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Theory of strain phase equilibria and diagrams

Chemical phase equilibria and phase diagrams are well established and have served as indispensable guides for designing materials through chemical tuning. However, a general thermodynamic theory for strain phase equilibria remains elusive despite extensive studies which have revealed dramatic impacts of mechanical strain on the stability of phases and domain states in solid-state materials. Here, we establish the thermodynamic theory of strain equilibria and a general framework for efficiently constructing multidomain and multiphase diagrams of arbitrarily strained solids under incoherent conditions. As examples, we obtain temperature-strain phase diagrams of ferroelectric PbTiO 3 , strongly correlated VO 2 , and unconventional ferroelectric Hf 0.5 Zr 0.5 O 2 . We reveal the analogs of the Gibbs phase rules, multiple- and multi-critical points, common-tangent construction, and level rule in strain equilibria to those in the familiar chemical phase equilibria. Finally, our strain equilibria theory offers a powerful framework for predicting the thermodynamic stability of structural phases and domains in strained solids and for guiding the strain engineering of their functional properties.

36 MATERIALS SCIENCE↗

Tuning the structure and superconductivity of SrNi 2⁢ P 2 by Rh substitution

The compound SrNi 2⁢ P 2 is unique among the ThCr 2 ⁢Si 2 class since it exhibits a temperature-induced transition upon cooling from an uncollapsed tetragonal (ucT) state to a one-third-collapsed orthorhombic (tcO) state where one out of every three P-rows bond across the Sr layers. This compound is also known for exhibiting bulk superconductivity below 1.4 K at ambient pressure. Here, in this paper, we report on the effects of Rh substitution in Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 on the structural and superconducting properties. We studied the variation of the nearest P-P distances as a function of the Rh fraction at room temperature, as well as its temperature dependence for selected compositions. We find that increasing the Rh fraction leads to a decrease in the transition temperature between the ucT and tcO states, until a full suppression of the tcO state for x ≥ 0.166. The superconducting transition first remains nearly insensitive to the Rh fraction, and then it increases to 2.3 K after the tcO state is fully suppressed. These results are summarized in a phase diagram, built upon the characterization by energy dispersive x-ray spectroscopy, x-ray diffraction, resistance, magnetization, and specific heat measurements done on crystalline samples with varying Rh content. The relationship between band structure, crystal structure, and superconductivity is discussed based on previously reported band structure calculations on SrRh 2 ⁢P 2 . Moreover, the effect of Rh fraction on the stress-induced structural transitions is also addressed by means of strain-stress studies done by uniaxial compression of single-crystalline micropillars of Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Hydrostatic and Uniaxial Pressure Tuning of Iron-Based Superconductors: Insights into Superconductivity, Magnetism, Nematicity, and Collapsed Tetragonal Transitions

Iron-based superconductors are well-known for their intriguing phase diagrams, which manifest a complex interplay of electronic, magnetic and structural degrees of freedom. Among the phase transitions observed are superconducting, magnetic, and several types of structural transitions, including a tetragonal-to-orthorhombic and a collapsed-tetragonal transition. In particular, the widely-observed tetragonal-to-orthorhombic transition is believed to be a result of an electronic order that is coupled to the crystalline lattice and is, thus, referred to asnematic transition. Nematicity is therefore a prominent feature of these materials, which signals the importance of the coupling of electronic and lattice properties. Correspondingly, these systems are particularly susceptible to tuning via pressure (hydrostatic, uniaxial, or some combination). We review efforts to probe the phase diagrams of pressure-tuned iron-based superconductors, with a strong focus on our own recent insights into the phase diagrams of several members of this mate-rial class under hydrostatic pressure. These studies on FeSe, Ba(Fe 1-x Co x ) 2 As 2 , Ca(Fe 1-x Co x ) 2 As 2 and CaK(Fe 1-x Ni x ) 4 As 4 were, to a significant extent, made possible by advances of what measurements can be adapted to the use under differing pressure environments. We point out the potential impact of these tools for the study of the wider class of strongly correlated electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robust d-Wave Superconductivity in the Square-Lattice t–J Model

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. Here, to explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Particle–hole asymmetric superconducting coherence peaks in overdoped cuprates

As doping increases in cuprate superconductors, the superconducting transition temperature increases to a maximum at the so-called optimal doping, and then decreases in the overdoped regime. In the past few decades, research has primarily focused on the underdoped and optimally doped regions of the phase diagram. Here, phenomena such as the pseudogap and strange metal non-superconducting states make it difficult to determine the superconducting pairing mechanism. More recently, experiments have shown unconventional behaviour in strongly overdoped cuprates, in both the normal and superconducting states. However, a real-space investigation of the unconventional superconductivity in the absence of the pseudogap is lacking, and the superconductor-to-metal phase transition in the overdoped regime remains controversial. Here we use scanning tunnelling microscopy to investigate the atomic-scale electronic structure of overdoped Bi 2 Sr 2 Ca n–1 Cu n O 2n + 4 + δ cuprates. We show that, at low energies, the spectroscopic maps are well described by dispersive d-wave quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a periodic and non-dispersive pattern emerges. The position of the coherence peaks exhibits particle–hole asymmetry that modulates with the same period. Finally, we propose that this behaviour is due to quasiparticle interference caused by pair-breaking scattering between flat antinodal Bogoliubov bands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Revealing pressure-driven structural transitions in the hybrid improper ferroelectric Sr 3 Sn 2 O 7

In this work, we combine diamond anvil cell techniques and synchrotron-based infrared spectroscopy with a detailed symmetry analysis and lattice dynamics calculations to uncover a series of pressure induced structural phase transitions in the hybrid improper ferroelectric Sr 3 Sn 2 O 7 . The microscopic character of each high pressure phase is determined by comparing the measured spectrum with the predicted vibrational patterns of several related but distinct candidate space groups. Our analysis reveals a sequence of compression-induced transitions from A2 1 am ↔ Pnab ↔ Acaa ↔ I4/mmm at room temperature. Remarkably, this space group progression matches the sequence of temperature-dependent structural transitions observed in Sr 3 Sn 2 O 7 between 77 and 1000 K. Other hybrid improper ferroelectrics display a similar set of transitions, suggesting that pressure and probably strain will be very effective tuning parameters for this entire class of materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning chemical precompression: Theoretical design and crystal chemistry of novel hydrides in the quest for warm and light superconductivity at ambient pressures

Over the past decade, a combination of crystal structure prediction techniques and experimental synthetic work has thoroughly explored the phase diagrams of binary hydrides under pressure. The fruitfulness of this dual approach is demonstrated in the recent identification of several superconducting hydrides with T c s approaching room temperature. We start with an overview of the computational procedures for predicting stable structures and estimating their propensity for superconductivity. A survey of phases with high T c reveals some common structural features that appear conducive to the strong coupling of the electronic structure with atomic vibrations that leads to superconductivity. We discuss the stability and superconducting properties of phases containing two of these—molecular H 2 units mixed with atomic H and hydrogenic clathrate-like cages—as well as more unique motifs. Lastly, we argue that ternary hydride phases, whose exploration is still in its infancy, are a promising route to achieve simultaneous superconductivity at high temperatures and stability at low pressures. Several ternary hydrides arise from the addition of a third element to a known binary hydride structure through site mixing or onto a new site, and several more are based on altogether new structural motifs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning charge density wave order and superconductivity in the kagome metals KV 3 Sb 5 – x Sn x and RbV 3 Sb 5 – x Sn x

The family of AV 3 Sb 5 (A = K, Rb, Cs) kagome metals exhibits charge density wave (CDW) order, proposed to be chiral, followed by a lower temperature superconducting state. Recent studies have proposed the importance of band structure saddle points proximal to the Fermi energy in governing these two transitions. Here we show the effects of hole doping achieved via chemical substitution of Sn for Sb on the CDW and superconducting states in both KV 3 Sb 5 and RbV 3 Sb 5 and generate a phase diagram. Furthermore, hole doping lifts the Γ pocket and van Hove singularities toward E F causing the superconducting T C in both systems to increase to about 4.5 K, while rapidly suppressing the CDW state.

36 MATERIALS SCIENCE↗

Nematic order driven by superconducting correlations

The interplay of nematicity and superconductivity has been observed in a wide variety of quantum materials. To explore this interplay, we consider a two-dimensional (2D) array of nematogens, local droplets with Z 3 nematicity, coupled to a network of Josephson junction wires. Using finite temperature classical Monte Carlo simulations, we elucidate the phase diagram of this model and show that the development of superconducting correlations and the directional delocalization of Cooper pairs can promote nematogen ordering, resulting in long-range nematic order. We obtain the transport properties of our model within an effective resistor network picture. We discuss these ideas in the context of the 2D electron gas at the (111) KTaO 3 interface and the doped topological insulators Nb x Bi 2 Se 3 and Cu x Bi 2 Se 3 . Overall, our work makes contact with Phil Anderson’s numerous contributions to broken symmetries driven by the saving of kinetic energy, including double exchange ferromagnetism and the interlayer tunneling theory of high Tc csuperconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pairing correlations in the cuprates: A numerical study of the three-band Hubbard model

We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an “optimal” value of the charge-transfer energy for the model where T c is largest. Finally, these results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pressure-temperature phase diagram of CaK ( Fe 1 – x Mn x ) 4 As 4 ( x = 0.024 )

Resistance measurements on single crystals of CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) were performed under hydrostatic pressure up to 5.15 GPa. The pressure dependence of the magnetic and superconducting transition temperatures and that of the superconducting upper critical field are reported. Furthermore, our results show that upon increasing pressure, the magnetic transition temperature T N is suppressed, whereas the superconducting transition temperature T c first increases and then decreases, exhibiting a maximum at a pressure p c corresponding to the intersection of the T N (p) and T c (p) lines. In addition, a minimum in the normalized slope of the superconducting upper critical field as well as a change in the pressure dependence of the inferred superconducting coherence length are observed at p c , suggesting a difference in the Fermi surface of the paramagnetic and antiferromagnetic states. Finally, CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) likely goes through a half-collapsed tetragonal phase transition at ~4.3 GPa, further demonstrating that the half-collapsed tetragonal transition pressure in the CaKFe 4 As 4 system is relatively insensitive to transition metal substitution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effects of the Order Parameter Anisotropy on the Vortex Lattice in UPt3

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt 3 for the applied magnetic field along the crystalline c -axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal plane that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt ±15° vortex lattice rotation was previously reported by Huxley et al. , Nature 406 , 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al. , Nature Physics 16 , 531-535 (2020), can be attributed directly to the symmetry breaking field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multiple magnetic orders in LaFeAs 1-x P x O uncover universality of iron-pnictide superconductors

The iron-pnictide superconductors have generated tremendous excitement as the competition between magnetism and superconductivity has allowed unique in-roads towards elucidating a microscopic theory of unconventional high-temperature superconductivity. In addition to the stripe spin density wave ($C^a_{2M}$) phase observed in the parent compounds of all iron-pnictide superconductors, two novel magnetic orders have recently been discovered in different parent structures: an out-of-plane collinear double-Q ($C^c_{4M}$) structure in the hole-doped (Ca, Sr, Ba) 1-x (Na) x Fe 2 As 2 and Ba 1-x K x Fe 2 As 2 families, and a spin vortex crystal “hedgehog” ($C^{ab}_{4M}$) structure in the CaKFe 4 As 4 family. Using neutron diffraction, we demonstrate that LaFeAs 1-x P x O contains all three magnetic orders within a single-phase diagram as a function of substitution, all of which compete strongly with superconductivity. Our experimental observations combined with theoretical modeling demonstrate how the reduction in electronic correlations by chemical substitution results in larger Fermi surfaces and the sequential stabilization of multiple magnetic anisotropies. Our work presents a unified narrative for the competing magnetic and superconducting phases observed in various iron-pnictide systems with different crystal structures and chemistry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phase diagrams of single-layer two-dimensional transition metal dichalcogenides: Landau theory

We report single layer (SL) two-dimensional transition metal dichalcogenides (TMDs), such as MoS 2 , ReS 2 , WSe 2 , and MoTe 2 have now become the focus of intensive fundamental and applied research due to their intriguing and tunable physical properties. These materials exhibit a broad range of structural phases that can be induced via elastic strain, chemical doping, and electrostatic field effect. These transformations, in turn, can open and close the band gap of SL-TMDs, leading to metal-insulator transitions, and lead to emergence of more complex quantum phenomena. These considerations necessitate detailed understanding of the mesoscopic mechanisms of these structural phase transitions. Here we develop a Landau-type thermodynamic description of SL-TMDs on a sample of the SL-(MoS 2 ) 1-x -(ReS 2 ) x system and analyze the free energy surfaces, phase diagrams, and order parameter behavior. Our results predict the existence of multiple structural phases with two-, six- and 12-fold degenerated energy minima for in-plane and out-of-plane order parameters. This analysis suggests that out-of-plane ferroelectricity can exist in many of these phases, with the switchable polarization being proportional to the out-of-plane order parameter. We further predict that the domain walls in SL-(MoS 2 ) 1-x -(ReS 2 ) x should become conductive above a certain strain threshold.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Manipulating high-temperature superconductivity by oxygen doping in Bi2Sr2CaCu2O8+δ thin flakes

Abstract Harnessing the fascinating properties of correlated oxides requires precise control of their carrier density. Compared to other methods, oxygen doping provides an effective and more direct way to tune the electronic properties of correlated oxides. Although several approaches, such as thermal annealing and oxygen migration, have been introduced to change the oxygen content, a continuous and reversible solution that can be integrated with modern electronic technology is much in demand. Here, we report a novel ionic field-effect transistor using solid Gd-doped CeO2 as the gate dielectric, which shows a remarkable carrier-density-tuning ability via electric-field-controlled oxygen concentration at room temperature. In Bi2Sr2CaCu2O8+δ (Bi-2212) thin flakes, we achieve a reversible superconductor–insulator transition by driving oxygen ions in and out of the samples with electric fields, and map out the phase diagram all the way from the insulating regime to the over-doped superconducting regime by continuously changing the oxygen doping level. Scaling analysis indicates that the reversible superconductor–insulator transition for the Bi-2212 thin flakes follows the theoretical description of a two-dimensional quantum phase transition. Our work provides a route for realizing electric-field control of phase transition in correlated oxides. Moreover, the configuration of this type of transistor makes heterostructure/interface engineering possible, thus having the potential to serve as the next-generation all-solid-state field-effect transistor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Persistence of charge density wave fluctuations in the absence of long-range order in a hole-doped kagome metal

The kagome metals 𝐴⁢V 3 ⁢Sb 5 (𝐴=K, Rb, Cs) exhibit a complex interplay between charge density wave (CDW) order and superconductivity. Here, in this study, we use ultrafast coherent phonon spectroscopy to probe the evolution of CDW order in hole-doped CsV 3 ⁢Sb 5−𝑥 ⁢Sn 𝑥 across a broad range of compositions (0 ≤ 𝑥 ≤ 0.68). While thermodynamic and diffraction measurements show long-range CDW order vanishes above 𝑥 ≈ 0.05, we observe persistent signatures of CDW fluctuations up to the highest doping levels, with correlation times on the order of several picoseconds. These results indicate the presence of a robust fluctuating charge order that survives well beyond the established CDW phase boundary. Furthermore, these fluctuations are enhanced near a doping-tuned quantum phase transition at 𝑥* ≈ 0.15, which coincides with a local minimum in the superconducting 𝑇 c double-dome. Additional measurements on Ti- and K-substituted samples confirm that this behavior is intrinsic to hole doping and not tied to disorder. Overall, our findings suggest that CDW fluctuations play a central role in the electronic phase diagram of 𝐴⁢V 3 ⁢Sb 5 and may mediate or compete with superconductivity.

Kongruengkit, Terawit [Univ. of California, Santa ↗

One-dimensional Holstein model revisited

Here, we analyze the global ground-state (quantum) phase diagram of the one-dimensional spinful Holstein model at half filling as a function of the strength of the electron-phonon coupling (represented by the strength of the phonon-induced attraction, U) and the phonon frequency ω 0 . In addition to reanalyzing the various asymptotic regimes, we carry out density-matrix renormalization group simulations to correct previous inferences concerning the antiadiabatic (large ω 0 ) and strong-coupling (large U) regimes. There are two distinct phases—a fully gapped commensurate charge-density-wave phase and a spin-gapped Luther-Emery phase with a gapless charge mode—separated by a phase boundary, with a shape that reflects different microscopic physics in the weak- and strong-coupling limits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Experimental Progress in Superconducting Nickelates

The superconducting nickelates were first proposed as potential analogs to the cuprate unconventional superconductors in 1999, but it took twenty years before superconductivity was successfully stabilized in epitaxial thin films. Since then, a flurry of both experimental and theoretical efforts have sought to understand the similarities and differences between the two systems and how they manifest in the macroscopic superconducting and normal state properties. Although the nickelates and cuprates indeed share many commonalities within their respective phase diagrams, several notable differences have also emerged, especially regarding their parent compounds, electronic hybridization, and fermiology. Here, we provide a survey of the rapidly developing landscape of layered nickelate superconductors, including recent experimental progress to probe not just the superconducting but also normal state and other ordered phases stabilized in these compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗