Orbital Magnetic Field Driven Metal-Insulator Transition in Strongly Correlated Electron Systems

TL;DR

The paper demonstrates for the Hubbard–Hofstadter model that an orbital magnetic field can induce a Mott insulator–metal transition, driven by a field-induced redistribution of spectral weight into magnetic minibands and enhanced plaquette-based electron hopping. Using DMFT extended to finite orbital fields, the authors reveal a first-order transition with a coexistence region, evidenced by simultaneous increases in kinetic and potential energies and by changes in the local spectral function and dc conductivity. The mechanism is linked to Aharonov–Bohm delocalization around plaquettes and spectral weight shifts, with quantitative agreement to strong-coupling analysis and robust behavior across bipartite and frustrated lattices, as well as qualitative relevance to VO$_2$, organic conductors, and moiré materials. The results offer a potential magnetic-field-based switching mechanism in strongly correlated systems and highlight the importance of orbital effects in magnetotransport phenomena. All methodological steps are validated against QMC benchmarks, confirming the reliability of the DMFT approach in capturing the essential physics of orbital-field–driven MITs.

Abstract

We study the effects of an orbital magnetic field on the Mott metal-insulator transition in the Hubbard-Hofstadter model. We demonstrate that sufficiently large magnetic fields induce a Mott insulator-to-metal phase transition supporting our claim with dynamical mean field theory (DMFT) numerical results. For both competing phases (metal and insulator) we observe a magnetic-fieldinduced metallization reflected in an enhancement of kinetic and potential energy. The kinetic energy of the Mott insulator increases due to the Aharonov-Bohm effect experienced by electrons virtually tunneling around an elementary plaquette which is, however, suppressed by strong correlations. The kinetic energy of the metallic phase, on the other hand, is more strongly affected by the magnetic field through a field-driven redistribution of spectral weight due to the formation of magnetic minibands. This leads to an increase of the kinetic energy which tends to stabilize the metallic state. Our theoretical results might be relevant for recent experimental studies on magnetic field driven insulator-to-metal transitions in strongly correlated materials such as VO2, $λ$-type organic conductors and moiré multilayers.

Figures (17)

• Figure 1: DMFT phase diagram of the $2d$ Hubbard model on a simple (bipartite) square lattice as a function of interaction strength $U$ and temperature $T$ at magnetic field $B\!=\!0$. $U_{c1}$ and $U_{c2}$ are the boundaries between the coexistence region (blue and orange shaded area) and the paramagnetic metallic (PM) and paramagnetic insulating (PI) phase, respectively. $U_c$ corresponds to the line where the thermodynamic phase transition occurs. P1 to P5 indicate the points for which calculations at finite orbital magnetic fields have been performed.
• Figure 2: Free energy $F$ (left panel) and dc conductivity $\sigma_{xx}(\omega\!=\!0)$ (middle panel) as a function of the orbital magnetic field $B$ as well as local spectral function $A(\omega)$ (right panel) plotted as a heat map in the $(\omega,B)$ plane for the parameter set P1 in Fig. \ref{['mainSMcombinded:fig:PhasediagramB0']} corresponding to $U\!=\!2.5$ and $T=0.01$. $B_\uparrow$ and $B_\downarrow$ indicate that calculations have been started from $B\!=\!0$ (S1) or $B\!=\!0.5$ (S2), respectively. For $A(\omega)$ only results for S2 are shown. Inset left panel: blow up of the transition region. Inset middle panel: Spectral function at the Fermi level $A(\omega\!=\!0)$ as a function of $B$.
• Figure 3: (a) Kinetic energy for $U\!=\!2.5$ and $T\!=\!0.01$ (point P1 in Fig. \ref{['mainSMcombinded:fig:PhasediagramB0']}) as a function of the orbital magnetic field $B$ obtained by the two sets of calculations $B_\uparrow$ and $B_\downarrow$ discussed in Fig. \ref{['mainSMcombinded:fig:InsulatorMetal']}. Yellow crosses correspond to the noninteracting kinetic energy $E_\text{kin}^0$ (shown in the inset) rescaled by the quasiparticle weight $Z$ and shifted by a magnetic field independent constant $C$. (b) Critical interactions $U_c$ and $U_{c2}$ (see Fig. \ref{['mainSMcombinded:fig:PhasediagramB0']}) as a function of $B$ compared to the kinetic energy of the noninteracting system for $T\!=\!0.01$. (c) Spectral width $W(B)$ of the noninteracting Hofstadter model as function of $B$. (d) Noninteracting density of states $A_0(\omega)$ for $B\!=\!0$ and $B\!=\!\frac{1}{3}$. Dashed lines indicate the (negative) contribution $-\omega A_0(\omega)$ to the kinetic energy. (e) Illustration of an electron hopping around a plaquette due to the magnetic field.
• Figure S1: Spectral function $A(\omega)$ for $U\!=\!2.5$ and $T\!=\!0.01$ (corresponding to P1 in the phase diagram of Fig. \ref{['mainSMcombinded:fig:PhasediagramB0']} of the main text) plotted as a heat map in the $(\omega,B)$ plane. Left panel (which is just a reproduction of the right panel of Fig. \ref{['mainSMcombinded:fig:InsulatorMetal']} of the main text): Results obtained via the second line of Eq. (\ref{['mainSMcombinded:equ:spectralfunctionDMFT']}) where the ED impurity self-energy $\Sigma_\text{imp}(i\nu)$ has been analytically continued by a Nevanlinna fit. Right panel: Results obtained from the first line of Eq. (\ref{['mainSMcombinded:equ:spectralfunctionDMFT']}) where the QMC impurity Green's function $G_\text{imp}(i\nu)$ has been analytically continued via the Maximum Entropy approach.
• Figure S2: Potential energy $E_\text{pot}\!=\!U\langle n_{i\uparrow}n_{i\downarrow}\rangle$ for point P1 in Fig. \ref{['mainSMcombinded:fig:PhasediagramB0']} of the main text corresponding to $U\!=\!2.5$ and $T\!=\!0.01$. Data are shown for scans where the magnetic field has been decreased from $B\!=\!0.5$ to $B\!=\!0$ (filled green circles, solution S2) and where the magnetic field has been increased from $B\!=\!0$ to $B\!=\!0.5$ (empty violet squares, solution S1), respectively. Yellow crosses depict the potential energy estimated from the Gutzwiller approximation where $Z$ is the quasiparticle renormalization factor of DMFT and $C\!=\!E_\text{pot}^\text{ins}$ corresponds to the potential energy of DMFT in the insulating state.