Interaction-driven spin polaron in itinerant flat-band ferromagnetism

TL;DR

This work investigates itinerant flat-band ferromagnetism and the formation of spin polarons in the Mielke–Tasaki model, where a quenched kinetic energy stabilizes spin-charge bound quasiparticles. It employs SMA and projected exact diagonalization (PED) within the flat-band subspace, augmented by inter-band mixing to include the dispersive upper band, to map excitations across momentum and energy. Two low-energy spin polarons appear around $q=0$ and $q=\pi$, following the Hartree dispersion $\varepsilon^{\downarrow}_{e}(k)$, and multiple high-energy spin-polaron branches indicate binding of a bare electron with optical magnons. By analyzing binding energies, the authors show low-energy spin polarons arise from virtual exchange (scaling with $W^2/U$), while high-energy spin polarons involve a combination of effective attraction and virtual exchange, with potential implications for spin-polaron crystals and superconductivity in moiré materials.

Abstract

Interaction effects are dramatically enhanced in flat-band systems due to quenched kinetics, facilitating the binding of single excitations into composite quasiparticles. In this work, we present a comprehensive study of spin polarons over the entire momentum and energy space within the Mielke-Tasaki model using projected exact diagonalization. We identify distinct low-energy spin polarons at momenta q=0 and q=π, and also find multiple high-energy branches of spin polaron. It is demonstrated that the interaction-induced Hartree dispersion plays a decisive role in determining the momentum sector of low-energy spin polarons. Furthermore, by introducing a finite bandwidth, we unravel the underlying binding mechanisms: the formation of low-energy spin polarons is governed by the conventional virtual exchange mechanism, whereas the high-energy spin polarons arise from a joint effect of the effective attraction and virtual exchange. Our results suggest promising avenues for realizing spin polaron crystals and exploring novel superconducting pairing mechanisms in moiré materials like twisted WSe2 and MoTe2.

Figures (8)

• Figure 1: Model and single-particle dispersion. (a) Mielke-Tasaki Model. (b) Sketches of the flat-band ferromagnetic ground state, the $e_{\downarrow}$, $e_{\downarrow}h_{\uparrow}$ and $e_{\downarrow}e_{\downarrow}h_{\uparrow}$ excitations. (c) Band structure of Mielke-Tasaki model. (d) Hartree band of a spin-$\downarrow$ electron in the flat-band ferromagnetic state.
• Figure 2: Spectrum and spectral function $A(q,\omega)$ of the $e_{\downarrow}h_{\uparrow}$ excitation. (a) Spectrum of the $e_{\downarrow}h_{\uparrow}$ excitation at different $\delta$. The dots are the results obtained from PED and the shaded gray region is the $e_{\downarrow}h_{\uparrow}$ continuum obtained by simply summing the energies of the bare constituents. The blue and red dispersion is the acoustic and optical magnon, respectively. The red arrow denotes the binding energy of the acoustic magnon. (b) Spectral function of the $e_{\downarrow}h_{\uparrow}$ excitation with quasiparticle operator $\beta^{\dagger}_{i} = \mathcal{P}\sum_{n}c^{\dagger}_{in\downarrow}c_{in\uparrow}\mathcal{P}$. All panels are calculated at $U_{A}=U_{B}=1$.
• Figure 3: Spectrum and spectral function $A(q,\omega)$ of the $e_{\downarrow}e_{\downarrow}h_{\uparrow}$ excitation. (a) Spectrum of the $e_{\downarrow}e_{\downarrow}h_{\uparrow}$ excitation at different $\delta$. The dots are the results obtained from PED and the shaded gray, red and blue regions are the $e_{\downarrow}e_{\downarrow}h_{\uparrow}$, $e_{\downarrow}\sigma^{-}_{o}$ and $e_{\downarrow}\sigma^{-}_{a}$ continua, respectively. The black dashed lines are the bare spin-$\downarrow$ electron Hartree dispersions. Three colored arrows denote the binding energies of the low-energy $q=0$, $q=\pi$ and high-energy spin polaron, respectively. (b) Spectrum of the $e_{\downarrow}e_{\downarrow}h_{\uparrow}$ excitation after including the inter-band mixing in the PED. The red dashed block shows the emergence of the spin polaron at $\delta=\delta_{c}$. (c) Spectral function of the $e_{\downarrow}e_{\downarrow}h_{\uparrow}$ excitation with quasiparticle operator $\beta^{\dagger}_{i}=\mathcal{P}c^{\dagger}_{iA\downarrow}c_{iA\uparrow}c^{\dagger}_{iB\downarrow}\mathcal{P}$. All panels are calculated at $U_{A}=U_{B}=1$.
• Figure 4: Relationship between the Hartree band and the spin polaron. (a) The binding energy of the low-energy spin polaron is presented over the entire BZ and for different $U_B/U_A$ with $\delta=2/\sqrt{3},1.5$ and $1.8$. The white dashed line marks the critical value of $U_B/U_A$ for a fixed $\delta$ at which the Hartree band becomes dispersionless. (b) shows the parameter regions of the $q=0$ and $q=\pi$ spin polarons, which are separated by the line at which the Hartree band becomes dispersionless with the relation $U_{B}/U_{A} = \delta/(\sqrt{\delta^{2}+4}-\delta)$.
• Figure 5: Binding mechanism of quasiparticles. (a) Sketch of the two binding mechanisms---the effective attraction and the virtual exchange. (b) The binding energies of acoustic magnon (red), low-energy $q=0$ (yellow), $q=\pi$ (blue) and high-energy spin polaron (green) at the corresponding $\delta$ and momentum $q$ by varying $U$. The red dashed line is plotted against the right y axis and the other three against the left. (c) The binding energies after introducing flat-band dispersion $\Delta$ (see text). The high-energy spin polaron is considered at $\Delta=0.1$ and the other three at $\Delta=0.3$. $\delta$'s are the same as those in (b). (d-f) The binding energies in the corresponding dashed blocks I, II, III in (c) with respect to $W^2/U$, where $W$ is the width of the Hartree dispersion. Inset in (f) shows the binding energy of the high-energy spin polaron by varying $\Delta$ from 0.08 to 0.15 while retaining $U=1$. All panels have $U_{A}=U_{B}=U$.