Quantum spin liquids unveil the genuine Mott state

Charge Transport in the Presence of Correlations and Disorder: Organic Conductors and Manganites

One of the most fascinating aspects of condensed matter is its ability to conduct electricity, which is particularly pronounced in conventional metals such as copper or silver. Such behavior stems from a strong tendency of valence electrons to delocalize in a periodic potential created by ions in the crystal lattice of a given material. In many advanced materials, however, this basic delocalization process of the valence electrons competes with various processes that tend to localize these very same valence electrons, thus driving the insulating behavior. The two such most important processes are the Mott localization, driven by strong correlation effects among the valence electrons, and the Anderson localization, driven by the interaction of the valence electrons with a strong disorder potential. These two localization processes are almost exclusively considered separately from both an experimental and a theoretical standpoint. Here, we offer an overview of our long-standing research on selected organic conductors and manganites, that clearly show the presence of both these localization processes. We discuss these results within existing theories of Mott-Anderson localization and argue that such behavior could be a common feature of many advanced materials.

Thermodynamic determination of the equilibrium first-order phase-transition line hidden by hysteresis in a phase diagram

In some materials exhibiting field-induced first-order transitions (FOTs), the equilibrium phase-transition line is hidden by the hysteresis region associated with the FOT. In general, phase diagrams form the basis for the study of material science, and the profiles of phase-transition lines separating different thermodynamic phases include comprehensive information about thermodynamic quantities, such as latent heat. However, in a field-induced FOT, the equilibrium phase-transition line cannot be precisely determined from measurements of resistivity, magnetization, etc, especially when the transition is accompanied by large hysteresis. Here, we demonstrate a thermodynamics-based method for determining the hidden equilibrium FOT line in a material exhibiting a field-induced FOT. This method is verified for the field-induced FOT between antiferromagnetic and ferrimagnetic states in magneto-electric compounds ([Formula: see text]. The equilibrium FOT line determined based on the Clausius-Clapeyron equation exhibits a reasonable profile in terms of the third law of thermodynamics, and it shows marked differences from the midpoints of the hysteresis region. Our findings highlight that for a field-induced FOT exhibiting large hysteresis, care should be taken for referring to the hysteresis midpoint line when discussing field-induced latent heat or magnetocaloric effects.

Chasing the spin gap through the phase diagram of a frustrated Mott insulator

The quest for entangled spin excitations has stimulated intense research on frustrated magnetic systems. For almost two decades, the triangular-lattice Mott insulator κ-(BEDT-TTF)₂Cu₂(CN)₃ has been one of the hottest candidates for a gapless quantum spin liquid with itinerant spinons. Very recently, however, this scenario was overturned as electron-spin-resonance (ESR) studies unveiled a spin gap, calling for reevaluation of the magnetic ground state. Here we achieve a precise mapping of this spin-gapped phase through the Mott transition by ultrahigh-resolution strain tuning. Our transport experiments reveal a reentrance of charge localization below T^⋆ = 6 K associated with a gap size of 30-50 K. The negative slope of the insulator-metal boundary, dT^⋆/dp < 0, evidences the low-entropy nature of the spin-singlet ground state. By tuning the enigmatic '6K anomaly' through the phase diagram of κ-(BEDT-TTF)₂Cu₂(CN)₃, we identify it as the transition to a valence-bond-solid phase, in agreement with previous thermal expansion and magnetic resonance studies. This spin-gapped insulating state persists at T → 0 until unconventional superconductivity and metallic transport proliferate.

Disorder-dominated quantum criticality in moiré bilayers

Moiré bilayer materials have recently attracted much attention following the discovery of various correlated insulating states at specific band fillings. Here we discuss the metal-insulator transitions (MITs) that have been observed in the same devices, but at fillings far from the strongly correlated regime dominated by Mott-like physics, displaying many similarities to other examples of disorder-dominated MITs. We propose a minimal theoretical model describing the interplay of interactions and disorder, which is able to capture all the universal aspects of quantum criticality, as observed in experiments performed on several devices.

How to Recognize the Universal Aspects of Mott Criticality?

In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner–Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition. We compare the available experimental data on these systems to three existing theoretical scenarios: spinon theory, Dynamical Mean Field Theory (DMFT) and percolation theory. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response.

Planar Heterojunction of Ultrathin CrTe3 and CrTe2 van der Waals Magnet

The fabrication of planar heterojunctions with magnetic van der Waals ultrathin crystals is essential for constructing miniaturized spintronic devices but is yet to be realized. Here, we report the growth of CrTe₃ and CrTe₂ ultrathin films with molecular beam epitaxy and characterize their morphological and electronic structure through low-temperature scanning tunneling microscopy/spectroscopy. The former is identified as a Mott insulator, and the latter has shown a robust magnetic order previously. Through vacuum annealing, CrTe₃ can be transformed into CrTe₂, whose relative ratio is controlled via the annealing time. This renders the feasibility of constructing CrTe₃-CrTe₂ planar heterojunctions, which express atomically sharp interfaces and smooth band bending. We also identified a superstructure conceivably formed via hybrid units of CrTe₃ and CrTe₂, whose electronic structure exhibits stunning tunability with the length of the superstructure. Our study sets a foundation for the development of magnetic tunneling junctions for building spintronic circuits and engineering electronic states in artificial superlattice structures.

Charge-Ordering and Structural Transition in the New Organic Conductor δ'-(BEDT-TTF)2CF3CF2SO3

We report structural, transport, and optical properties and electronic structure calculations of the δ'-(BEDT-TTF)₂CF₃CF₂SO₃ (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) organic conductor that has been synthesized by electrocrystallization. Electronic structure calculations demonstrate the quasi-one-dimensional Fermi surfaces of the compound, while the optical spectra are characteristic for a dimer-Mott insulator. The single-crystal X-ray diffraction measurements reveal the structural phase transition at 200 K from the ambient-temperature monoclinic P2₁/m phase to the low-temperature orthorhombic Pca2₁ phase, while the resistivity measurements clearly show the first order semiconductor-semiconductor transition at the same temperature. This transition is accompanied by charge-ordering as it is confirmed by splitting of charge-sensitive vibrational modes observed in the Raman and infrared spectra. The horizontal stripe charge-order pattern is suggested based on the crystal structure, band structure calculations, and optical spectra.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Continuous Mott transition in semiconductor moiré superlattices

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics^1-6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids^4-7, exciton condensates⁸ and unconventional superconductivity¹. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice^9-22, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe₂/WSe₂ moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to ~5% of the Curie-Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions^4,23.

Pressure-Tuned Superconducting Dome in Chemically-Substituted κ-(BEDT-TTF)2Cu2(CN)3

The quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 has been established as the prime example of a genuine Mott insulator that can be tuned across the first-order insulator–metal transition either by chemical substitution or by physical pressure. Here, we explore the superconducting state that occurs at low temperatures, when both methods are combined, i.e., when κ-[(BEDT-TTF)1−x(BEDT-STF)x]2Cu2(CN)3 is pressurized. We discovered superconductivity for partial BEDT-STF substitution with x = 0.10–0.12 even at ambient pressure, i.e., a superconducting state is realized in the range between a metal and a Mott insulator without magnetic order. Furthermore, we observed the formation of a superconducting dome by pressurizing the substituted crystals; we assigned this novel behavior to disorder emanating from chemical tuning.

Entropic evidence for a Pomeranchuk effect in magic-angle graphene

In the 1950s, Pomeranchuk¹ predicted that, counterintuitively, liquid ³He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene^2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1k_B per unit cell (k_B is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30 kelvin, the bandwidth of magnetic excitations is about 3 kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

Rise and fall of Landau's quasiparticles while approaching the Mott transition

Landau suggested that the low-temperature properties of metals can be understood in terms of long-lived quasiparticles with all complex interactions included in Fermi-liquid parameters, such as the effective mass m^⋆. Despite its wide applicability, electronic transport in bad or strange metals and unconventional superconductors is controversially discussed towards a possible collapse of the quasiparticle concept. Here we explore the electrodynamic response of correlated metals at half filling for varying correlation strength upon approaching a Mott insulator. We reveal persistent Fermi-liquid behavior with pronounced quadratic dependences of the optical scattering rate on temperature and frequency, along with a puzzling elastic contribution to relaxation. The strong increase of the resistivity beyond the Ioffe–Regel–Mott limit is accompanied by a ‘displaced Drude peak’ in the optical conductivity. Our results, supported by a theoretical model for the optical response, demonstrate the emergence of a bad metal from resilient quasiparticles that are subject to dynamical localization and dissolve near the Mott transition.

Charge transport in strongly correlated electron systems is not fully understood. Here, the authors show that resilient quasiparticles at finite frequency persist into the bad-metal regime near a Mott insulator, where dynamical localization results in a ‘displaced Drude peak’ and strongly enhanced dc resistivity.

Possible observation of the signature of the bad metal phase and its crossover to a Fermi liquid in κ-(BEDT-TTF)2Cu(NCS)2 bulk and nanoparticles by Raman scattering

κ-(BEDT-TTF)2Cu(NCS)2 has been investigated by Raman scattering in both bulk and nanoparticle compounds. Phonon modes from 20 to 1600 cm-1 have been assigned. Focusing on the unexplored low frequency phonons, a plateau in frequencies is observed in the bulk phonons between 50 and 100 K and assigned to the signature of the bad metal phase. Nanoparticles of κ-(BEDT-TTF)2Cu(NCS)2 exhibit anomalies at 50 K associated to the crossover from a bad metal to a Fermi liquid whose origins are discussed.

Low temperature injected-caused charge carrier instability in n-type silicon below insulator-to-metal transition

We report on the electric transport properties of Si heavily doped with Sb at concentration just below the insulator-to-metal transition in the temperature range 1.9-3.0 K for current density J  <  0.2 A cm^-2. The change in the sign of the temperature dependence of the differential resistivity [Formula: see text] was observed: the d[Formula: see text]/dT is positive if J  <  0.045 A cm^-2 whereas it becomes negative at J  >  0.045 A cm^-2. The effect is explained assuming the exchange by electrons between the upper Hubbard band (UHB) and the conduction band. The obtained J dependencies of the activation energy, nonequilibrium concentration, mobility and scattering time of the conduction electrons correspond well to this hypothesis. The reason for charge instability is the Coulomb repulsion between electrons occupying states both in the UHB and conduction band. The estimated J dependencies of the conduction electrons lifetime and concentration of the D^- states in the UHB strongly supports this assumption.

Internal strain tunes electronic correlations on the nanoscale

In conventional metals, charge carriers basically move freely. In correlated electron materials, however, the electrons may become localized because of strong Coulomb interactions, resulting in an insulating state. Despite considerable progress in the last decades, elucidating the driving mechanisms that suppress metallic charge transport, the spatial evolution of this phase transition remains poorly understood on a microscopic scale. Here, we use cryogenic scanning near-field optical microscopy to study the metal-to-insulator transition in an electronically driven charge-ordered system with a 20-nm spatial resolution. In contrast to common mean-field considerations, we observe pronounced phase segregation with a sharp boundary between metallic and insulating regions evidencing its first-order nature. Considerable strain in the crystal spatially modulates the effective electronic correlations within a few micrometers, leading to an extended "zebra" pattern of metallic and insulating stripes. We can directly monitor the spatial strain distribution via a gradual enhancement of the optical conductivity as the energy gap is depressed. Our observations shed new light on previous analyses of correlation-driven metal-insulator transitions.

Low-Energy Excitations in Quantum Spin Liquids Identified by Optical Spectroscopy

The electrodynamic response of organic spin liquids with highly frustrated triangular lattices has been measured in a wide energy range. While the overall optical spectra of these Mott insulators are governed by transitions between the Hubbard bands, distinct in-gap excitations can be identified at low temperatures and frequencies, which we attribute to the quantum-spin-liquid state. For the strongly correlated β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, we discover enhanced conductivity below 175  cm^{-1}, comparable to the energy of the magnetic coupling J≈250  K. For ω→0, these low-frequency excitations vanish faster than the charge-carrier response subject to Mott-Hubbard correlations, resulting in a dome-shaped band peaked at 100  cm^{-1}. Possible relations to spinons, magnons, and disorder are discussed.