Motivated by measurements of compressibility and STM spectra in twisted bilayer graphene, we analyze the pattern of symmetry breaking for itinerant fermions near a van Hove singularity. Making use of an approximate SU(4) symmetry of the Landau functional, we show that the structure of the spin/isospin order parameter changes with increasing filling via a cascade of transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate van Hove peak in a particular fashion, consistent with the STM data and compressibility measurements, providing a unified interpretation of the cascade of transitions in twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific underlying fermionic model. We argue that an analogous van Hove scenario explains the cascade of phase transitions in non-twisted Bernal bilayer and rhombohedral trilayer graphene.

cond-mat.mes-hall↗

arXiv2022

Odd-frequency pairing and time-reversal symmetry breaking for repulsive interactions

We study the pairing of fermions by an interaction consisting of a Hubbard repulsion, mimicking a screened Coulomb potential, and a dynamical phonon-mediated attraction. For such interaction, the gap equation allows even- and odd-frequency solutions $Δ_e$ and $Δ_o$. We show that odd-frequency pairing does not develop within the Eliashberg approximation due to over-critical pair-breaking from the self-energy. When vertex corrections are included, the pairing interaction gets stronger, and $Δ_o$ can develop. We argue that even in this case keeping the self-energy is still a must as it cancels out the thermal piece in the gap equation. We further argue that $Δ_o$ is not affected by Hubbard repulsion and for strong repulsion is comparable to a reduced $Δ_e$. The resulting superconducting state is a superposition $Δ_e \pm i Δ_o$, which spontaneously breaks the time-reversal symmetry, despite that the pairing symmetry is an ordinary $s$-wave.

cond-mat.supr-con↗

arXiv2022

Twists and turns of superconductivity from a repulsive dynamical interaction

We review recent theoretical progress in understanding spatially uniform $s$-wave superconductivity which arises from a fermion-fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the transferred frequency. Such a situation holds, e.g., for systems with a screened Coulomb and retarded electron-phonon interaction. We show that despite repulsion, superconductivity is possible in a certain range of system parameters. However, at $T=0$ the gap function on the Matsubara axis, $Δ(ω_m)$, must pass through zero and change sign at least once. These zeros of $Δ(ω_m)$ have a topological interpretation in terms of dynamical vortices, and their presence imposes a constraint on the variation of the phase of the gap function along the real frequency axis, which can potentially be extracted from ARPES and other measurements. We discuss how superconductivity vanishes when the repulsion becomes too strong, and obtain a critical line which terminates at $T=0$ at a quantum-critical point for superconductivity. We show that the behavior of the gap function near this point is highly non-trivial. In particular, an infinitesimally small $Δ(ω_m)$ contains a singular $δ-$function piece $ω_m δ(ω_m)$. We argue that near the critical point superconductivity may be a mixed state with even-frequency and odd-frequency gap components.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

arXiv2022

Quantum phase transition in a clean superconductor with repulsive dynamical interaction

We consider a model of electrons at zero temperature, with a repulsive interaction which is a function of the energy transfer. Such an interaction can arise from the combination of electron-electron repulsion at high energies and the weaker electron-phonon attraction at low energies. As shown in previous works, superconductivity can develop despite the overall repulsion due to the energy dependence of the interaction, but the gap $Δ(ω)$ must change sign at some (imaginary) frequency $ω_0$ to counteract the repulsion. However, when the constant repulsive part of the interaction is increased, a quantum phase transition towards the normal state occurs. We show that, as the phase transition is approached, $Δ$ and $ω_0$ must vanish in a correlated way such that $1/|\log[Δ(0)]| \sim ω_0^2$. We discuss the behavior of phase fluctuations near this transition and show that the correlation between $Δ(0)$ and $ω_0$ locks the phase stiffness to a non-zero value.

cond-mat.supr-con↗