Competing Order Parameters Research Articles

Features of the formation of the rotationally ordered phases in perovskites

Based on the phenomenological theory, the conditions for the formation of a sequences of the rotationally ordered phase states observed in orthoaluminates, orthoferrites and several other ABX3 compounds with a perovskite structure have been studied. It was shown that the specificity of the phase state formation is due to the competition between two critical order parameters characterizing the in-phase and antiphase rotations of the octahedra. The condensation of one order parameter blocks the appearance of the other. The blocking can be overcome by the interaction of the competing order parameters with the displacements of the cation A. In this case, the degree of stretching of the A–X bonds is of great importance. The consequence of the removal of the blocking is the formation of the phase states described by two competing order parameters. The conditions under which a change in the critical order parameter occurs have discussed.

Topological symplectic Kondo effect

Multiple conduction channels interacting with a quantum impurity -- a spin in the conventional ``multi-channel Kondo effect'' or a topological mesoscopic device (``topological Kondo effect'') -- has been proposed as a platform to realize anyonic quasi-particles. However, the above implementations require either perfect channel symmetry or the use of Majorana fermions. Here we propose a Majorana-free mesoscopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and $\mathbb Z_3$ parafermions) even in the absence of perfect channel symmetry. In addition to the detailed prescription of the implementation, we present the strong coupling solution by mapping the model to the multi-channel Kondo effect associated to an internal $SU(2)$ symmetry and exploit conformal field theory (CFT) to predict the non-trivial scaling of a variety of observables, including conductance, as a function of temperature. This work does not only open the door for robust Kondo-based anyon platforms, but also sheds light on the physics of strongly correlated materials with competing order parameters.

Frozen Deconfined Quantum Criticality

There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear-deconfine-at the critical point. Nevertheless, many numerical MonteCarlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane CP^{1} antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub frozen. At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.

Valence-skipping and quasi-two-dimensionality of superconductivity in a van der Waals insulator

Valence fluctuation of interacting electrons plays a crucial role in emergent quantum phenomena in correlated electron systems. The theoretical rationale is that this effect can drive a band insulator into a superconductor through charge redistribution around the Fermi level. However, the root cause of such a fluctuating leap in the ionic valency remains elusive. Here, we demonstrate a valence-skipping-driven insulator-to-superconductor transition and realize quasi-two-dimensional superconductivity in a van der Waals insulator GeP under pressure. This is shown to result from valence skipping of the Ge cation, altering its average valency from 3+ to 4+, turning GeP from a layered compound to a three-dimensional covalent system with superconducting critical temperature reaching its maximum of 10 K. Such a valence-skipping-induced superconductivity with a quasi-two-dimensional nature in thin samples, showing a Berezinskii-Kosterlitz-Thouless-like character, is further confirmed by angle-dependent upper-critical-field measurements. These findings provide a model system to examine competing order parameters in valence-skipping systems.

Puzzle of bicriticality in the XXZ antiferromagnet

Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy Z-axis has asymptotically either a tetracritical phase-diagram or a triple point in the field-temperature plane. Neither experiments nor Monte Carlo simulations procure such phase diagrams. Instead, they find a bicritical phase-diagram. Here this discrepancy is resolved: after generalizing a ubiquitous condition identifying the tetracritical point, we employ new renormalization-group recursion relations near the isotropic fixed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the experiments and simulations results can only be understood if their trajectories flow towards the fluctuation-driven first order transition (and the associated triple point), but reach this limit only for prohibitively large system sizes or correlation lengths. In the crossover region one expects a bicritical phase diagram, as indeed is observed. A similar scenario may explain puzzling discrepancies between simulations and renormalization-group predictions for a variety of other phase diagrams with competing order parameters.

Quantum phase transitions in a bidimensional O(N) × ℤ2 scalar field model

We analyze the possible quantum phase transition patterns occurring within the O(N) × ℤ2 scalar multi-field model at vanishing temperatures in (1 + 1)-dimensions. The physical masses associated with the two coupled scalar sectors are evaluated using the loop approximation up to second order. We observe that in the strong coupling regime, the breaking O(N) × ℤ2→ O(N), which is allowed by the Mermin-Wagner-Hohenberg-Coleman theorem, can take place through a second-order phase transition. In order to satisfy this no-go theorem, the O(N) sector must have a finite mass gap for all coupling values, such that conformality is never attained, in opposition to what happens in the simpler ℤ2 version. Our evaluations also show that the sign of the interaction between the two different fields alters the transition pattern in a significant way. These results may be relevant to describe the quantum phase transitions taking place in cold linear systems with competing order parameters. At the same time the super-renormalizable model proposed here can turn out to be useful as a prototype to test resummation techniques as well as non-perturbative methods.

Latent superconductivity at parallel interfaces in a superlattice dominated by another collective quantum phase

We theoretically examine behavior of superconductivity at parallel interfaces separating the domains of another dominant collective excitation, such as charge density waves or spin density waves. Due to their competitive coupling in a two-component Ginzburg-Landau model, suppression of the dominant order parameter at the interfacial planes allows for nucleation of the (hidden) superconducting order parameter at those planes. In such a case, we demonstrate how the number of the parallel interfacial planes and the distance between them are linked to the number and the size of the emerging superconducting gaps in the system, as well as the versatility and temperature evolution of the possible superconducting phases. These findings bear relevance to a broad selection of known layered superconducting materials, as well as to further design of artificial (e.g., oxide) superlattices, where the interplay between competing order parameters paves the way towards otherwise unattainable superconducting states, some with enhanced superconducting critical temperature.

Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological p -wave superfluid

We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ifmmode\pm\else\textpm\fi{}}(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III'. In addition, there are two other types of late-time dynamics---phase I where both order parameters decay to zero and phase II where ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ asymptotes to a nonzero constant while ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III' is unstable with respect to breaking the time-reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III' is replaced by the Floquet topological phase III that is seen in the integrable chiral $p$-wave model.

Hidden order and multipolar exchange striction in a correlated f-electron system

The nature of order in low-temperature phases of some materials is not directly seen by experiment. Such "hidden orders" (HOs) may inspire decades of research to identify the mechanism underlying those exotic states of matter. In insulators, HO phases originate in degenerate many-electron states on localized f or d shells that may harbor high-rank multipole moments. Coupled by intersite exchange, those moments form a vast space of competing order parameters. Here, we show how the ground-state order and magnetic excitations of a prototypical HO system, neptunium dioxide NpO2, can be fully described by a low-energy Hamiltonian derived by a many-body ab initio force theorem method. Superexchange interactions between the lowest crystal-field quadruplet of Np4+ ions induce a primary noncollinear order of time-odd rank 5 (triakontadipolar) moments with a secondary quadrupole order preserving the cubic symmetry of NpO2 Our study also reveals an unconventional multipolar exchange striction mechanism behind the anomalous volume contraction of the NpO2 HO phase.

Machine learning techniques provide insight into materials with competing order parameters

Atomically disordered systems are extremely complicated to model, but a new probabilistic algorithm allows them to be quantitatively analyzed. This could lead to the discovery of new physics.

Protected superconductivity at the boundaries of charge-density-wave domains

Solid 4He may acquire superfluid characteristics due to the frustration of the solid phase at grain boundaries. Here, introducing a negative-U generalized Hubbard model and a coarse-grained semiclassical pseudospin model, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDW) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDW breaks apart in domains with topologically protected filamentary superconductivity at the interfaces. Our transport measurements, carried out in underdoped La2−xSrxCuO4, with the magnetic field acting as a control parameter, are shown to be in excellent agreement with our theoretical prediction. Assuming superconductivity and CDW phases have similar energies, at intermediate temperatures, the magnetic field drives the system from a fluctuating superconductor to a CDW as expected in the clean limit. Lowering the temperature, the expected clean quantum critical point is avoided and a filamentary phase appears, analogous to ‘glassy’ supersolid phenomena in 4He. The transition line ends at a second quantum critical point at high-fields. Within our scenario, the filamentary superconducting phase is parasitic with CDW and bulk superconducting phases playing the role of primary competing order parameters.

Coupled structural distortions, domains, and control of phase competition in polar SmBaMn2O6

Materials with coupled or competing order parameters display highly tunable ground states, where subtle perturbations reveal distinct electronic and magnetic phases. These phases generally are underpinned by complex crystal structures, but the role of structural complexity in these phases often is unclear. We use group theoretic methods and first-principles calculations to analyze a set of coupled structural distortions that underlie the polar charge- and orbitally- ordered antiferromagnetic ground state of $A$-site ordered SmBaMn$_2$O$_6$. We show that these distortions play a key role in establishing the ground state and stabilizing a network of domain wall vortices. Furthermore, we show that the crystal structure provides a knob to control competing electronic and magnetic phases at structural domain walls and in epitaxially strained thin films. These results provide new understanding of the complex physics realized across multiple length scales in SmBaMn$_2$O$_6$ and demonstrate a framework for systematic exploration of correlated and structurally complex materials.

Probing Phase Separation and Local Lattice Distortions in Cuprates by Raman Spectroscopy

It is generally accepted that high temperature superconductors emerge when extra carriers are introduced in the parent state, which looks like a Mott insulator. Competition of the order parameters drives the system into a poorly defined pseudogap state before acquiring the normal Fermi liquid behavior with further doping. Within the low doping level, the system has the tendency for mesoscopic phase separation, which seems to be a general characteristic in all high Tc compounds, but also in the materials of colossal magnetoresistance or the relaxor ferroelectrics. In all these systems, metastable phases can be created by tuning physical variables, such as doping or pressure, and the competing order parameters can drive the compound to various states. Structural instabilities are expected at critical points and Raman spectroscopy is ideal for detecting them, since it is a very sensitive technique for detecting small lattice modifications and instabilities. In this article, phase separation and lattice distortions are examined on the most characteristic family of high temperature superconductors, the cuprates. The effect of doping or atomic substitutions on cuprates is examined concerning the induced phase separation and hydrostatic pressure for activating small local lattice distortions at the edge of lattice instability.

One-loop effective potential for two-dimensional competing scalar order parameters

Using the method of the effective potential of quantum field theory, we compute the quantum corrections to the phase diagram of systems with competing order parameters. This is specially useful to study metallic systems with competing antiferromagnetic and superconducting ground states. We focus on the two-dimensional case that is relevant for high Tc superconductors and heavy fermion systems. We consider two different types of couplings between the order parameters and obtain the modifications in the phase diagrams due to critical quantum fluctuations in these systems with conflicting orders. We consider z=1, as well as a dissipative z=2 dynamics, typical of antiferromagnetic metals close to the magnetic quantum critical point. Our results show that these depend strongly on both dimensionality and dynamics of the propagators describing the excitations of the possible ordered states. We find stable unconventional coexisting phases, as well as the enhancement of the region of coexistence by fluctuations.

Leggett mode in a two-component Fermi gas with dipolar interactions

We develop an effective field theory to understand collective modes of a three-dimensional two-component Fermi superfluid with dipolar inter-particle interactions, which are modeled by an idealized separable potential. We first examine the phase transition of the system at zero temperature, as the fermionic superfluidity is known to be characterized by two competing order parameters. We find that for strong interactions there exists a regime where the two order parameters are out-of-phase and coupled, giving rise to an undamped massive Leggett mode. This is in addition to the well-known gapless phonon mode. We show that the Leggett mode can be seen in the spectral function of the in-medium Cooper pairs, and in principle could be measured through Bragg spectroscopy.

Weak-coupling superconductivity in an anisotropic three-dimensional repulsive Hubbard model

We study a three-dimensional single-band repulsive Hubbard model at weak coupling. We establish the superconducting phase diagram in the parameter space of the chemical potential and the out-of-plane hopping strength. The model continuously connects the Hubbard model in two and three dimensions. We confirm previously-established results in these limits, and identify a rich structure of competing order parameters in between. Specifically, we find five types of $p$- and $d$-wave orders. In several regions of the phase diagram, even when the Fermi surface is a corrugated cylinder, the ground state is a time-reversal-symmetry-breaking superconductor with nodes, i.e. a Weyl superconductor.

Friedel oscillations and Majorana zero modes in inhomogeneous superconductors

We study the modulations of the superconducting order parameter in the vicinity of edges, magnetic and non-magnetic impurities by self-consistently solving the gap equations of a system with competing interactions in the Cooper channel. It is shown that the presence or absence of Friedel-like oscillations of the superconducting order parameter crucially depends on its symmetry and can, hence, be used to obtain information about the symmetry properties of the condensate. Furthermore, the appearance of competing order parameters at inhomogeneities is discussed. We show that this can lead to the presence of a topologically trivial region close to the boundary of a system that is topologically nontrivial in its bulk. The resulting shift in position of the Majorana bound states is demonstrated to significantly affect its signatures in Josephson-junction experiments. We discuss Josephson scanning tunneling microscopy as a probe to resolve the Friedel-like oscillations as well as the spatial texture of competing s-wave superconductivity and Majorana bound states in the vicinity of the edge of the system.

Itinerant quantum multicriticality of two-dimensional Dirac fermions

We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $\epsilon=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an \emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the \emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.

Quantum corrections for the phase diagram of systems with competing order

We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios: regions of the phase diagram where there is a bicritical point, at which both phases vanish continuously, and the case where both phases coexist homogeneously. We consider different types of couplings between the order parameters, including a bilinear one. This kind of coupling breaks time-reversal symmetry and it is only allowed if both order parameters transform according to the same irreducible representation. This occurs in many physical systems of actual interest like competing spin density waves, different types of orbital antiferromagnetism, elastic instabilities of crystal lattices, vortices in a multigap SC and also applies to describe the unusual magnetism of the heavy fermion compound URu2Si2. Our results show that quantum corrections have an important effect on the phase diagram of systems with competing orders.

Giant magnetostriction effect near onset of spin reorientation in MnBi

In materials undergoing spontaneous symmetry breaking transitions, the emergence of multiple competing order parameters is pervasive. Employing in-field x-ray diffraction, we investigate the temperature and magnetic field dependence of the crystallographic structure of MnBi, elucidating the microscopic interplay between lattices and spin. The hexagonal phase of MnBi undergoes a spin reorientation transition (TSR), whereby the easy axis direction changes from the c axis to the basal plane. Across TSR, an abrupt symmetry change is accompanied by a clear sign change in the magnetostrictive coefficient, revealing that this transition corresponds to the onset of the spin reorientation. In the vicinity of TSR, a significantly larger in-plane magnetostrictive effect is observed, presenting the emergence of an intermediate phase that is highly susceptible to an applied magnetic field. X-ray linear dichroism shows that asymmetric Bi and Mn p orbitals do not play a role in the spin reorientation. This work suggests that the spin reorientation is caused by structural modification rather than changes in the local electronic configuration, providing a strategy for manipulating the magnetic anisotropy by external strain.