Primary charge-4e superconductivity from doping a featureless Mott insulator

TL;DR

The paper proposes a concrete route to primary charge-$4e$ superconductivity at zero temperature by doping a featureless Mott insulator with $SU(4)$ symmetry, realized as a bilayer Hubbard model with tunable $SU(4)$ and $Sp(4)$ symmetries. Through a projection to a low-energy generalized ESD model and a $t/|\epsilon|$ expansion, the authors show that SU(4) favors a primary charge-$4e$ superconducting state via quartet condensation, while Sp(4) supports a conventional primary charge-$2e$ SC; this distinction is rooted in group-theoretic center constraints. They confirm the predictions with extensive DMRG simulations, identifying algebraic quartetting correlations for SU(4) at low doping and robust quartet binding energies, alongside a flavor-gap that signals quartet stability. Finite-temperature analyses and phase diagrams are discussed, highlighting how symmetry-enforced constraints and kinetic-energy-driven pairing mechanisms cooperate to realize high-charge superconductivity, and outlining potential platform implementations in ultracold atoms and moiré materials.

Abstract

Superconductivity is usually understood as a phase in which charge-$2e$ Cooper pairs are condensed. Charge-$4e$ superconductivity has largely been discussed as a vestigial order at finite temperature emerging from charge-$2e$ states. Primary charge-$4e$ superconducting phases at zero temperature remain scarce in both experiments and microscopic models. Here we argue that a doped featureless Mott insulator with $SU(4)$ symmetry provides a natural platform for primary charge-$4e$ superconductivity, based on perturbative renormalization group arguments and group theoretic considerations. As a concrete realization, we construct a bilayer Hubbard model with tunable onsite $SU(4)$ and $Sp(4)$ symmetries that exhibits a featureless Mott insulating phase at half filling. Its low energy physics is captured by a generalized ESD model, featuring an effective Hamiltonian that is purely kinetic within the constrained Hilbert space. Using density matrix renormalization group (DMRG) simulations, we find a primary charge-$4e$ superconducting phase in the $SU(4)$ ESD model and a conventional primary charge-$2e$ phase in the $Sp(4)$ case. We further characterize the corresponding normal states and discuss the resulting finite temperature phase diagram.

Figures (8)

• Figure 1: Illustration of the low energy Hilbert space. The four colors denote the four flavors of electrons, and two layers are divided by the grey dashed line. In the $\nu=2$ sector, the $\mathbf{6}$ vector irrep of $SU(4)$ is decomposed into the $\mathbf{5}$ vector $\left| \gamma^a(\mathbf{i}) \right>$ and the $\mathbf{1}$ singlet $\left| \eta(\mathbf{i}) \right>$ under $Sp(4)$. For both $SU(4)$ and $Sp(4)$, in $\nu=3$ sector there are $4+4=8$ states related via layer exchange, and in $\nu=4$ sector there is a unique singlet state.
• Figure 2: Infinite DMRG simulation results for ESD model Eq. (\ref{['eq:bH']}) with $L_x=8$. Here $x = 0.25$ and $\epsilon=0$ with $r_1=r_5=2/\sqrt{3}$ for $SU(4)$ ESD model, and for $Sp(4)$ model $x=0.125$, $\epsilon=0$, $\delta=0.4t$, and $r_1=0.828$, $r_5=1.15$ corresponding to $J_V/J_L=0.95$. The plot shows the log-log plot of the quartet-quartet correlation function $C_{4e}(d)$ for $SU(4)$ (blue) and pair-pair correlation function $C_{2e}(d)$ for $Sp(4)$ (orange) against distance $d$. The bond dimension is $m=15000$ for $SU(4)$ model and $m=8000$ for $Sp(4)$ model. Inset: correlation length $\xi/\xi_e$ with respect to different bond dimensions for $SU(4)$ ESD model, where $\xi_{4e(2e)}$ corresponds the correlation length of quartetting (pairing), and $\xi_e$ is the single particle correlation length.
• Figure 3: Finite DMRG simulation results of quartet binding energy and flavor gap in $SU(4)$ ESD model with $r_1=r_5=2/\sqrt{3}$ and $\epsilon=\delta=0$. Starting from the featureless Mott insulator at $x = 0$ ($\nu = 4$), we dope four holes into the system and compute the binding energy and flavor gap for fixed $L_y = 10$ and $L_x = 10, 20, 40, 50, 60$. The results are well converged with respect to the bond dimension. The extrapolation to $L_x\rightarrow+\infty$ shows that both the binding energy and the flavor gap remain finite in the thermodynamic limit along the $x$ direction, suggesting the formation of a stable quartet and the existence of a primary charge-$4e$ SC phase. The inset shows the nonlocal nature of the quartets, where the onsite Cooper pairs are marked as blue dotes, and quartet are circled by blue ellipsis.
• Figure 4: Schematic phase diagram of (a) $SU(4)$ ESD model ($\delta= 0$), and (b) $Sp(4)$ ESD model with (b1) $\delta\gtrsim 0$, and (b2) $\delta\gg t,\epsilon$.
• Figure S1: States in $\nu=2$ sector organized into $SU(4)$ weight basis, where $\left| \eta \right>$ naturally becomes the singlet under $Sp(4)$.