Orbital Lattice Research Articles

Enhancement of Selective Catalytic Oxidation of Lignin β‐O‐4 Bond via Orbital Modulation and Surface Lattice Reconstruction

The orbital modulation and surface lattice reconstruction represent an effective strategy to regulate the interaction between catalyst interface sites and intermediates, thereby enhancing catalytic activity and selectivity. In this study, the crystal surface of Au‐K/CeO2 catalyst can undergo reversible transformation by tuning the coordination environment of Ce, which enables the activation of the Cβ‐H bond and the oxidative cleavage of the Cβ‐O and Cα‐Cβ bonds, leading to the cleavage of 2‐phenoxy‐1‐phenylethanol. The t2g orbitals of Au 5d hybridize with the 2p orbitals of lattice oxygen in CeO2 via π‐coordination, modulating the coordination environment of Ce 4f and reconstructing the lattice oxygen in the CeO2 framework, as well as increasing the oxygen vacancies. The interface sites formed by the synergy between Au clusters in the reconstructed Ce‐OL1‐Au structure and doped K play dual roles. On the one hand, it activates the Cβ‐H bond, facilitating the enolization of the pre‐oxidized 2‐phenoxy‐1‐phenylethanone. On the other hand, through single‐electron transfer involving Ce3+ 4f1 and the adsorption by oxygen vacancies, it enhances the oxidative cleavage of the Cβ‐O and Cα‐Cβ bonds. This study elucidates the complex mechanistic roles of the structure and properties of Au‐K/CeO2 catalyst in the selective catalytic oxidation of lignin β‐O‐4 bond.

Coexistence of topological and bipolar magnetic semiconducting behavior in 2D metal-organic frameworks with a p-orbital coloring-triangle lattice

Coexistence of topological and bipolar magnetic semiconducting behavior in 2D metal-organic frameworks with a <i>p</i>-orbital coloring-triangle lattice

P/s-orbital hybridization induced by Mg-doping to active Na sites in Na2FePO4F cathode for long-life and high-rate sodium-ion batteries

The iron-based fluorophosphate Na2FePO4F (NFPF) is considered as a potential cathode for sodium-ion batteries due to the low-cost, non-toxicity and appropriate working voltage. However, the inferior intrinsic electronic conductivity and the restrained active Na sites bring the limits for full realization of electrochemical properties. Herein, Mg2+ with d0 orbital was introduced in FeO4F2 structure, aimed at activating the Na+ at Na1 site and enhancing the electronic conductivity. Different from the 3d transition metal (TM) elements that form 3d-O2p orbital interactions in the FeO4F2 structure, the Mg with d° contributes p and s orbitals mainly in Mg-O bonds, which corresponds to more stable orbital interaction and lattice structure. The electron distribution of bridge O due to the Mg-doping leads to the wooden barrel effect near the Mg site, thus activating Na+ at Na1 site by lowering the energy barrier of Na+ migration from Na1 to Na2 site. Hence, the obtained NFMPF electrode delivers high specific capacity (121.4 vs. 108.7 mAh g−1 at 0.1 C) and better cycling stability (73.8% vs. 54.2 % after 1000 cycles at 20 C). Overall, regulating the electronic structure and activating Na+ at inactive site is the key to break the bottleneck of low activity, which can be an effective strategy to design cathode materials with excellent electrochemical performance.

Nanoribbons of large-gap quantum spin Hall insulator: electronic structures and transport properties

Two-dimensional Bi grown on semiconductor substrate, a large-gap quantum spin Hall insulator characterized by a (p x , p y )-orbital hexagonal lattice, has been theoretically proposed and experimentally confirmed. Here, by combining tight-binding modeling with first-principles calculations, we investigate the electronic structures and quantum transport properties of Bi nanoribbons (NRs), focusing on the topological edge states for nanoelectronics. We reveal that band gap emerges due to the quantum confinement, and the gaps size depends crucially on the width and edge shape: for zigzag NRs, the gap decreases monotonically with the increase of width; while for armchair NRs, it can be categorized into three subgroups with band-gap hierarchies of Eg(3p−1)>Eg(3p)>Eg(3p+1) , so that the overall relation is an oscillating dependence dumped by 1/width decay. Quantum transport calculations demonstrate that the conductance is quantized to 2 e2/h , and an applied gate voltage can efficiently regulate the conductance plateau, originating from the interplay between gate voltage and topological gaps. Furthermore, the quantized conductance remains robust against strong disorder, suggesting the unique advantage of topological states for electronic transport. This work not only provides fundamental insights into the electronic properties of topological insulator nanostructures, but also sheds light on the potential applications of exotic states for quantum devices compatible with semiconductor technology.

Electronic structure and topological phase transition in multi-orbital triangular lattice with rotation and mirror symmetry breaking

Triangular lattice is one of the most generic structures in the two-dimensional (2D) limit with numerous exotic properties, such as magnetic frustration and quantum spin liquid. Here, we investigate the electronic properties of a multi-orbital (p x , p y , p z ) triangular lattice while focusing on the role of rotation and mirror symmetry breaking in regulating the topological phase diagram. The tight-binding modeling reveals that rotation symmetry () breaking splits the Dirac point and preserves the nodal loop. A further inclusion of broken horizontal mirror symmetry () destroys the nodal loop. Consequently, with spin–orbit coupling (SOC), the (p x , p y , p z )-orbital triangular lattice is topologically non-trivial with only or symmetry breaking. With both symmetries breaking, it becomes trivial, except when the SOC is large enough to initiate band inversion. For real materials, we propose that the recently grown AgSe/AgTe monolayer in a binary honeycomb structure is an ideal system to realize the multi-orbital triangular lattice. The first-principles calculations demonstrate that free-standing AgSe and AgTe are Z 2 non-trivial. On the Ag(111) substrate, AgSe becomes trivial because of the breaking of both and symmetries, whereas AgTe remains non-trivial because of the strong SOC of Te. Our work not only provides physical insights into the experimentally synthesized 2D binary honeycomb structures but also highlights the manipulation of electronic and topological properties through symmetry/orbital physics, which are valuable for designing new quantum materials and devices.

Realization of flat bands by lattice intercalation in kagome metals

Recently there has been intense interest in kagome metals, which are expected to host flat bands (FBs). However, the observed ``FBs'' are not flat over the whole two-dimensional Brillouin zone and overlap strongly with other bands. In fact, the FB does not truly exist in a default $d$-orbital kagome lattice, and the conditions for its existence in kagome metals are unknown. Here, based on tight-binding model analyses of the interplay between orbital and lattice symmetry, we establish such conditions. We show that for a single $d$-orbital kagome lattice assuming large crystal field splitting (CFS), only the ${d}_{{z}^{2}}$ orbital gives rise to a FB, while ${d}_{xy}, {d}_{{x}^{2}\ensuremath{-}{y}^{2}}, {d}_{xz}$, and ${d}_{yz}$ orbitals can only produce a FB with a rotated $d$-orbital basis so that they conform with the underlying kagome lattice symmetry. Most importantly, we demonstrate that both conditions of $d$-orbital rotation and large CFS can be ideally satisfied by intercalating the kagome lattice with a hexagonal sublattice without disrupting the destructive interference of FB wave function. Furthermore, we propose layered metalorganic frameworks as promising candidate kagome metals to realize FBs.

Ultracold Feshbach molecules in an orbital optical lattice

Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

Topological band transition between hexagonal and triangular lattices with (p x , p y ) orbitals

By combining tight-binding modelling with density functional theory based first-principles calculations, we investigate the band evolution of two-dimensional (2D) hexagonal lattices with (p x , p y ) orbitals, focusing on the electronic structures and topological phase transitions. The (p x , p y )-orbital hexagonal lattice model possesses two flat bands encompassing two linearly dispersive Dirac bands. Breaking the A/B sublattice symmetry could transform the model into two triangular lattices, each featuring a flat band and a dispersive band. Inclusion of the spin–orbit coupling and magnetization may give rise to quantum spin Hall and quantum anomalous Hall (QAH) states. As a proof of concept, we demonstrate that half-hydrogenated stanene is encoded by a triangular lattice with (p x , p y ) orbitals, which exhibits ferromagnetism and QAH effect with a topological gap of ∼0.15 eV, feasible for experimental observation. These results provide insights into the structure-property relationships involving the orbital degree of freedom, which may shed light on future design and preparation of 2D topological materials for novel electronic/spintronic and quantum computing devices.

Making an artificial px,y -orbital honeycomb electron lattice on a metal surface

We theoretically demonstrate that the desired ${p}_{x,y}$-orbital honeycomb electron lattice can be readily realized by arranging CO molecules into a hexagonal lattice on a Cu(111) surface with scanning tunneling microscopy (STM). The electronic structure of the Cu surface states in the presence of CO molecules is calculated with various methods, i.e., density functional theory (DFT) simulations, the muffin-tin potential model, and the tight-binding model. Our calculations indicate that, by measuring the local density of states (LDOS) pattern using STM, the $p$-orbital surface bands can be immediately identified in experiment. We also give an analytic interpretation of the $p$-orbital LDOS pattern with the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ method. Meanwhile, different from the case of graphene, the $p$-orbital honeycomb lattice has two kinds of edge states, which can also be directly observed in STM experiment. Our work points out a feasible way to construct a ${p}_{x,y}$-orbital honeycomb electron lattice in a real system, which may have exotic properties, such as Wigner crystal, ferromagnetism, $f$-wave superconductivity, and the quantum anomalous Hall effect. Furthermore, we also propose a simple way to calculate and identify the modified Cu surface bands in the Cu/CO systems with the DFT simulations. Considering the recent works about a $p$-orbital square lattice in similar systems [M. R. Slot et al., Nat. Phys. 13, 672 (2017); L. Ma et al., Phys. Rev. B 99, 205403 (2019)], our work once again illustrates that the artificial electron lattice on a metal surface is an ideal platform to study the orbital physics in a controllable way.

Structural and transport properties of Y1-x(Dy)xPdBi (0 ≤ x ≤ 1) topological semi-metallic thin films

We report the effect of 4f electron doping on structural, electrical, and magneto-transport properties of Dy doped half Heusler Y1-x(Dy)xPdBi (x = 0, 0.2, 0.5, and 1) thin films grown by pulsed laser deposition. The electrical transport measurements show a typical semi-metallic behavior in the temperature range of 3 K ≤ T ≤ 300 K and a sharp drop in resistivity at low temperatures (&amp;lt;3 K) for all the samples. Magneto-transport measurements and Shubnikov de-Hass oscillations at high magnetic fields demonstrate that for these topologically non-trivial samples, Dy doping induced variation of spin–orbit coupling strength and lattice density plays an active role in modifying the Fermi surface, carrier concentration, and the effective electron mass of massless carriers. There is a uniform suppression of the onset of superconductivity-like phenomena with increased Dy doping, which is possibly related to the increasing local exchange field arising from the 4f electrons in Dy. Our results indicate that we can tune various band structure parameters of YPdBi by f electron doping, and strained thin films of Y1-x(Dy)xPdBi show surface dominated relativistic carrier transport at low temperatures.

Ferromagnetic percolation transition in a multiorbital flat band assisted by Hund's coupling

By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a ${p}_{x}, {p}_{y}$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground-state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.

Quantum Degenerate Fermi Gas in an Orbital Optical Lattice.

Spin-polarized samples and spin mixtures of quantum degenerate fermionic atoms are prepared in selected excited Bloch bands of an optical checkerboard square lattice. For the spin-polarized case, extreme band lifetimes above 10s are observed, reflecting the suppression of collisions by Pauli's exclusion principle. For spin mixtures, lifetimes are reduced by an order of magnitude by two-body collisions between different spin components, but still remarkably large values of about 1s are found. By analyzing momentum spectra, we can directly observe the orbital character of the optical lattice. The observations demonstrated here form the basis for exploring the physics of Fermi gases with two paired spin components in orbital optical lattices, including the regime of unitarity.

Room temperature organic exciton\u2013polariton condensate in a lattice

Interacting Bosons in artificial lattices have emerged as a modern platform to explore collective manybody phenomena and exotic phases of matter as well as to enable advanced on-chip simulators. On chip, exciton–polaritons emerged as a promising system to implement and study bosonic non-linear systems in lattices, demanding cryogenic temperatures. We discuss an experiment conducted on a polaritonic lattice at ambient conditions: We utilize fluorescent proteins providing ultra-stable Frenkel excitons. Their soft nature allows for mechanically shaping them in the photonic lattice. We demonstrate controlled loading of the coherent condensate in distinct orbital lattice modes of different symmetries. Finally, we explore the self-localization of the condensate in a gap-state, driven by the interplay of effective interaction and negative effective mass in our lattice. We believe that this work establishes organic polaritons as a serious contender to the well-established GaAs platform for a wide range of applications relying on coherent Bosons in lattices.

Orbital degrees of freedom in artificial electron lattices on a metal surface

Orbital degree of freedom plays a fundamental role in condensed matter physics. Recently, a new kind of artificial electron lattice has been realized in experiments by confining the metal surface electrons with adsorbed molecular lattice. A most recent example is the Lieb lattice realized by CO adsorption on Cu(111) surface [M. R. Slot, et al., Nat. Phys. 13, 672(2017)]. The Lieb lattice is of special interest due to its flat band physics. Here, by first-principles calculations, muffin-tin potential model and tight binding model, we demonstrate that, the high energy states observed in the experiment actually correspond to the artificial $p$-orbitals of the electron lattice. Our numerical results, together with the experimental observation, show that artificial $p$-orbital fermionic lattice has already been realized in solid state system. This opens a new avenue to investigate the orbital degree of freedom in a controllable way.

Kohn-Luttinger superconductivity on two orbital honeycomb lattice

Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pairing instability further has a twelve-fold degeneracy while the $f$-wave pairing instability has a ten-fold degeneracy. We analyze the symmetry breaking perturbations to this model. Combining this with a Ginzburg-Landau analysis, we conclude that close to Van Hove filling, a spin singlet $d+id$ pairing state should form (consistent with several other investigations of twisted bilayer graphene), whereas away from Van Hove filling we propose an unusual spin and orbital singlet $f$-wave pairing state.

Graph theory data for topological quantum chemistry.

Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn etal., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

π-Flux Dirac Bosons and Topological Edge Excitations in a Bosonic Chiralp-Wave Superfluid

We study the topological properties of elementary excitations in a staggered p_{x}±ip_{y} Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous p_{x}+ip_{y} momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the p_{x}+ip_{y} and p_{x}-ip_{y} condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.

Correction: Interplay of spin–orbit coupling and lattice distortion in metal substituted 3D tri-chloride hybrid perovskites

Correction for ‘Interplay of spin–orbit coupling and lattice distortion in metal substituted 3D tri-chloride hybrid perovskites’ by C. Katan et al., J. Mater. Chem. A, 2015, 3, 9232–9240.

Opendf - An Implementation of the Dual Fermion Method for Strongly Correlated Systems

The dual fermion method is a multiscale approach for solving lattice problems of interacting strongly correlated systems. In this paper, we present the opendfcode, an open-source implementation of the dual fermion method applicable to fermionic single- orbital lattice models in dimensions D = 1, 2, 3 and 4. The method is built on a dynamical mean field starting point, which neglects all local correlations, and perturbatively adds spatial correlations. Our code is distributed as an open-source package under the GNU public license version 2.