Sublattice Polarization Research Articles

Visible-Photo-Assisted Phase Switching of Antiferroelectric-to-Ferroelectric Orders in an I3 --Intercalated 2D Perovskite.

Antiferroelectric (AFE) has emerged as a promising branch of electroactive materials, due to intriguing physical attributes stemming from the electric field-induced antipolar-to-polar phase transformation. However, the requirement of extremely high electric field strength to switch adjacent sublattice polarization poses great challenges for exploiting new molecular AFE system. Although photoirradiation is striking as a noncontact and nondestructive manipulation tool to optimize physical properties, optical control of antiferroelectricity still remains unexplored. Here, by adopting light-sensitive I3 - anion into 2D perovskite family, we design a new I3 --intercalated molecular AFE of (t-ACH)2EA2Pb3I10(I3)0.5 ⋅ ((H3O)(H2O))0.5 (1, t-ACH=trans-4-aminomethyl-1-cyclohexanecarboxylate, EA=ethylammonium). The I3 --intercalating gives an ultra-narrow band gap of 1.65 eV with strong absorption. In term of AFE structure, the anti-parallel alignment of electric dipoles results in a large spontaneous polarization of 4.3 μC/cm2. Strikingly, 1 merely shows AFE behaviour in the dark even under ultrahigh voltage, while the field-induced ferroelectric state can be facilely obtained upon visible illumination. Such unprecedented visible-photo-assisted phase switching ascribes to the incorporation of photoactive I3 - anions that reduces AFE-to-ferroelectric switching barrier. This pioneering work on the photo-assisting transformation of ferroic orders paves a way to develop future photoactive materials with potential applications.

Visible‐Photo‐Assisted Phase Switching of Antiferroelectric‐to‐Ferroelectric Orders in an I3−‐Intercalated 2D Perovskite

AbstractAntiferroelectric (AFE) has emerged as a promising branch of electroactive materials, due to intriguing physical attributes stemming from the electric field‐induced antipolar‐to‐polar phase transformation. However, the requirement of extremely high electric field strength to switch adjacent sublattice polarization poses great challenges for exploiting new molecular AFE system. Although photoirradiation is striking as a noncontact and nondestructive manipulation tool to optimize physical properties, optical control of antiferroelectricity still remains unexplored. Here, by adopting light‐sensitive I3− anion into 2D perovskite family, we design a new I3−‐intercalated molecular AFE of (t‐ACH)2EA2Pb3I10(I3)0.5 ⋅ ((H3O)(H2O))0.5 (1, t‐ACH=trans‐4‐aminomethyl‐1‐cyclohexanecarboxylate, EA=ethylammonium). The I3−‐intercalating gives an ultra‐narrow band gap of 1.65 eV with strong absorption. In term of AFE structure, the anti‐parallel alignment of electric dipoles results in a large spontaneous polarization of 4.3 μC/cm2. Strikingly, 1 merely shows AFE behaviour in the dark even under ultrahigh voltage, while the field‐induced ferroelectric state can be facilely obtained upon visible illumination. Such unprecedented visible‐photo‐assisted phase switching ascribes to the incorporation of photoactive I3− anions that reduces AFE‐to‐ferroelectric switching barrier. This pioneering work on the photo‐assisting transformation of ferroic orders paves a way to develop future photoactive materials with potential applications.

Phonon Landau Quantization and Enhanced Lifetime in Deformed Graphene.

The pseudomagnetic field effect may offer unique opportunities for the emergence of intriguing phenomena. To date, investigations into pseudomagnetic field effects on phonons have been limited to sound waves in metamaterials. The revelation of this exotic effect on the atomic vibration of natural materials remains elusive. Our simulations of twisted graphene nanoribbons reveal well-defined Landau spectra and sublattice polarization of phonon states, mimicking the behavior of Dirac Fermions in magnetic fields. Both valley-specified helical edge currents and snake orbits are obtained. Analysis of dynamics indicates that phonon Landau states have extended lifetimes, which are crucial for the realization of Landau-level lasing. Our findings demonstrate the occurrence of the phonon pseudomagnetic field effect in natural materials, which has important implications for the mechanical tuning of phonon quantum states at the atomic scale.

Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θGr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.

Strong second-harmonic generation by sublattice polarization in non-uniformly strained monolayer graphene

Despite the potential of graphene for building a variety of quantum photonic devices, its centrosymmetric nature forbids the observation of second harmonic generation (SHG) for developing second-order nonlinear devices. To activate SHG in graphene, extensive research efforts have been directed towards disrupting graphene’s inversion symmetry using external stimuli like electric fields. However, these methods fail to engineer graphene’s lattice symmetry, which is the root cause of the forbidden SHG. Here, we harness strain engineering to directly manipulate graphene’s lattice arrangement and induce sublattice polarization to activate SHG. Surprisingly, the SHG signal is boosted 50-fold at low temperatures, which can be explained by resonant transitions between strain-induced pseudo-Landau levels. The second-order susceptibility of strained graphene is found to be larger than that of hexagonal boron nitride with intrinsic broken inversion symmetry. Our demonstration of strong SHG in strained graphene offers promising possibilities for developing high-efficiency nonlinear devices for integrated quantum circuits.

Spectroscopic signature of sublattice polarization in the lattice dynamics of an antiferroelectric crystal

Antiferroelectric systems are identified by an internal sublattice polarization that is typically hidden from experimental probes. An analysis of the far-infrared polar lattice dynamics in the model antiferroelectric francisite reveals a spectroscopic signature that scales with the sublattice polarization.

Manipulation of electromagnetic waves induced by pseudomagnetic fields in two dimensional photonic crystals

Many interesting phenomena, such as quantization of Landau levels and quantum Hall effect, can occur in an electronic system under a strong magnetic field. However, photons do not carry charge, and they do not have many properties induced by external magnetic fields, either. Recently, the pseudomagnetic field, an artificial synthetic gauge field, has attracted intense research interest in classical wave systems, in which the propagation of the wave can be manipulated like in a real magnetic field. The photonic crystal is an optical structure composed of periodic material distributions and provides a good platform for studying the control of electromagnetic waves. In this work, we construct a uniform pseudomagnetic field by introducing uniaxial linear gradient deformation of metallic rods in a two-dimensional photonic crystal. The strong pseudomagnetic field leads to the quantization of photonic Landau levels in photonic crystal. The sublattice polarization of <i>n</i> = 0 Landau level is also demonstrated in our simulations. Unlike the real magnetic field, the pseudomagnetic fields of photonic crystal is opposite in two inequivalent energy valleys, and the time-reversal symmetry of the system is not broken. Our designed gradient photonic crystals support the transport of edge state in the gap between <i>n</i> = 0 and <i>n</i> = ±1 Landau levels. The edge state can propagate unidirectionally when it is excited by a chiral source. When a gaussian beam impinges on the photonic crystal, the propagating paths of two splitting beams can be controlled, which gives rise to the bend of two beams. Two photonic crystals with opposite pseudomagnetic fields are assembled together, and the interesting phenomenon of “snake-state” can be obtained. Our proposal opens the way for designing information processing devices by manipulating electromagnetic waves.

Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene.

We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i)applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii)changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid ^{3}He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. We comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.

Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy.

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. By analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $\nu$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $\nu=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices.

Imaging tunable quantum Hall broken-symmetry orders in graphene.

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy1-5. The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders6-11. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy12 or by dielectric screening of the Coulomb interaction13. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders14. Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition15,16. Under dielectric screening, a sublattice-unpolarized ground state13 emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions6-10. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Inducing a topological transition in graphene nanoribbon superlattices by external strain.

Armchair graphene nanoribbons, when forming a superlattice, can be classified into different topological phases, with or without edge states. By means of tight-binding and classical molecular dynamics (MD) simulations, we studied the electronic and mechanical properties of some of these superlattices. MD shows that fracture in modulated superlattices is brittle, as for unmodulated ribbons, and occurs at the thinner regions, with staggered superlattices achieving a larger fracture strain than inline superlattices. We found a general mechanism to induce a topological transition with strain, related to the electronic properties of each segment of the superlattice, and by studying the sublattice polarization we were able to characterize the transition and the response of these states to the strain. For the cases studied in detail here, the topological transition occurred at ∼3-5% strain, well below the fracture strain. The topological states of the superlattice - if present - are robust to strain even close to fracture. The topological transition was characterized by means of the sublattice polarization of the states.

Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands.

Graphene moiré superlattices are outstanding platforms to study correlated electron physics and superconductivity with exceptional tunability. However, robust superconductivity has been measured only in magic-angle twisted bilayer graphene (MA-TBG) and magic-angle twisted trilayer graphene (MA-TTG). The absence of a superconducting phase in certain moiré flat bands raises a question on the superconducting mechanism. In this work, we investigate electronic structure and electron-phonon coupling in graphene moiré superlattices based on atomistic calculations. We show that electron-phonon coupling strength λ is dramatically different among graphene moiré flat bands. The total strength λ is very large (λ>1) for MA-TBG and MA-TTG, both of which display robust superconductivity in experiments. However, λ is an order of magnitude smaller in twisted double bilayer graphene (TDBG) and twisted monolayer-bilayer graphene (TMBG) where superconductivity is reportedly rather weak or absent. We find that the Bernal-stacked layers in TDBG and TMBG induce sublattice polarization in the flat-band states, suppressing intersublattice electron-phonon matrix elements. We also obtain the nonadiabatic superconducting transition temperature T_{c} that matches well with the experimental results. Our results clearly show a correlation between strong electron-phonon coupling and experimental observations of robust superconductivity.

Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene.

We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moiré bands of magic angle twisted bilayer graphene. For moiré band filling 3>|ν|>2, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near |ν|=3, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of magic angle twisted bilayer graphene flat band correlations.

Magnetic generation of normal pseudo-spin polarization in disordered graphene

Spin to pseudo-spin conversion by which the non-equilibrium normal sublattice pseudo-spin polarization could be achieved by magnetic field has been proposed in graphene. Calculations have been performed within the Kubo approach for both pure and disordered graphene including vertex corrections of impurities. Results indicate that the normal magnetic field B_z produces pseudo-spin polarization in graphene regardless of whether the contribution of vertex corrections has been taken into account or not. This is because of non-vanishing correlation between the sigma _z and tau _z provided by the co-existence of extrinsic Rashba and intrinsic spin–orbit interactions which combines normal spin and pseudo-spin. For the case of pure graphene, valley-symmetric spin to pseudo-spin response function is obtained. Meanwhile, by taking into account the vertex corrections of impurities the obtained response function is weakened by several orders of magnitude with non-identical contributions of different valleys. This valley-asymmetry originates from the inversion symmetry breaking generated by the scattering matrix. Finally, spin to pseudo-spin conversion in graphene could be realized as a practical technique for both generation and manipulation of normal sublattice pseudo-spin polarization by an accessible magnetic field in a easy way. This novel proposed effect not only offers the opportunity to selective manipulation of carrier densities on different sublattice but also could be employed in data transfer technology. The normal pseudo-spin polarization which manifests it self as electron population imbalance of different sublattices can be detected by optical spectroscopy measurements.

Multiferroic properties of the antiferroelectric-antiferromagnetic Cu9O2(SeO3)4Cl6

The recently experimentally observed multiferroic properties of the antiferroelectric-antiferromagnetic - Cu9O2(SeO3)4Cl6 are studied using a microscopic model and a Green's function technique. The sublattice polarization increases with decreasing temperature and increasing magnetic field h. For the total polarization which is zero without electric field E is observed a double hysteresis loop. The dielectric constant shows two anomalies at the two transition temperatures TN and TE. The magnetodielectric ratio increases with increasing magnetic field below TN. It is shown that a large magnetoelectric coupling g (E=0) or a strong external electric field E (g=const) induces a weak ferromagnetism in this compound. In analogy g (h=0) or an external magnetic field h (g=const) can lead to a weak ferroelectricity.

Polarization rotation by external electric field in the two-dimensional antiferroelectric squaric acid H2C4O4

A pseudospin model for description of the influence of the electric field, confined to the plane of sublattice polarization, on the two-dimensional squaric acid antiferroelectrics is developed. The system behavior is analyzed in terms of the parameters of ferroelectric and antiferroelectric ordering, as well as the non-collinearity angle $\theta$, which is the angle between sublattice polarizations. The temperature-electric field $T-E_1$ phase diagram is constructed. Most of the field-induced transitions are found to be associated with polarization rotation. The observed phases include the collinear ferroelectric and non-collinear ferrielectric with almost antiparallel and perpendicular polarizations of the sublattices, respectively. The diagram also contains two regions, where the non-collinearity angle varies continuously between, nominally, 0 and 90$^\circ$ and between 90$^\circ$ and 180$^\circ$. The first and second order transition lines, supercritical lines, critical end points, and critical points on the $T-E_1$ phase diagram are detected.

Influence of external field direction on polarization rotation in antiferroelectric squaric acid H2C4O4

Using the previously developed model we explore the processes of polarization rotation in antiferroelectric crystals of squaric acid by the electric fields directed arbitrarily within the ac plane. Except for some particular directions of the field, the two-step polarization reorientation at low temperatures is predicted: first, to the noncollinear phase with perpendicular sublattice polarizations and then to the collinear ferroelectric phase. However, when the field is directed along the axis of spontaneous sublattice polarizations, the intermediate noncollinear phase is absent; when the field is at 45° to this axis, the field for transition to the ferroelectric phase tends to infinity. The ground state proton configurations and the directions of the sublattice polarization vectors are determined for all field orientations. The T-E phase diagrams are constructed for the fields directed along the diagonals of the ac plane and for the above discussed particular directions of the field.

Valley polarization caused by crystalline symmetry breaking.

In two-dimensional (2D) hexagonal lattices with inversion asymmetry, time-reversal (T) connected valleys are at the center of current valleytronic research. In order to trigger valley polarization, dynamical processes and/or magnetism have been considered. In this work, we propose a new mechanism, valley-contrasting sublattice polarization (VCSP), to polarize valleys by reducing the crystalline symmetry that connects the valleys. In our mechanism, significant valley polarization could be readily generated without magnetism, an electric field, or an optical process. Based on tight-binding model analysis and first-principle calculations, the control of valley polarization via crystalline symmetry can be successfully realized in concrete LaOBiS2 polytypes with Peierls-like structure distortion. Our results provide an unprecedented possibility for exploring valley-contrasting physics.

Strain-induced topological phase transition with inversion of the in-plane electric polarization in tiny-gap semiconductor SiGe monolayer

Our density functional theory calculations show that tiny-gap semiconductor SiGe monolayer is a quantum valley Hall insulator with a spontaneous electric polarization and, under a small biaxial strain, undergoes a topological phase transition between the states with opposite valley Chern numbers. The topological phase transition entails abrupt inversion of the in-plane electric polarization corresponding to inversion of the sublattice pseudospin polarization, while the out-of-plane electric polarization shows a linear response to the biaxial strain as well as to the perpendicular electric field regardless of the phase transition. Thus, the quantum valley Hall state entails in-plane ferroelectricity corresponding to a sublattice pseudospin ferromagnetism.