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arXiv:1811.12034 · Physical review. B./Physical review. B

Rashba-metal to Mott-insulator transition

Valentina Brosco, Massimo Capone

Published Jun 22, 2020• 9 citations
arXivHTMLPDF

Abstract

The recent discovery of materials featuring strong Rashba spin-orbit coupling (RSOC) and strong electronic correlation raises questions about the interplay of Mott and Rashba physics. In this work, we employ cluster perturbation theory to investigate the spectral properties of the two-dimensional Hubbard model in the presence of a significant or large RSOC. We show that RSOC strongly favors metallic phases and competes with Mott localization, leading to an unconventional scenario for the Mott transition, which is no longer controlled by the ratio between the Hubbard $U$ and an effective bandwidth. The results show a strong sensitivity to the value of the RSOC.

DOI
10.1103/physrevb.101.235149

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Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.
We investigate the metal-insulator transition (MIT) and phase diagram of the half-filled Fermi Hubbard model with Rashba-type spin-orbit coupling (SOC) on a square optical lattice. The interplay between the atomic interactions and SOC results in distinctive features of the MIT. Significantly, in addition to the diverse spin ordered phases, a nonmagnetic insulating phase emerges in a considerably large regime of parameters near the Mott transition. This phase has a finite single-particle gap but vanishing magnetization and spin correlation exhibits a power-law scaling, suggesting a potential algebraic spin-liquid ground state. These results are confirmed by the non-perturbative cluster dynamical mean-field theory.
Unraveling the nature of the doping-induced transition between a Mott insulator and a weakly correlated metal is crucial to understanding novel emergent phases in strongly correlated materials. For this purpose, we study the evolution of spectral properties upon doping Mott insulating states by utilizing the cluster perturbation theory on the Hubbard and t−−Jt--Jt−−J-like models. Specifically, a quasifree dispersion crossing the Fermi level develops with small doping, and it eventually evolves into the most dominant feature at high doping levels. Although this dispersion is related to the free-electron hopping, our study shows that this spectral feature is, in fact, influenced inherently by both electron-electron correlation and spin-exchange interaction: the correlation destroys coherence, while the coupling between spin and mobile charge restores it in the photoemission spectrum. Due to the persistent impact of correlations and spin physics, the onset of gaps or the high-energy anomaly in the spectral functions can be expected in doped Mott insulators.
Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g)4{({t}_{2g})}^{4}(t2g​)4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard UUU and spin-orbit coupling $\ensuremath{\lambda}$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\ensuremath{\lambda}$ at intermediate UUU. In the strong UUU coupling limit, we find a nonmagnetic insulator with an effective angular momentum $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}\ensuremath{\ne}0$ near the excitonic phase, smoothly connected to the $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}=0$ regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics