We show that the Mott metal-insulator transition in the standard one-band Hubbard model can be understood as a topological phase transition. Our approach is inspired by the observation that the mid-gap pole in the self-energy of a Mott insulator resembles the zero-energy spectral pole of the localized surface state in a topological insulator. We use NRG-DMFT to solve the infinite-dimensional Hubbard model, and represent the resulting local self-energy in terms of the boundary Green's function of an auxiliary tight-binding chain without interactions. The auxiliary system is of generalized SSH model type; the Mott transition corresponds to a dissociation of domain walls.
We study roles of electron correlations on topological insulators on the honeycomb lattice with the spin-orbit interaction. Accurate variational Monte Carlo calculations show that the increasing on-site Coulomb interactions cause a strong suppression of the charge Drude weight in the helical-edge metallic states leading to a presumable Mott transition from a conventional topological insulator to an edge Mott insulator before a transition to a bulk antiferromagnetic insulator. The intermediate bulk-topological and edge-Mott-insulator phase has a helical spin-liquid character with the protected …
Surface chiral Abelian topological order on multilayer cluster Mott insulators
University of Chinese Academy of Sciences（中国科学院大学）；Southeast University（东南大学）；Peking University（北京大学）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
We investigate properties of a topological Mott insulator in one dimension by examining the bulk topological invariant and the entanglement spectrum of a correlated electron model. We clarify how gapless edge states in a non-interacting topological band insulator evolve into spinon edge states in a topological Mott insulator. Furthermore, we propose a topological Mott transition, which is a new type of topological phase transition and never observed in free fermion systems. This unconventional transition occurs in spin liquid phases in the Mott insulator and is accompanied by zeros of the sing…
Magnetopological mechanics in Maxwell lattice frustrated Mott insulators
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $\mathbb{Z}_{4}$ spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also sho…
Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small ran…
The electronic structure at the interface between a topological band insulator and a Mott insulator is studied within layer dynamical mean field theory. To represent the bulk phases of these systems, we use the generalized Bernevig-Hughes-Zhang model that incorporates the Hubbard-like onsite Coulomb energy U in addition to the spin-orbit coupling term that causes band inversion. The topological and Mott insulating phases are realized by appropriately choosing smaller and larger values of U, respectively. As expected, the interface is found to be metallic because of the localized edge state. Wh…
We consider quantum phase transitions out of topological Mott insulators in which the ground state of the fractionalized excitations (fermionic spinons) is topologically non-trivial. The spinons in topological Mott insulators are coupled to an emergent compact U(1) gauge field with a so-called "axion" term. We study the confinement transitions from the topological Mott insulator to broken symmetry phases, which may occur via the condensation of dyons. Dyons carry both "electric" and "magnetic" charges, and arise naturally in this system because the monopoles of the emergent U(1) gauge theory a…
Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities in…
We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by t…
We propose a new correlated topological state which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in the bulk, characterized by the Z3 spin-Berry phase, result in gapless corner modes emerging only in spin excitations (i.e., the single-particle excitations remain gapped around the corner). We demonstrate the emergence of the HOTMI in a Hubbard model on the kagome lattice, and elucidate how strong correlations change gapless corner modes at the noninteracting…
A set of broken symmetry two-dimensional ground states are predicted in (111)-oriented (LaNiO$_3$)$_N$/(LaAlO$_3$)$_M$ ($N$/$M$) superlattices, based on density functional theory (DFT) calculations including a Hubbard $U$ term. An unanticipated Jahn-Teller distortion with $d_{z^2}$ orbital polarization and a FM Mott insulating (and multiferroic) phase emerges in the double perovskite (1/1), that shows strong susceptibility to strain-controlled orbital engineering. The LaNiO$_3$ bilayer with graphene topology has a switchable multiferroic (ferromagnetic (FM) and ferroelectric) insulating ground…
Mott insulator to metal transitions under electric field are currently the subject of numerous fundamental and applied studies. This puzzling effect, which involves non-trivial out-of-equilibrium effects in correlated systems, is indeed at play in the operation of a new class of electronic memories, the Mott memories. However the combined electronic and thermal effects are difficult to disentangle in Mott insulators undergoing such transitions. We report here a comparison between the properties under electric field of a canonical Mott insulator and a model built on a realistic 2D resistor netw…
Describing the doped Fullerenes using a generalized Hubbard model, we study the Mott transition for different integer fillings of the t_1u band. We use the opening of the energy-gap E_g as a criterion for the transition. E_g is calculated as a function of the on-site Coulomb interaction U using fixed-node diffusion Monte Carlo. We find that for systems with doping away from half-filling the Mott transitions occurs at smaller U than for the half-filled system. We give a simple model for the doping dependence of the Mott transition.
The organic system, $κ$-[(BEDT-TTF)$_{1-x}$(BEDT-STF)$_x$]$_2$Cu$_2$(CN)$_3$, showing the Mott transition between a nonmagnetic Mott insulating (NMI) state and a Fermi liquid (FL), is systematically studied by calorimetric measurements. An increase of the electronic heat capacity at the transition from the NMI state to the FL state which keeps the triangular dimer lattice demonstrates that the charge sector lost in the Mott insulating state is recovered in the FL state. We observed that the remaining low-energy spin excitations in the Mott insulating state show unique temperature dependence, a…
We study how a finite hybridization between a narrow correlated band and a wide conduction band affects the Mott transition. At zero temperature, the hybridization is found to be a relevant perturbation, so that the Mott transition is suppressed by Kondo screening. In contrast, a first-order transition remains at finite temperature, separating a local moment phase and a Kondo- screened phase. The first-order transition line terminates in two critical endpoints. Implications for experiments on f-electron materials such as the Cerium alloy Ce$_{0.8}$La$_{0.1}$Th$_{0.1}$ are discussed.
We point out certain symmetry induced constraints on topological order in Mott Insulators (quantum magnets with an odd number of spin $\tfrac{1}{2}$ per unit cell). We show, for example, that the double semion topological order is incompatible with time reversal and translation symmetry in Mott insulators. This sharpens the Hastings-Oshikawa-Lieb-Schultz-Mattis theorem for 2D quantum magnets, which guarantees that a fully symmetric gapped Mott insulator must be topologically ordered, but is silent on which topological order is permitted. An application of our result is the Kagome lattice quant…
We address how the nature of linearly dispersing edge states of two dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion $U$ in finite ribbons of two models of topological band insulators. Using an inhomogeneous cluster slave rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical $U$ that depends w…
NiS$_2$ has been widely regarded as a model system to study the bandwidth-controlled Mott transition, as enabled by isovalent Se chemical substitution on the S sites. Motivated by advances in electrolyte gating, we theoretically investigate the filling-controlled Mott transition induced by gating, which has the advantage of avoiding dopant disorder and stoichiometric changes. We use combined Density Functional Theory (DFT) and Dynamical Mean Field Theory (DMFT) to study such a filling-controlled transition and compare it with the case of bandwidth control. We draw a temperature-filling phase d…
Topological band insulators have recently been discovered in spin-orbit coupled two and three dimensional systems. In this work, we theoretically predict a class of topological Mott insulators where interaction effects play a dominant role. In actinide elements, simple rocksalt compounds formed by Pu and Am lie on the boundary of metal to insulator transition. We show that interaction drives a quantum phase transition to a topological Mott insulator phase with a single Dirac cone on the surface.
We consider extended Hubbard models with repulsive interactions on a Honeycomb lattice and the transitions from the semi-metal phase at half-filling to Mott insulating phases. In particular, due to the frustrating nature of the second-neighbor repulsive interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spinful fermion models, respectively. We present the mean-field phase diagram and consider the effects of fluctuations within the random phase approximation (RPA). Functional renormalization group analysis also show tha…
We theoretically investigate a two-dimensional heterostructure composed of a topological insulator (TI) and a Mott insulator (MI), and clarify what kind of electronic states can be realized at the interface. By using inhomogeneous dynamical mean-field theory, we confirm that the topological edge state penetrating into the MI region induces a heavy-fermion like mid-gap state. We further elucidate the nature of the spatially-modulated quasi-particle weight of the mid-gap state, and discuss the effects of local correlation in the TI region. The optical conductivity and the Drude weight are also c…
We investigate proximity effects in a correlated heterostructure of a two-dimensional Mott insulator (MI) and a topological insulator (TI) by employing inhomogeneous dynamical mean-field theory. We show that the edge state of the TI induces strongly renormalized mid-gap states inside the MI region, which still have a remnant of the helical energy-spectrum. The penetration of low-energy electrons, which is controlled by the interface tunneling $V$, largely enhances the electron mass inside the MI and also splits a single Dirac-cone at edge sites into the spatially-separated two Dirac-cones in t…
The Mott transition in honeycomb compounds with significant spin-orbit coupling is explored. At finite temperatures we identify a novel semimetallic phase located between a topological insulator and a topological Mott insulator. This semimetal is characterized by having no charge gap, no quasiparticles and gapped spin excitations with non-trivial topological properties. While charge conduction is incoherent involving mean-free paths violating the Mott-Ioffe-Regel limit, spin excitations can be transported ballistically along the edges giving rise to a quantized spin conductance. Such bad topol…
In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin-orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin-orbit Rashba coupling and the Coulomb repulsion. The spin-orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. …
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition betwee…
Recently, the field of strongly correlated electrons has begun an intense search for a correlation induced topological insulating phase. An example is the quadratic band touching point which arises in a checkerboard lattice at half-filling, and in the presence of interactions gives rise to topological Mott insulators. In this work, we perform a mean-field theory computation to show that such a system shows instability to topological insulating phases even away from half-filling (chemical potential $μ= 0 $). The interaction parameters consist of on-site repulsion ($ U $), nearest-neighbour repu…
We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of st…
We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the…
We reconsider the Mott transition problem in the presence of long range Coulomb interactions. Using an extended DMFT, that sums an important class of diagrams absent in ordinary DMFT, we show that in the presence of Coulomb the Mott transition in two and three dimensions is discontinuous as envisioned by Mott.
Whether the newly discovered KxFe2-ySe2 systems are doped Mott or band insulators is key to how superconductivity emerges at lower temperature. With extant theoretical studies supporting conflicting scenarios, a more realistic approach is urgently called for. Here, we use LDA+DMFT to study this issue in KxFe2-ySe2. We find that the undoped KFe1.6Se2 system is a new kind of Mott-Kondo insulator (MKI). Electron doping this MKI drives a Mott transition to an orbital-selective non-Fermi liquid metal. Good agreement with spectral and transport responses supports our view, implying that superconduct…
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties by means of dynamical mean-field theory (DMFT). We characterize topological phases by numerically evaluating t…
Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Ir-based pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At we…
We investigate the thermoelectric response of correlated electron systems near the density driven Mott transition using the dynamical mean field theory.
We investigate the continuous variation of electronic states from a Fermi liquid to a quantum spin liquid induced by chemical substitution in the organic dimer-Mott system of $κ$-[(BEDSe-TTF)$_x$(BEDT-TTF)$_{1-x}$]$_2$Cu[N(CN)$_2$]Br. Electrical transport measurements reveal that the mixing of BEDSe-TTF into the BEDT-TTF layers induces a quantum Mott transition around $x$=0.10. Although a charge gap disappears at this point, magnetic susceptibility and heat capacity measurements indicate that fermionic low-energy excitations remain in the insulating salts, suggesting that fermionic spin excita…
We propose an order parameter for the one dimensional Mott-Hubbard transition and provide numerical evidence and general theoretical arguments for the correctness of our proposal. In addition, we discuss some of the implications of this picture of the one dimensional Mott-Hubbard transition and speculate about possible higher dimensional analogs.
We study a bilayer Kane-Mele-Hubbard model with lattice distortion and inter-layer spin exchange interaction under cylinder geometry. Our analysis based on real-space dynamical mean field theory with continuous-time quantum Monte Carlo demonstrates the emergence of a topological edge Mott insulating (TEMI) state which hosts gapless edge modes only in collective spin excitations. This is confirmed by the numerical calculations at finite temperatures for the spin-Hall conductivity and the single-particle excitation spectrum; the spin Hall conductivity is almost quantized, $σ^{xy}_\mathrm{spin}\s…
For continuous Mott metal-insulator transitions in layered two dimensional systems, we demonstrate the phenomenon of dimensional decoupling: the system behaves as a three-dimensional metal in the Fermi liquid side but as a stack of decoupled two-dimensional layers in the Mott insulator. We show that the dimensional decoupling happens at the Mott quantum critical point itself. We derive the temperature dependence of the interlayer electric conductivity in various crossover regimes near such a continuous Mott transition, and discuss experimental implications.
Relativistic Weyl fermion (WF) often appears in the band structure of three dimensional magnetic materials and acts as a source or sink of the Berry curvature, i.e., the (anti-)monopole. It has been believed that the WFs are stable due to their topological indices except when two Weyl fermions of opposite chiralities annihilate pairwise. Here, we theoretically show for a model including the electron-electron interaction that the Mott gap opens for each WF without violating the topological stability, leading to a topological Mott insulator dubbed {\it Weyl Mott insulator } (WMI). This WMI is ch…
We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this…
We investigate the Mott transition using a cluster extension of dynamical mean field theory (DMFT). In the absence of frustration we find no evidence for a finite temperature Mott transition. Instead, in a frustrated model, we observe signatures of a finite temperature Mott critical point in agreement with experimental studies of kappa-organics and with single site DMFT. As the Mott transition is approached, a clear momentum dependence of the electron lifetime develops on the Fermi surface with the formation of cold regions along the diagonal direction of the Brillouin zone. Furthermore the va…
We investigate the Mott transitions in the two-orbital Hubbard model with different bandwidths. By combining dynamical mean field theory with the exact diagonalization, we discuss the stability of itinerant quasi-particle states in each band. We demonstrate that separate Mott transitions occur at different Coulomb interaction strengths in general, which merge to a single transition only under special conditions. In particular, it is clarified that the $xy$ and pair-hopping components of the Hund coupling play a key role to control the nature of the Mott transitions.
The magnetic properties and Mott transition of the Hubbard model on the square lattice with frustration are studied at half-filling and zero temperature by the variational cluster approximation. When the on-site repulsion $U$ is large, magnetically disordered state is realized in highly frustrated region between the Néel and collinear phases, and no imcommensurate magnetic states are found there. As for the Mott transition, in addition to the Mott gap and double occupancy, which clarify the nature of the transition, the structure of the self-energy in the spectral representation is studied in …
We investigate the interplay between the strong correlation and the spin-orbital coupling in the Kane-Mele-Hubbard model and obtain the qualitative phase diagram via the variational cluster approach. We identify, through an increase of the Hubbard $U$, the transition from the topological band insulator to either the spin liquid phase or the easy-plane antiferromagnetic insulating phase, depending on the strength of the spin-orbit coupling. A nontrivial evolution of the bulk bands in the topological quantum phase transition is also demonstrated.
Correlation-Induced Topological Reconstruction in a Periodically Driven Kagome Mott Insulator
National Institute of Science Education and Research（印度科学与教育国立研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国立中心）；Technische Universität Braunschweig（布伦瑞克工业大学）
