Free energy of a two-liquid system of charge carriers in strongly coupled electron and phonon fields and common nature of three phases in hole-doped cuprates

Hole-doped cuprates exhibit partially coexisting pseudogap, charge ordering and superconductivity; we show that there exists a class of systems in which they have a single nature as it has recently been supposed. Since the charge-ordered phase exhibits large frozen deformation of the lattice, we develop a method for calculating the phase diagram of a system with strong long-range (Frӧhlich) electron-phonon interaction. Using a variational approach, we calculate the free energy of a two-liquid system of carriers with cuprate-like dispersion comprising a liquid of autolocalized carriers (large polarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing it with the free energy of pure Fermi liquid and calculating (with standard methods of Bose liquid theory) a temperature of the superfluid transition in the large-bipolaron liquid we identify regions in the phase diagram with the presence of pseudogap (caused by the impact of the (bi)polarons potential on delocalized quasiparticles), charge ordering and superconductivity. They are located in the same places in the diagram as in hole-doped cuprates, and, as in the latter, the shape of the calculated phase diagram is resistant to wide-range changes in the characteristics of the system. As in cuprates, the calculated temperature of the superconducting transition increases with the number of conducting planes in the unit cell, the superfluid density decreases with doping at overdoping, the bipolaron density (and bipolaronic plasmon energy) saturates at optimal doping. Thus, the similarity of the considered system with hole-doped cuprates is not limited to the phase diagram. The results obtained allow us to discuss ways of increasing the temperature of the superfluid transition in the large-bipolaron liquid and open up the possibility of studying the current-carrying state and properties of the bipolaron condensate.

Possible charge ordering and anomalous transport in graphene/graphene quantum dot heterostructure

Observations of superconductivity and charge density waves (CDW) in graphene have been elusive thus far due to weak electron-phonon coupling (EPC) interactions. Here, we report a unique observation of anomalous transport and multiple charge ordering phases at high temperatures (T1∼213K,T2∼325K) in a 0D-2D van der Waals (vdW) heterostructure comprising of single layer graphene (SLG) and functionalized (amine) graphene quantum dots (GQD). The presence of functionalized GQD contributed to charge transfer with shifting of the Dirac point ∼ 0.05 eV above the Fermi level (ab initio   simulations) and carrier densityn∼-0.3×1012 cm-2confirming p-doping in SLG and two-fold increase in EPC interaction was achieved. Moreover, we elucidate the interplay between electron-electron and electron-phonon interactions to substantiate high temperature EPC driven charge ordering in the heterostructure through analyses of magnetotransport and weak anti-localization (WAL) framework. Our results provide impetus to investigate strongly correlated phenomena such as CDW and superconducting phase transitions in novel graphene based heterostructures.

Crystallization of heavy fermions via epitaxial strain in spinel LiV2O4 thin film

The mixed-valent spinel LiV2O4 is known as the first oxide heavy-fermion system. There is a general consensus that a subtle interplay of charge, spin, and orbital degrees of freedom of correlated electrons plays a crucial role in the enhancement of quasi-particle mass, but the specific mechanism has remained yet elusive. A charge-ordering (CO) instability of V3+ and V4+ ions that is geometrically frustrated by the V pyrochlore sublattice from forming a long-range CO down to T = 0 K has been proposed as a prime candidate for the mechanism. Here, we uncover the hidden CO instability by applying epitaxial strain on single-crystalline LiV2O4 thin films. We find a crystallization of heavy fermions in a LiV2O4 film on MgO, where a charge-ordered insulator comprising of a stack of V3+ and V4+ layers along [001], the historical Verwey-type ordering, is stabilized by the in-plane tensile and out-of-plane compressive strains from the substrate. Our discovery of the [001] Verwey-type CO, together with previous realizations of a distinct [111] CO, evidence the close proximity of the heavy-fermion state to degenerate CO states mirroring the geometrical frustration of the V pyrochlore lattice, which supports the CO instability scenario for the mechanism behind the heavy-fermion formation.

True Atomic-Resolution Surface Imaging and Manipulation under Ambient Conditions via Conductive Atomic Force Microscopy

A great number of chemical and mechanical phenomena, ranging from catalysis to friction, are dictated by the atomic-scale structure and properties of material surfaces. Yet, the principal tools utilized to characterize surfaces at the atomic level rely on strict environmental conditions such as ultrahigh vacuum and low temperature. Results obtained under such well-controlled, pristine conditions bear little relevance to the great majority of processes and applications that often occur under ambient conditions. Here, we report true atomic-resolution surface imaging via conductive atomic force microscopy (C-AFM) under ambient conditions, performed at high scanning speeds. Our approach delivers atomic-resolution maps on a variety of material surfaces that comprise defects including single atomic vacancies. We hypothesize that atomic resolution can be enabled by either a confined, electrically conductive pathway or an individual, atomically sharp asperity at the tip-sample contact. Using our method, we report the capability of in situ charge state manipulation of defects on MoS₂ and the observation of an exotic electronic effect: room-temperature charge ordering in a thin transition metal carbide (TMC) crystal (i.e., an MXene), α-Mo₂C. Our findings demonstrate that C-AFM can be utilized as a powerful tool for atomic-resolution imaging and manipulation of surface structure and electronics under ambient conditions, with wide-ranging applicability.

Coexistence and Coupling of Multiple Charge Orderings and Spin States in Hexagonal Ferrite

The coupling between charge and spin orderings in strongly correlated systems plays a crucial role in fundamental physics and device applications. As a candidate of multiferroic materials, LuFe₂O₄ with a nominal Fe^2.5+ valence state has the potential for strong charge-spin interactions; however, these interactions have not been fully understood until now. Here, combining complementary characterization methods with theoretical calculations, two types of charge orderings with distinct magnetic properties are revealed. The ground states of LuFe₂O₄ are decided by the parallel/antiparallel coupling of both charge and spin orderings in the adjacent FeO double layers. Whereas the ferroelectric charge ordering remains ferrimagnetic below 230 K, the antiferroelectric ordering undergoes antiferromagnetic-ferrimagnetic-paramagnetic transitions from 2 K to room temperature. This study demonstrates the unique aspects of strong spin-charge coupling within LuFe₂O₄. Our results shed light on the coexistence and competing nature of orderings in quantum materials.

Polyhedron and Charge Ordering in Interfacial Reconstruction of a Hexagonal Ferrite/Sapphire Heterostructure

Interfacial reconstruction, emanating from the symmetry breaking at the interface, plays a key role in modulating the microstructures and properties of heterostructures. The appeal of revealing such a reconstruction resides in the underlying mechanism connected to the function of heterostructures and new insights into designing a new interface device. Here, we demonstrate an interfacial reconstruction in a large lattice-mismatch system, h-LuFeO₃/α-Al₂O₃ heterostructure. Combining the atomic-resolution imaging and spectroscopy of scanning transmission electron microscopy, the periodic variation of FeO immediate coordination and charge ordering of iron are revealed, indicating a strong lattice-charge coupling in the reconstruction. Such a reconstruction reported here suggests that polyhedral and electronic flexibility is important for the reconstruction formation and presents possibilities for further construction of more functional heterostructures.

A framework for the description of charge order, pseudo and superconducting gap, critical temperature and pairing interaction in cuprate superconductors

A unified phenomenological description framework is proposed for the evaluation of some of the most important observables of the cuprate superconductors: the pseudogap (PG) ΔPG, the local superconducting amplitudes ΔSC(ri), the critical temperatureTcand charge ordering (CO) parameters. Recent detailed measurements of CO structures and CO wavelengthsλCOare faithfully reproduced by solutions of a Cahn-Hilliard differential equation with a free energy potentialVGLthat produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to theVGLamplitude. The local SC amplitude and phaseθiare connected by Josephson couplingEJ(rij) and the SC long-range order transition occurs whenEJ∼kBTc. The calculated results of the wavelengthλCO, ΔPG,ΔSCandTccalculations are in good agreement with a variety of experiments.

A Room-Temperature Verwey-type Transition in Iron Oxide, Fe5 O6

Functional oxides whose physicochemical properties may be reversibly changed at standard conditions are potential candidates for the use in next‐generation nanoelectronic devices. To date, vanadium dioxide (VO₂) is the only known simple transition‐metal oxide that demonstrates a near‐room‐temperature metal–insulator transition that may be used in such appliances. In this work, we synthesized and investigated the crystals of a novel mixed‐valent iron oxide with an unconventional Fe₅O₆ stoichiometry. Near 275 K, Fe₅O₆ undergoes a Verwey‐type charge‐ordering transition that is concurrent with a dimerization in the iron chains and a following formation of new Fe−Fe chemical bonds. This unique feature highlights Fe₅O₆ as a promising candidate for the use in innovative applications. We established that the minimal Fe−Fe distance in the octahedral chains is a key parameter that determines the type and temperature of charge ordering. This model provides new insights into charge‐ordering phenomena in transition‐metal oxides in general.

Superlattice-induced ferroelectricity in charge-ordered La1/3Sr2/3FeO3

Charge-order-driven ferroelectrics are an emerging class of functional materials, distinct from conventional ferroelectrics, where electron-dominated switching can occur at high frequency. Despite their promise, only a few systems exhibiting this behavior have been experimentally realized thus far, motivating the need for new materials. Here, we use density-functional theory to study the effect of artificial structuring on mixed-valence solid-solution La1/3Sr2/3FeO3 (LSFO), a system well studied experimentally. Our calculations show that A-site cation (111)-layered LSFO exhibits a ferroelectric charge-ordered phase in which inversion symmetry is broken by changing the registry of the charge order with respect to the superlattice layering. The phase is energetically degenerate with a ground-state centrosymmetric phase, and the computed switching polarization is 39 μC/[Formula: see text], a significant value arising from electron transfer between [Formula: see text] octahedra. Our calculations reveal that artificial structuring of LSFO and other mixed valence oxides with robust charge ordering in the solid solution phase can lead to charge-order-induced ferroelectricity.

Photoenhanced metastable c-axis electrodynamics in stripe-ordered cuprate La1.885Ba0.115CuO4

The emergence of superconductivity in high-temperature cuprates arises out of a rich landscape of competing order. For example, stripe order can hoard the electrons needed to form Cooper pairs and establish superconductivity. Intriguingly, the complex interactions of such intertwined orders can be manipulated with light, where nonequilibrium dynamics alter the primacy of one order over another. Following photoexcitation of La_2−xBa_xCuO₄ (x = 0.115) with near-infrared pulses, we observe a long-lived state that exhibits enhanced superconducting correlations well above the equilibrium superconducting transition temperature. Our analysis reveals that this metastable phase arises from a collapse of stripe order, providing an important demonstration of light-directed control in quantum materials.

Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La_2−xBa_xCuO₄ (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm² results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La_2−xBa_xCuO₄ is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

Strongly Compressed Few-Layered SnSe2 Films Grown on a SrTiO3 Substrate: The Coexistence of Charge Ordering and Enhanced Interfacial Superconductivity

High pressure has been demonstrated to be a powerful approach of producing novel condensed-matter states, particularly in tuning the superconducting transition temperature (T_c) of the superconductivity in a clean fashion without involving the complexity of chemical doping. However, the challenge of high-pressure experiment hinders further in-depth research for underlying mechanisms. Here, we have successfully synthesized continuous layer-controllable SnSe₂ films on SrTiO₃ substrate using molecular beam epitaxy. By means of scanning tunneling microscopy/spectroscopy (STM/S) and Raman spectroscopy, we found that the strong compressive strain is intrinsically built in few-layers films, with a largest equivalent pressure up to 23 GPa in the monolayer. Upon this, unusual 2 × 2 charge ordering is induced at the occupied states in the monolayer, accompanied by prominent decrease in the density of states (DOS) near the Fermi energy (E_F), resembling the gap states of CDW reported in transition metal dichalcogenide (TMD) materials. Subsequently, the coexistence of charge ordering and the interfacial superconductivity is observed in bilayer films as a result of releasing the compressive strain. In conjunction with spatially resolved spectroscopic study and first-principles calculation, we find that the enhanced interfacial superconductivity with an estimated T_c of 8.3 K is observed only in the 1 × 1 region. Such superconductivity can be ascribed to a combined effect of interfacial charge transfer and compressive strain, which leads to a considerable downshift of the conduction band minimum and an increase in the DOS at E_F. Our results provide an attractive platform for further in-depth investigation of compression-induced charge ordering (monolayer) and the interplay between charge ordering and superconductivity (bilayer). Meanwhile, it has opened up a pathway to prepare strongly compressed two-dimensional materials by growing onto a SrTiO₃ substrate, which is promising to induce superconductivity with a higher T_c.

Quenching of Charge and Spin Degrees of Freedom in Condensed Matter

Electrons in condensed matter have internal degrees of freedom, such as charge, spin, and orbital, leading to various forms of ordered states through phase transitions. However, in individual materials, a charge/spin/orbital ordered state of the lowest temperature is normally uniquely determined in terms of the lowest-energy state, i.e., the ground state. Here, recent results are summarized showing that under rapid cooling, this principle does not necessarily hold, and thus, the cooling rate is a control parameter of the lowest-temperature state beyond the framework of the thermoequilibrium phase diagram. Although the cooling rate utilized in low-temperature experiments is typically 2 × 10^-3 to 4 × 10^-1 K s^-1 , the use of optical/electronic pulses facilitates rapid cooling, such as 10² -10³ K s^-1 . Such an unconventionally high cooling rate allows some systems to kinetically avoid a first-order phase transition, resulting in a quenched charge/spin state that differs from the ground state. It is also demonstrated that quenched states can be exploited as a non-volatile state variable when designing phase-change memory functions. The present findings suggest that rapid cooling is useful for exploring and controlling the metastable electronic/magnetic state, which is potentially hidden behind the ground state.

Spin Chains and Electron Transfer at Stepped Silicon Surfaces

High-index surfaces of silicon with adsorbed gold can reconstruct to form highly ordered linear step arrays. These steps take the form of a narrow strip of graphitic silicon. In some cases--specifically, for Si(553)-Au and Si(557)-Au--a large fraction of the silicon atoms at the exposed edge of this strip are known to be spin-polarized and charge-ordered along the edge. The periodicity of this charge ordering is always commensurate with the structural periodicity along the step edge and hence leads to highly ordered arrays of local magnetic moments that can be regarded as "spin chains." Here, we demonstrate theoretically as well as experimentally that the closely related Si(775)-Au surface has--despite its very similar overall structure--zero spin polarization at its step edge. Using a combination of density-functional theory and scanning tunneling microscopy, we propose an electron-counting model that accounts for these differences. The model also predicts that unintentional defects and intentional dopants can create local spin moments at Si(hhk)-Au step edges. We analyze in detail one of these predictions and verify it experimentally. This finding opens the door to using techniques of surface chemistry and atom manipulation to create and control silicon spin chains.

Recent progress in high-pressure studies on organic conductors

Recent high-pressure studies of organic conductors and superconductors are reviewed. The discovery of the highest T_c superconductivity among organics under high pressure has triggered the further progress of the high-pressure research. Owing to this finding, various organic conductors with the strong electron correlation were investigated under high pressures. This review includes the pressure techniques using the cubic anvil apparatus, as well as high-pressure studies of the organic conductors up to 10 GPa showing extraordinary temperature and pressure dependent transport phenomena.

Theoretical aspects of charge correlations in θ-(BEDT-TTF)2X

A review is given on the theoretical studies of charge correlations in θ-(BEDT-TTF)₂X. Various studies show that within a purely electronic model on the θ-type lattice with on-site U and nearest neighbor V_p and V_c interactions, the diagonal stripe, c-axis three-fold, and the vertical stripe charge correlations are favored in the regime V_p <V_c , V_p ∼V_c , and V_p >V_c , respectively. In the realistic parameter regime of V_p ∼V_c , there is competition between the c-axis three fold state and diagonal stripe state. Since these are different from the experimentally observed a-axis three fold and the horizontal stripe charge correlations, additional effects have to be included in order to understand the experiments. The electron-lattice coupling, which tends to distort the lattice into the θ _d -type, is found to favor the horizontal stripe state, suggesting that the occurrence of this stripe ordering in the actual materials may not be of purely electronic origin. On the other hand, distant electron-electron interactions have to be considered in order to understand the a-axis three fold correlation, whose wave vector is close to the nesting vector of the Fermi surface. These studies seem to suggest that the minimal model to understand the charge correlation in θ-(BEDT-TTF)₂X may be more complicated than expected. Future problems regarding the competition between different types of charge correlations are discussed.

Organic metal (EDO-TTF)2PF6 with multi-instability

The multi-instability of the electronic structure of (EDO-TTF)₂PF₆, where EDO-TTF means ethylene-dioxytetrathiafulvalene, is reviewed. This complex showed the metal-insulator transition at 280 K associated with distinct molecular deformations. The mechanism is interpreted as the cooperation of Peierls transition, charge ordering, and the order-disorder transition of the countercomponent. The charge ordering pattern in the low-temperature phase is of the novel [0, 0, 1, 1] type. The sensitivity of the electronic state to external perturbations is demonstrated applying not only static but also instantaneous stimuli. In the latter case, the photo-induced phase transition is ultrafast and highly efficient. One photon causes the transition of several hundreds of donor molecules in the low-temperature phase to relax into a highly conducting metastable state within about 1.5 ps. In the early stage of the transient state, the charge ordering of the [1, 0, 1, 0] type occurs. As for the chemical modifications of this material, the partial deuteration of this complex increases the metal-insulator transition temperature. The introduction of a methyl group greatly modulates the electronic structure of the complex, i.e. (methyl-EDO-TTF)₂X (X=BF₄, ClO₄) shows a two-dimensional electronic structure. The working hypotheses for developing the systems with multi-instability are described.

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)2I3

The quasi-two-dimensional molecular conductor α-(BEDT-TTF)₂I₃ exhibits anomalous transport phenomena where the temperature dependence of resistivity is weak but the ratio of the Hall coefficient at 10 K to that at room temperature is of the order of 10⁴. These puzzling phenomena were solved by predicting massless Dirac fermions, whose motions are described using the tilted Weyl equation with anisotropic velocity. α-(BEDT-TTF)₂I₃ is a unique material among several materials with Dirac fermions, i.e. graphene, bismuth, and quantum wells such as HgTe, from the view-points of both the structure and electronic states described as follows. α-(BEDT-TTF)₂I₃ has the layered structure with highly two-dimensional massless Dirac fermions. The anisotropic velocity and incommensurate momenta of the contact points, ±k₀, originate from the inequivalency of the BEDT-TTF sites in the unit cell, where ±k₀ moves in the first Brillouin zone with increasing pressure. The massless Dirac fermions exist in the presence of the charge disproportionation and are robust against the increase in pressure. The electron densities on those inequivalent BEDT-TTF sites exhibit anomalous momentum distributions, reflecting the angular dependences of the wave functions around the contact points. Those unique electronic properties affect the spatial oscillations of the electron densities in the vicinity of an impurity. A marked behavior of the Hall coefficient, where the sign of the Hall coefficient reverses sharply but continuously at low temperatures around 5 K, is investigated by treating the interband effects of the magnetic field exactly. It is shown that such behavior is possible by assuming the existence of the extremely small amount of electron doping. The enhancement of the orbital diamagnetism is also expected. The results of the present research shed light on a new aspect of Dirac fermion physics, i.e. the emergence of unique electronic properties owing to the structure of the material.