Electronic modes induced by spin and charge perturbations in Mott and Kondo insulators

TL;DR

The paper establishes that electronic modes can be induced inside the band gap of Mott and Kondo insulators by spin or charge perturbations, a consequence of spin–charge separation in strongly correlated systems. By combining Bethe ansatz analysis, effective inter-unit-cell theory, and extensive numerical calculations (DDMRG, CPT, Lanczos) across HM, PAM, KLM, and ladder/bilayer geometries in 1D and 2D, the authors derive dispersion relations for emergent modes and show their dependence on the perturbation's momentum and energy. They categorize the origins of these modes into charge perturbations (doping and η-density excitations) and spin perturbations (magnetization and spin fluctuations), and demonstrate symmetry-based connections (η-SU(2), particle–hole, Shiba transformation) that link doped states to nonzero-η states and magnetized states to doped counterparts. The results generalize the mechanism behind unconventional band-structure changes under perturbations and suggest routes for band-structure engineering in strong-correlation electronics, with implications for controllable in-gap states and potential device functionalities.Overall, the work unifies a broad set of perturbations under a single framework where emergent in-gap electronic modes are governed by combinations of unperturbed electronic and spin/charge dispersions, subject to symmetry constraints, across diverse strongly correlated models and dimensions.

Abstract

Electronic band structures usually remain unaffected by doping via a chemical-potential shift or by increasing the temperature in conventional band insulators. In contrast, it has been shown that those of Mott and Kondo insulators can be altered by doping or by increasing the temperature: electronic modes are induced within the band gap, exhibiting momentum-shifted magnetic dispersion relations from the band edges. Here, this study demonstrates that the underlying mechanism of the remarkable strong-correlation effects can be generalized to the emergence of electronic modes caused by various spin and charge perturbations, including magnetization of spin-gapped Mott and Kondo insulators. These emergent modes can alter the band structure if a macroscopic number of spins or charges are excited by the perturbations at a given moment. The origins and dispersion relations of these emergent modes, particularly why and how the dispersion relations depend on the momentum and energy of the perturbations, are elucidated by investigating the selection rules and using the Bethe ansatz and the effective theory for weak inter-unit-cell hopping. The validity and generality of the theoretical results across different models and spatial dimensions are verified by numerical calculations for the one- and two-dimensional Hubbard models, periodic Anderson models, Kondo lattice models, and ladder and bilayer Hubbard models. This study provides crucial insights into why and how spin and charge perturbations can alter the band structure in strongly correlated insulators, thereby paving the way for band-structure engineering in strong-correlation electronics, which enables previously unexplored functionalities by exploiting the unconventional characteristics revealed in this paper.

Figures (16)

• Figure 1: Excitation from the ground state at half filling in the 1D HM. (a) $A_{\rm GS}(k,\omega)t$, (b) $S(k,\omega)t/3$, (c) $N(k,\omega)t/4$. (d)--(f) Dispersion relations obtained using the Bethe ansatz. (d) Holon modes (brown curves), spinon modes (blue curves), and holon-spinon continua (light-yellow regions) in electronic excitation. (e) Two-spinon continuum (light-yellow region) and lower edge of the continuum (blue curve) in spin excitation. (f) Two-holon continuum (light-yellow region) in charge excitation. The solid green lines indicate $\omega=0$.
• Figure 2: Excitation from the ground state at half filling in the 2D HM. (a) $A_{\rm GS}({\bm k},\omega)t$. (b) Lowest spin-excitation energies in a $4\times 4$-site cluster (red diamonds). The blue curve indicates the dispersion relation of the spin-wave mode extracted from (c). (c) $\frac{1}{2\pi}{\rm Im}\chi({\bm k},\omega)t$ for $\omega>0$. The solid green lines indicate $\omega=0$.
• Figure 3: Electronic excitation from the ground state at half filling in the ladder HM [(a), (g)], 1D PAM [(b), (h)], 1D KLM [(c), (i)], bilayer HM [(d), (j)], 2D PAM [(e), (k)], and 2D KLM [(f), (l)]. (a)--(f) $A_{\rm GS}(k_\parallel,0,\omega)t+A_{\rm GS}({k_\parallel},\pi,\omega)t$ [(a)], $A_{\rm GS}({\bm k},\omega)t$ [(b), (c), (f)], ${\bar{A}}_{\rm GS}({\bm k_\parallel},0,\omega)t+{\bar{A}}_{\rm GS}({\bm k_\parallel},\pi,\omega)t$ [(d)], and ${\bar{A}}_{\rm GS}({\bm k},\omega)t$ [(e)]. (g)--(l) Dispersion relations of electronic excitations in the effective theory; $\omega=\varepsilon^{\cal A}_{{\bm k}_\parallel}$ (solid blue curves), $\omega=-\varepsilon^{\cal R}_{-{\bm k}_\parallel}$ (solid brown curves), $\omega=\varepsilon^{\bar{\cal A}}_{{\bm k}_\parallel}$ (solid purple curves), $\omega=-\varepsilon^{\bar{\cal R}}_{-{\bm k}_\parallel}$ (solid orange curves), $\omega=\varepsilon^{{\cal A}{\cal T}}_{{\bm k}_\parallel;{\bm p}_\parallel}$ (light-yellow regions for $\omega>0$), and $\omega=-\varepsilon^{{\cal R}{\cal T}}_{-{\bm k}_\parallel;-{\bm p}_\parallel}$ (light-yellow regions for $\omega<0$). The solid green lines indicate $\omega=0$.
• Figure 4: Spin excitation from the ground state at half filling in the ladder HM [(a), (g)], 1D PAM [(b), (h)], 1D KLM [(c), (i)], bilayer HM [(d), (j)], 2D PAM [(e), (k)], and 2D KLM [(f), (l)]. (a)--(c) $S(k_\parallel,\pi,\omega)t/3$ [(a)] and $S(k,\omega)t/3$ [(b), (c)]. (d)--(f) Lowest spin-excitation energies for $N_{\rm u}=\sqrt{10}\times\sqrt{10}$ (orange squares) [(f)], $3\times 3$ (magenta circles) [(f)], and $\sqrt{8}\times\sqrt{8}$ (red diamonds) [(d)--(f)]. The brown curves indicate the least-squares fitting in the form of $\omega=Jd\gamma_{{\bm k}_{\parallel}}+\Delta E$. (g)--(l) Dispersion relations of spin excitations in the effective theory; $\omega=e^{\cal T}_{{\bm k}_\parallel}$ (solid blue curves) and $\omega=e^{{\cal A}{\cal R}}_{{\bm k}_\parallel;{\bm p}_\parallel}$ (light-yellow regions). The solid green lines indicate $\omega=0$.
• Figure 5: Charge excitation from the ground state at half filling in the ladder HM [(a), (b)], 1D PAM [(d), (e)], bilayer HM [(c)], and 2D PAM [(f)]. (a), (d) $N(k_\parallel,\pi,\omega)t/4$ [(a)] and $N(k,\omega)t/4$ [(d)]. (b), (c), (e), (f) Dispersion relations of charge excitations in the effective theory; $\omega=e^{{\cal C}^0}_{{\bm k}_\parallel}$ (solid orange curves) and $\omega=e^{{\cal A}{\cal R}}_{{\bm k}_\parallel;{\bm p}_\parallel}$ (light-yellow regions). The solid green lines indicate $\omega=0$.