Frustrated Lattices Research Articles

Flat Band Generation Through Interlayer Geometric Frustration in Intercalated Transition Metal Dichalcogenides.

Electronic flat bands can lead to rich many-body quantum phases by quenching the electron's kinetic energy and enhancing many-body correlation. The reduced bandwidth can be realized by either destructive quantum interference in frustrated lattices, or by generating heavy band folding with avoided band crossing in Moiré superlattices. Here a general approach is proposed to introduce flat bands into widely studied transition metal dichalcogenide (TMD) materials by dilute intercalation. A flat band with vanishing dispersion is observed by angle-resolved photoemission spectroscopy (ARPES) over the entire momentum space in intercalated Mn1/4TaS2. Polarization-dependent ARPES measurements combined with symmetry analysis reveal the orbital characters of the flat band. Supercell tight-binding simulations suggest that such flat bands arising from destructive interference between Mn and Ta on S through hopping pathways, are ubiquitous in a range of TMD families as well as for different intercalation configurations. The findings establish a new material platform to manipulate flat band structures and explore their corresponding emergent correlated properties.

Correlated physics, charge and magnetic orders in moiré kagomé systems

Abstract Moiré systems have emerged as an ideal platform for exploring the interaction effects and correlated states. However, most of the experimental systems were based on either the triangular or honeycomb lattice. In this study, based on the self-consistent Hartree-Fock calculation, we investigate the phase diagram of the Kagomé lattice in a recently discovered system with two degenerate Γ valley orbitals and strong spin-orbit coupling. By focusing on the filling factors of 1/2, 1/3 and 2/3, we identified various symmetry-breaking states by adjusting the screening length and dielectric constant. At the half filling, we discovered that the spin-orbit coupling induced Dzyaloshinskii-Moriya interaction stabilized a classical magnetic sate with 120° ordering. Additionally, we observed a transition to a ferromagnetic state with out-of-plane ordering. In the case of 1/3 filling, the system is ferromagnetically ordered due to the lattice frustration. Furthermore, for 2/3 filling, the system exhibits a pinned droplet state and a 120° magnetic ordered state at weak and immediate coupling strengths, respectively. For strong coupling case, when dealing with non-integer filling, the system is always charged ordered with sublattice polarization. Our study serves as a starting point for exploring the effects of correlation in moiré Kagomé system.

Observation of Enhanced Long-Range Ferromagnetic Order in B-Site Ordered Double Perovskite Oxide Cd2CrSbO6.

A B-site ordered double perovskite oxide Cd2CrSbO6 was synthesized under high-pressure and high-temperature conditions. The compound crystallizes to a monoclinic structure with a space group of P21/n. The charge configuration is confirmed to be that of Cd2+/Cr3+/Sb5+. The magnetic Cr3+ ions form a tetrahedral structural frustrated lattice, while a long-range ferromagnetic phase transition is found to occur at TC = 16.5 K arising from the superexchange interaction via the Cr-O-Cd-O-Cr pathway. Electrical transport measurements indicate that Cd2CrSbO6 is an insulator that can be described by the Mott 3D variable range hopping mechanism. First-principles calculations reproduce well the ferromagnetic and insulating ground state of Cd2CrSbO6 with an energy band gap of 1.55 eV. The intrinsic ferromagnetic insulating nature qualifies Cd2CrSbO6 as a promising candidate for possible spintronics applications.

Superconducting diode effect and interference patterns in kagome CsV3Sb5.

The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.

Directly imaging spin polarons in a kinetically frustrated Hubbard system.

The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions1-8. However, in kinetically frustrated lattices, itinerant spin polarons-bound states of a dopant and a spin flip-have been theoretically predicted even in the absence of superexchange coupling9-14. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect15,16. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems10,11. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials17-20.

3D self-organization of spin crossover multi-layers emerging from the alliance of elastic anisotropy and lattice frustration

The present work is devoted to the study of the non-equilibrium properties of 3D switchable spin-crossover (SCO) multi-layers by accounting for lattice frustration effects and elastic anisotropy. The investigations are performed using an extended version of the original electro-elastic model which includes the lattice volume change at the spin transition between the low-spin (LS) and the high-spin (HS) states. The numerical simulations were made using Monte Carlo (MC) Metropolis technique for the spin state subsystem, combined with a semi-analytical method of mechanical relaxation of the lattice positions, which revealed to be very efficient in terms of computational time. To enhance the quality of the results, the scattered lattice positions were interpolated using the radial basis functions method. The 3D character of the simulations allows the molecules to leave the plane of the 2D layers, thus leading to corrugations and buckling which considerably relax the elastic strain. Various configurations of elastic interactions are then studied, among which, those accounting for anisotropic elastic constants and others including an intrinsic elastic frustration in the LS state. As a result, multi-stepped low-temperature relaxation processes are reproduced for the temporal evolution of the metastable HS fraction, displaying the emergence of complex self-organizations of the spin states and structure in the plateaus regions. In addition to the usual checkerboard antiferro-like HS–LS patterns, spontaneous spatial self-organization into alternated HS and LS layers are also obtained, recalling experimental data of Fe-picolylamine and other compounds of literature, which remained an open theoretical problem to date.

Quantum simulation and Anderson localization in vector rogue waves of Bose-Einstein condensate

We report the existence of vector rogue waves in a coupled Bose-Einstein condensate, trapped in a bichromatic optical lattice, which is an appropriate platform for quantum simulation. Such two-component Bose-Einstein condensate plays a vital role to beget hybrid mixtures and structural transition of nonlinear excitations like rogue waves and solitons. An efficient manipulation of rogue waves is embraced, where we identify the slowing down and stopping of dark rogue wave by lattice engineering. This may nurture quantum memory application and transform the rogue wave mixture immiscible. The existence of Anderson localized rogue wave at the central frustrated lattice site is confirmed by showing the exponential nature and localization length of the condensate. A merging of a dual Anderson rogue waves is manifested in their coherent control. Numerical stability analysis is also carried out for a wide range of trap parameters for experimental viability.

Electronic Flat Band in Distorted Colouring Triangle Lattice.

Dispersionless flat bands (FBs) in momentum space, given rise to electron destructive interference in frustrated lattices, offer opportunities to enhance electronic correlations and host exotic many-body phenomena, such as Wigner crystal, fractional quantum hall state, and superconductivity. Despite successes in theory, great challenges remain in experimentally realizing FBs in frustrated lattices due to thermodynamically structural instability. Here, the observation of electronic FB in a potassium distorted colouring triangle (DCT) lattice is reported, which is supported on a blue phosphorene-gold network. It is verified that the interaction between potassium and the underlayer dominates and stabilizes the frustrated structures. Two-dimensional electron gas is modulated by the DCT lattice, and in turn results in a FB dispersion due to destructive quantum interferences. The FB exhibits suppressed bandwidth with high density of states, which is directly observed by scanning tunneling microscopy and confirmed by the first-principles calculation. This work demonstrates that DCT lattice is a promising platform to study FB physics and explore exotic phenomena of correlation and topological matters.

Exploring the phase diagram of 3D artificial spin-ice

Artificial spin-ices consist of lithographic arrays of single-domain magnetic nanowires organised into frustrated lattices. These geometries are usually two-dimensional, allowing a direct exploration of physics associated with frustration, topology and emergence. Recently, three-dimensional geometries have been realised, in which transport of emergent monopoles can be directly visualised upon the surface. Here we carry out an exploration of the three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed within a diamond-bond lattice geometry. We find a rich phase diagram, consisting of a double-charged monopole crystal, a single-charged monopole crystal and conventional spin-ice with pinch points associated with a Coulomb phase. In experimental demagnetised systems, broken symmetry forces formation of ferromagnetic stripes upon the surface, forbidding the lower energy double-charged monopole crystal. Instead, we observe crystallites of single magnetic charge, superimposed upon an ice background. The crystallites are found to form due to the distribution of magnetic charge around the 3D vertex, which locally favours monopole formation.

Twisted chiral superconductivity in photodoped frustrated Mott insulators

Recent advances in ultrafast pump-probe spectroscopy provide access to hidden phases of correlated matter, including light-induced superconducting states, but the theoretical understanding of these nonequilibrium phases remains limited. Here we report how a new type of chiral superconducting phase can be stabilized in photodoped frustrated Mott insulators. The metastable phase features a spatially varying order parameter with a $120^\circ$ phase twist which breaks both time-reversal and inversion symmetry. Under an external electric pulse, the $120^\circ$ chiral superconducting state can exhibit a second-order supercurrent perpendicular to the field in addition to a first-order parallel response, similar to a nonlinear anomalous Hall effect. This phase can be tuned by artificial gauge fields when the system is dressed by high-frequency periodic driving. The mechanism revealed in this study applies to Mott insulators on various frustrated lattices and the hidden superconducting phase can be realized in both cold-atom quantum simulators and correlated solids.

Spectrum, Lifshitz transitions and orbital current in frustrated fermionic ladders with a uniform flux

Ultracold Fermi gases with synthetic gauge field represent an excellent platform to study the combined effect of lattice frustration and an effective magnetic flux close to one flux quantum per particle. The minimal theoretical model to accomplish this task is a system of spinless noninteracting fermions on a triangular two-chain flux ladder. In this paper we consider this model close to half-filling, with interchain hopping amplitudes alternating along the zigzag bonds of the ladder and being small. In such setting qualitative changes in the ground state properties of the model, most notably the flux-induced topological Lifshitz transitions are shifted towards the values of the flux per a diatomic plaquette ($f$) close to the flux quantum ($f\sim 1/2$). Geometrical frustration of the lattice breaks the $k \to \pi - k$ particle-hole spectral symmetry present in non-frustrated ladders, and leads to splitting of the degeneracies at metal-insulator transitions. A remarkable feature of a translationally invariant triangular ladder is the appearance of isolated Dirac node at the Brillouin zone boundary, rendering the ground state at $f=1/2$ semi-metallic. We calculate the flux dependence of the orbital current and identify Lifshitz critical points by the singularities in this dependence at a constant chemical potential $\mu$ and constant particle density $\rho$. The absence of the particle-hole symmetry in the triangular ladder leads to the asymmetry between particle ($\rho>1$) and hole ($\rho<1$) doping and to qualitatively different results for the phase diagram, Lifshitz points and the flux dependence of the orbital current in the settings $\rho={\rm const}$ and $\mu={\rm const}$.

Spontaneous resolution of two chiral metal–organic frameworks through local geometric and lattice frustration effects

Two chiral metal–organic frameworks that are differentiated by their Cd-centred helical twists are prepared by spontaneous chiral resolution from rigid, aliphatic, and achiral precursors.

LANDAU SUB-BAND FIELDS IN CH3NH3PBI3 CRYSTALS WITHIN WIGNER–SEITZ PRIMITIVE CELL

The titling of orientations is believed to influence electrostatic and steric interactions on sub-band touching levels, positions and density of states in a CH3NH3PbI3 perovskite crystal. Sub-band touching exhibit recursive properties that sometimes result in forming new material properties like an adjusted band gap, a modified sub band energy level, a modified ground level excitation state, a modified density of state or a lattice frustration when exposed to an external magnetic field in the Bravais lattice. A geometrical structural model with a tight-bound sub band structure was developed in this study. It was analyzed with an aim of describing how its tight-bound electrons are influenced by a rational magnetic field to distort tilting and rotation in CH3NH3PbI3 lattice. The model had a rotating and tilting orientation angle, (ψ) with a precision angle, Φ. It was analyzed. The findings showed that, out of all the sum of angles in all the orientations, it is only the precession angle that was to influence electrostatic and steric interactions and only two angles were found to influence the lead–iodine-bond lengths, density of states modify sub bands level tilting. The finding also showed that a magnetic field has a significant influence on sub band touching of immediate neighbouring sub bands since it since a frustration in the lattice was exhibited as a recursive property. It was then concluded that a sum of density of states below an energy gap in a CH3NH3PbI3 lattice under an irrational magnetic field had a significant influence on sub band touching the magnitudes and thus influencing its density of states.

Chemical Pressure Tuning Magnetism from Pyrochlore to Triangular Lattices.

Geometrically frustrated lattices combined with magnetism usually host quantum fluctuations that suppress magnetic orders and generate highly entangled ground states. Three-dimensionally (3D) frustrated magnets generally exist in the diamond and pyrochlore lattices, while two-dimensionally (2D) frustrated geometries contain Kagomé, triangular, and honeycomb lattices. In this work, we reported using chemical pressure to tune the magnetism of the pyrochlore lattice in LiYbSe2 into a triangular lattice by doping Ga or In. Li3-xGaxYb3Se6 and Li3-xInxYb3-yInySe6/Li3-xInxYb3-y□ySe6 crystallize in a trigonal α-NaFeO2 structure-type (space group R3̅m) and can be synthesized using either LiCl or Se flux. In Li3-xGaxYb3Se6, Ga3+ and Li+ are mixed, leaving Yb3+ on the triangular plane. Instead of just Li+ being replaced in Li3-xGaxYb3Se6, In3+ was observed in both the Li+ and Yb3+ layers in Li3-xInxYb3-yInySe6 depending on the reaction conditions. Dominant antiferromagnetic interactions are revealed by magnetic measurements in both Li3-xGaxYb3Se6 and Li3-xInxYb3-yInySe6/Li3-xInxYb3-y□ySe6. However, no long-range magnetic order is detected in thermomagnetic measurements above 1.8 K due to geometrical frustration. Thus, Li3-xGaxYb3Se6, Li3-xInxYb3-yInySe6/Li3-xInxYb3-y□ySe6, and the LiYbSe2 previously discovered by our group provide an ideal platform to understand the complex structure-magnetism correlations from 3D to 2D frustrated lattices.

Route toward classical frustration and band flattening via optical lattice distortion

We propose and experimentally explore a method for realizing frustrated lattice models using a Bose-Einstein condensate held in an optical square lattice. A small lattice distortion opens up an energy gap such the lowest band splits into two. Along the edge of the first Brillouin zone for both bands a nearly flat energy-momentum dispersion is realized. For the excited band a highly degenerate energy minimum arises. By loading ultracold atoms into the excited band, a classically frustrated $XY$ model is formed, describing rotors on a square lattice with competing nearest and next nearest tunnelling couplings. Our experimental optical lattice provides a regime, where a fully coherent Bose-Einstein condensate is observed, and a regime where frustration is expected. If we adiabatically tune from the condensate regime to the regime of frustration, the momentum spectra shows a complete loss of coherence. Upon slowly tuning back to the condensate regime, coherence is largely restored. Good agreement with model calculations is obtained.

Signatures of spin-liquid state in a 3D frustrated lattice compound KSrFe2(PO4)3 with S = 5/2

A quantum spin-liquid is a spin disordered state of matter in which spins are strongly correlated and highly entangled with low-energy excitations. It has been often found in two-dimensional S = ½, highly frustrated spin networks but rarely observed in three-dimensional (3D) frustrated quantum magnets. Here, KSrFe2(PO4)3, forming a complicated 3D frustrated lattice with a spin moment S = 5/2, is investigated by thermodynamic, neutron diffraction measurements and electronic structure calculations. Despite the relatively sizable Curie–Weiss temperature θCW = −70 K, a conventional magnetic long-range order is confirmed to be absent down to 0.19 K. The magnetic heat capacity data follow the power-law behavior at the lowest temperature region, supporting gapless excitations in a 3D spin-liquid state. Strong geometrical spin frustration responsible for the spin-liquid feature is understood as originating from the almost comparable five competing nearest-neighbor antiferromagnetic exchange interactions, which form the complicated 3D frustrated spin network. All these results suggest that the compound KSrFe2(PO4)3, representing a unique 3D spin frustrated network, could be a rare example of forming a gapless spin-liquid state even with a large spin moment of S = 5/2.

Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality

Chiral three-spin interactions can suppress long-range magnetic order and stabilize quantum spin liquid states in frustrated lattices. We study a spin-1/2 model on the kagome lattice involving a staggered three-spin interaction J_\chiJχ in addition to Heisenberg exchange couplings J_1J1 on nearest-neighbor bonds and J_dJd across the diagonals of the hexagons. We explore the phase diagram using a combination of a classical approach, parton mean-field theory, and variational Monte Carlo methods. We obtain a variety of noncoplanar magnetic orders, including a phase that interpolates between cuboc-1 and cuboc-2 states. In the regime of dominant J_{\chi}Jχ, we find a classically disordered region and argue that it may harbor a gapless chiral spin liquid with a spinon Fermi surface. Our results show that the competition between the staggered three-spin interaction and Heisenberg exchange interactions gives rise to unusual ground states of spin systems.

Microscopic origin of magnetism in monolayer 3d transition metal dihalides

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $M{X}_{2}$ ($M$=V, Mn, Ni and $X$=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered $3d$ transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

Quantum simulation of rogue waves in Bose-Einstein condensate: An exact analytical method

A quantum simulator environment is considered in Bose-Einstein condensate under bichromatic optical lattice, manifesting rogue waves. We report an exact analytical model to produce rogue wave excitations, the dynamics of which is investigated by solving the corresponding scalar Gross-Pitaevskii equation. A qualitative understanding of the formation mechanism at various trap parameters is provided by assuming the rogue wave excitation as a mixture of bright and dark solitary waves, which offers a novel illustration of the previous conjecture for rogue waves in Bose-Einstein condensate. We identify the lattice parameters for controlling the spatio-temporal variations of the condensate density. An Anderson-like localization is identified where the condensate is seen to preserve the rogue wave nature at the central frustrated site for larger lattice frustration.

Quantum phase of the chromium spinel oxide HgCr2O4 in high magnetic fields

In this study, we have performed the magnetocaloric effect and the specific heat measurements of chromium spinel oxide $\mathrm{Hg}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$, wherein the magnetic ${\mathrm{Cr}}^{3+}$ ions form a highly frustrated pyrochlore lattice with significant spin-lattice coupling. In addition to the known magnetic-field-induced phases, our thermodynamic measurements detect a quantum phase just before the saturation of the magnetization, which has not been expected from the classical theories of the pyrochlore lattice antiferromagnet with spin-lattice coupling. Based on recent theoretical model calculation, we discuss the possibility of a spin nematic state appearing for this quantum phase.