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arXiv:2401.08753 · Physical review. B./Physical review. B

Deconfined Fermi liquid to Fermi liquid transition and superconducting instability

Xiaofan Wu, Hui Yang, Ya-Hui Zhang

Published Sep 10, 2024• 10 citations
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Abstract

Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling ${J}_{\ensuremath{\perp}}$. Across the transition the Fermi-surface volume per flavor jumps by $1/2$ of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high ${T}_{\text{c}}$ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ and future experiments in bilayer optical lattice.

DOI
10.1103/physrevb.110.125122

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Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling J\ensuremath⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​. Across the transition the Fermi-surface volume per flavor jumps by 1/21/21/2 of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high Tc{T}_{\text{c}}Tc​ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a U(1)\ifmmode×\else\texttimes\fiU(1)\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)U(1)\ifmmode×\else\texttimes\fiU(1) gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and future experiments in bilayer optical lattice.
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A Z2{\mathbb{Z}}_{2}Z2​ fractionalized Fermi liquid (FL*) is a novel state of strongly correlated quantum matter. Although it is metallic, it violates Luttinger's theorem on the volume enclosed by the Fermi surface obeyed by conventional metals; this is possible due to the presence of emergent gauge excitations. The authors study here the superconducting states that can arise out of instabilities of such a topological metal. In particular, they focus on a FL* topological metal that has favorable energetics on the square lattice with nematic order, relevant to the cuprate superconductors. They find that a Higgs transition out of this FL* results in confinement of the anyonic degrees of freedom, and the resulting state is a superconductor with broken translation symmetry or time-reversal invariance. In the process, they also establish a complete mapping between bosonic and fermionic descriptions of time-reversal invariant gapped insulating Z2{\mathbb{Z}}_{2}Z2​ spin liquid states on the rectangular lattice, which, on doping with charge carriers, can give rise to FL* phases. They also note a possible connection to the recent observation of pair density waves in the superconducting state of the underdoped cuprates.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
We study the effects of a small density of holes, $\ensuremath{\delta}$, on a square-lattice antiferromagnet undergoing a continuous transition from a N\'eel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero $\ensuremath{\delta}$, it is likely that the critical point broadens into a non-Fermi-liquid ``holon-metal'' phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio ${\mathrm{lim}}_{\ensuremath{\delta}\ensuremath{\rightarrow}0}{\mathcal{A}}_{F}∕\ensuremath{\delta}$ (where AF{\mathcal{A}}_{F}AF​ is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at $\ensuremath{\delta}>0$, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as $\ensuremath{\delta}\ensuremath{\rightarrow}0$. We demonstrate that the electronic spectrum at the $\ensuremath{\delta}\ensuremath{\rightarrow}0$ transition is described by the ``boundary'' critical theory of an impurity coupled to a (2+1)(2+1)(2+1)-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble ``Fermi arc'' spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.
Strange metal behavior is traditionally associated with an underlying putative quantum critical point at zero temperature. However, in many correlated metals, e.g., high-Tc{T}_{c}Tc​ cuprate superconductors, strange metallicity persists at low temperatures over an extended range of microscopic parameters, suggesting the existence of an underlying quantum critical phase, whose possible physical origins remain poorly understood. Systematic investigations of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL) phase are therefore crucial to better understand this puzzling behavior. In a previous study [Bashan et al., Phys. Rev. Lett. 132, 236501 (2024)], we considered a solvable large-NNN model consisting of itinerant electrons coupled to local two-level systems (TLSs) via spatially random interactions, inspired by the possibility of emergent metallic glassiness due to frustrated competing orders, and found that the system hosts an NFL phase with tunable exponents at intermediate couplings. In this paper, we expand our investigation to the following: (i) We study the extent to which this NFL phase is generic by considering various deformations of our theory, including coupling of electrons to multiple operators of the TLSs and arbitrarily directed TLS fields. We find that the physical picture obtained in Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)] qualitatively persist in a wide region of parameter space, showcasing the robustness of the NFL phase. (ii) We analyze the superconducting instability caused by the coupling of TLSs to electrons, and find a rich structure, including quantum critical pairing associated with the NFL phase and conventional BCS-like pairing in the weak and strong coupling limits. (iii) We elaborate on the analysis of Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)], including single-particle, transport, and thermodynamic properties.