Mott Critical Point Research Articles

Truncated mass divergence in a Mott metal

The Mott metal-insulator transition represents one of the most fundamental phenomena in condensed matter physics. Yet, basic tenets of the canonical Brinkman-Rice picture of Mott localization remain to be tested experimentally by quantum oscillation measurements that directly probe the quasiparticle Fermi surface and effective mass. By extending this technique to high pressure, we have examined the metallic state on the threshold of Mott localization in clean, undoped crystals of NiS2. We find that i) on approaching Mott localization, the quasiparticle mass is strongly enhanced, whereas the Fermi surface remains essentially unchanged; ii) the quasiparticle mass closely follows the divergent form predicted theoretically, establishing charge carrier slowdown as the driver for the metal-insulator transition; iii) this mass divergence is truncated by the metal-insulator transition, placing the Mott critical point inside the insulating section of the phase diagram. The inaccessibility of the Mott critical point in NiS2 parallels findings at the threshold of ferromagnetism in clean metallic systems, in which criticality at low temperature is almost universally interrupted by first-order transitions or novel emergent phases such as incommensurate magnetic order or unconventional superconductivity.

Universal power-law exponents in differential tunneling conductance for planar insulators near Mott criticality at low temperatures

We consider the low-temperature differential tunneling conductance G for interfaces between a planar insulating material in the Mott-class and a metal. For values of the applied potential difference that are not very small, there is a experimentally observed universal regime in which , where m is a universal exponent. We consider the theoretical prediction of the values of m by using the method of effective field theory (EFT), which is appropriate for discussing universal phenomena. We describe the Mott material by the EFT pertaining the long-distance behavior of a spinless Hubbard-like model with nearest neighbors interactions previously considered. At the Mott transition, the EFT is known to be given by a double Abelian Chern–Simons theory. The simplest realization of this theory at the tunneling interface yields a Conformal Field Theory with central charges and Jain filling fraction describing a pair of independent counter-propagating chiral bosons (one charged and one neutral). Tunneling from the material into the metal is, therefore, described by this EFT at the Mott critical point. The resulting tunneling conductance behaves as , yielding the prediction m = 1/2, which compares well (within a deviation) with the results for this exponent in two experimental studies considered here.

Electrodynamics in Organic Dimer Insulators Close to Mott Critical Point

Organic layered charge-transfer salts κ -(BEDT-TTF) 2 X form highly frustrated lattices of molecular dimers in which strong correlations give rise to Mott insulating states situated close to the metal-to-insulator phase boundary. The salts κ -(BEDT-TTF) 2 Cu 2 (CN) 3 and κ -(BEDT-TTF) 2 Ag 2 (CN) 3 have been considered as prime candidates for a quantum spin liquid, while κ -(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl has been suggested as a prototypical charge-order-driven antiferromagnet. In this paper, we summarize and discuss several key results, including some not reported previously, obtained in search to clarify the competition of these two ground states. The origin of anomalous dielectric response found at low temperatures in all three salts is also discussed. We conclude by pointing out the relevant new insights into the role of frustration and random disorder in the suppression of magnetic ordering and formation of the spin liquid state.

Anisotropic quantum spin Hall effect, spin-orbital textures, and the Mott transition

We investigate the interplay between topological effects and Mott physics in two dimensions on a graphenelike lattice, via a tight-binding model containing an anisotropic spin-orbit coupling on the next-nearest-neighbor links and the Hubbard interaction. We thoroughly analyze the resulting phases, namely, a topological band insulator phase or anisotropic quantum spin Hall phase until moderate-strength interactions and a N\'eel and a spiral phase at large interactions in the Mott regime, as well as the formation of a spin-orbital texture in the bulk at the Mott transition. The emergent magnetic orders at large interactions are analyzed through a spin-wave analysis and mathematical arguments. At weak interactions, by analogy with the Kane-Mele model, the system is described through a ${\mathbb{Z}}_{2}$ topological invariant. In addition, we describe how the anisotropic spin-orbit coupling already produces an exotic spin texture at the edges. The physics at the Mott transition is described in terms of a U(1) slave-rotor theory. Taking into account gauge fluctuations around the mean-field saddle-point solution, we show how the spin texture now proliferates into the bulk above the Mott critical point. The latter emerges from the response of the spinons under the insertion of monopoles and this becomes more pronounced as the spin-orbit coupling becomes prevalent. We discuss implications of our predictions for thin films of the iridate compound Na${}_{2}$IrO${}_{3}$ and also graphenelike systems.

Importance of subleading corrections for the Mott critical point

The interaction-induced metal-insulator transition should be in the Ising universality class. Experiments on layered organic superconductors suggest that the observed critical endpoint of the first-order Mott transition belongs instead to a different universality class. To address this question, we use dynamical mean-field theory and a cluster generalization that is necessary to account for short-range spatial correlations in two dimensions. Such calculations can give information on crossover effects, in particular quantum ones, that are not included in the simplest mean-field. In the cluster calculation, a canonical transformation that minimizes the sign problem in continuous-time quantum Monte Carlo calculations allows us to obtain very accurate results for double occupancy. These results show that there are important subleading corrections that can lead to apparent exponents that are different from mean-field. Experiments on optical lattices could verify our predictions.

Effect of disorder on the charge‐carrier dynamics in κ ‐(D8‐ET)2Cu[N(CN)2]Br

AbstractWe have applied resistance fluctuation spectroscopy to study the intrinsic low‐frequency dynamics of the charge carriers in the system κ ‐(D8‐ET)2Cu[N(CN)2]Br for two different cooling rates. A strong increase of both the resistance and the noise level is observed below the thermodynamic glass‐transition temperature Tg. Surprisingly, the data of the normalized spectral weight 〈(δR)2〉/R2 fall on top of each other for both cooling rates except for temperatures near the Mott critical point (T0 ≃ 35 K) and below 28 K. The suppression of the peak in 〈(δR)2〉/R2 associated with the Mott transition suggests that disorder is an additional parameter in the generalized phase diagram. The enhanced noise level below 28 K might be explained by a disorder‐induced staggered magnetic moment in the metallic state close to the antiferromagnetic Mott insulator. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of randomness on the Mott transition in κ‐(BEDT‐TTF)2X

AbstractWe present a detailed transport study in the organic superconductor κ‐(BEDT‐TTF)2Cu[N(CN)2]Br that is irradiated by X‐rays. Weak molecular disorder introduced by X‐ray irradiation induces the Anderson‐type localization insulating state from the strongly correlated metallic/superconducting state. The hydrostatic pressure to the localization insulator restores the metallic properties. These observations indicate that the stronger electron correlations upon approaching the Mott transition enhance Anderson‐type electron localization due to disorder introduced by X‐ray irradiation. In the metallic state with weak disorder or under pressure, the resistivity shows a T2 dependence, which suggests that the dominant electron scattering comes from the electron–electron correlations of a Fermi‐liquid metal. The coefficient A of the T2 term, however, seems not to follow the Fermi‐liquid theory fully as the origin of the T2 dependence in a case of the disorder effect. Further studies of the competition and/or cooperation of the Mott and Anderson transitions close to the Mott critical point are important for understanding the critical behavior of the electrons in real materials.

Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model

For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength $U$, temperature $T$, and filling $n$ shows that, upon increasing $n$ toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T $=$ 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.

Lattice softening effects at the Mott critical point of Cr-doped V2O3

We have performed sound velocity measurements in (V${}_{1\ensuremath{-}x}$Cr${}_{x}$)${}_{2}$O${}_{3}$ in the vicinity of the critical point of the first-order Mott transition line. The pressure sweeps at constant temperature reveal a large dip in the ${c}_{33}$ compression modulus; this dip sharpens as the critical point is approached. We do not observe signs of criticality on the shear modulus ${c}_{44}$, which is consistent with a transition governed by a scalar order parameter, in accordance with the dynamic mean field theory (DMFT) description of the transition. However, the amplitude of the effect is an order of magnitude smaller than the one obtained from DMFT calculations for a single-band Hubbard model. We analyze our results using a simple model with the electronic response function obtained from the scaling relations for the conductivity.

Effective field theory and integrability in two-dimensional Mott transition

We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density–density interactions. By means of a two-dimensional Jordan–Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a quantum group symmetry as a consequence of a recently found solution of the Zamolodchikov tetrahedron equation. A projection (from three to two space–time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U q ( sl ( 2 ) ^ ) ⊗ U q ( sl ( 2 ) ^ ) , with deformation parameter q = −1. Based on this result, the low-energy effective field theory for the model is obtained and shown to be a lattice double Chern–Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the effective filed theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas–liquid transition which belongs to the Ising universality class.

Universality of Liquid-Gas Mott Transitions at Finite Temperatures

We explain, in a consistent manner, the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally.

SU(2) Gauge Theory of the Hubbard Model: Emergence of an Anomalous Metallic Phase near the Mott Critical Point

We propose one possible mechanism for an anomalous metallic phase appearing frequently in two spatial dimensions, that is, local pairing fluctuations. Introducing a pair-rotor representation to decompose bare electrons into collective pairing excitations and renormalized electrons, we derive an SU(2) gauge theory of the Hubbard model as an extended version of its U(1) gauge theory. Since our effective SU(2) gauge theory admits two kinds of collective bosons corresponding to pair excitations and density fluctuations, respectively, an intermediate phase appears naturally between the spin liquid Mott insulator and Fermi liquid metal of the U(1) gauge theory, characterized by softening of density-fluctuation modes as the Fermi liquid, but gapping of pair-excitation modes. We show that this intermediate phase is identified with an anomalous metallic phase because there are no electronlike quasiparticles although it is metallic.

Quantum Mott Transition and Multi-Furcating Criticality

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 induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent $z=4$. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and $^3$He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.

Cluster dynamical mean field analysis of the mott transition.

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 variation of the effective mass is no longer equal to the inverse of the quasiparticle residue, as in DMFT, and is reduced approaching the Mott transition.

Mott Transition vs Multicritical Phenomenon of Superconductivity and Antiferromagnetism –Application to κ-(BEDT-TTF)2X–

Interplay between the Mott transition and the multicritical phenomenon of d-wave superconductivity (SC) and antiferromagnetism (AF) is studied theoretically. We describe the Mott transition, which is analogous to a liquid-gas phase transition, in terms of an Ising-type order parameter $\eta$. We reveal possible mean-field phase diagrams produced by this interplay. Renormalization group analysis up to one-loop order gives flows of coupling constants, which in most cases lead to fluctuation-induced first-order phase transitions even when the SO(5) symmetry exists betwen the SC and AF. Behaviors of various physical quantities around the Mott critical point are predicted. Experiments in $\kappa$-(BEDT-TTF)$_2$X are discussed from this viewpoint.

Finite Temperature Mott Transition in the Hubbard Model in Infinite Dimensions

We study the second order finite temperature Mott transition point in the fully frustrated Hubbard model at half filling, within Dynamical Mean Field Theory. Using quantum Monte Carlo simulations we show the existence of a finite temperature second order critical point by explicitly demonstrating the existence of a divergent susceptibility as well as by finding coexistence in the low temperature phase. We determine the location of the finite temperature Mott critical point in the (U,T) plane. Our study verifies and quantifies a scenario for the Mott transition proposed in earlier studies (Reviews of Modern Physics 68, 13, 1996) of this problem.