Structure In Momentum Space Research Articles

Theory of topological exciton insulators and condensates in flat Chern bands

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

Near-Field Spin Chern Number Quantized by Real-Space Topology of Optical Structures.

The Chern number has been widely used to describe the topological properties of periodic structures in momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new spin Chern number is intrinsically quantized and equal to the structure's Euler characteristic. The relationship is robust against continuous deformation of the structure's geometry and is irrelevant to the specific material constituents or external excitation. Our Letter enriches topological physics by extending the Chern number to real space, opening exciting possibilities for exploring the real-space topological properties of light.

Introducing antiferromagnetic ordering on the surface states of a Bi2Se3 topological insulator by europium doping

Topological insulators (TIs) are materials with an insulating bulk characterized by a gapped band structure, along with gapless metallic surface states having a Dirac cone with a helical spin structure in momentum space.

Friedel oscillation in non-Fermi liquid: lesson from exactly solvable Hatsugai–Kohmoto model

When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai–Kohmoto model which has been intensively explored in recent years. Combining T-matrix approximation and linear-response-theory, an interesting picture emerges, if two interaction-induced quasi-particles bands in NFL are partially occupied, FO in this situation is determined by a novel structure in momentum space, i.e. the ‘average Fermi surface’ (average over two quasi-particle Fermi surface), which highlights the inter-band particle-hole excitation. We hope our study here provides a counterintuitive example in which FO with Fermi surface coexists with NFL quasi-particle, and it may be useful to detect hidden ‘average Fermi surface’ structure in other correlated electron systems.

Anomalous Hall effect in kagome ferromagnet YbMn6Sn6 single crystal

The rare-earth based magnetic kagome materials RMn6Sn6 have attracted tremendous interest for their potential to host exotic topological quantum states. Here, we report the observation of the anomalous Hall effect in the kagome ferromagnet YbMn6Sn6 single crystal. YbMn6Sn6 has an easy-plane ferromagnetic structure till 2 K without magnetic ordering of the R ions. The low-temperature magnetoresistance is positive and does not exhibit a tendency to saturate up to 5 T. The magnetoresistance becomes negative with the increasing temperature. An intrinsic anomalous Hall conductivity with the value of 40.2 Ω−1·cm−1 is obtained in YbMn6Sn6, which is associated with the Berry curvature of electronic band structure in momentum space. Our results indicate that YbMn6Sn6 may be an excellent platform to study the relationship between the magnetic and electronic structure and to explore novel quantum phenomenon.

Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene.

We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. The degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is d-wave-like and spin singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.

Covariant dynamics on the momentum space

A geometrical interpretation of Schrödinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum space structure. Some specific examples are discussed in the context of flat space deformations and the Euclidean Snyder (spherical momentum space) model. In this formulation the dynamics for the deformations of the flat momentum space becomes trivial, while different versions of the Snyder model turn out to be dynamically equivalent.

Topological phase transitions in Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7 </sub> under strain regulation

Topological electronic materials exhibit many novel physical properties, such as low dissipation transport and high carrier mobility. These extraordinary properties originate from their non-trivial topological electronic structures in momentum space. In recent years, topological phase transitions based on topological electronic materials have gradually become one of the hot topics in condensed matter physics. Using first-principles calculations, we explore the topological phase transitions driven by in-plane strain in ternary pyrochlore oxide Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub>. Firstly, we analyze the atomic-orbital-resolved band structure and find that the O (p<sub><i>x</i></sub>+p<sub><i>y</i></sub>) and p<sub><i>z</i></sub> orbitals of the system near the Fermi level have band inversion, indicating the emergence of topological phase transitions in the system. Then the tight-binding models are constructed to calculate the <i>Z</i><sub>2</sub> topological invariants, which can determine the topologically non-trivial feature of the system. Finally, topological properties such as surface states and a three-dimensional Dirac cone are studied. It is found that Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub> without strain is a semimetal with a quadratic band touching point at Fermi level, while the in-plane strain can drive the topological phase transition via breaking crystalline symmetries. When the system is under the –1% in-plane compression strain and without considering the spin orbit coupling (SOC), the application of strain results in two triply degenerate nodal points formed in the –<i>Z</i> to <i>Γ</i> direction and <i>Γ</i> to <i>Z</i> direction, respectively. When the SOC is included, there are two fourfold degenerate Dirac points on the –<i>Z</i> to <i>Γ</i> path and <i>Γ</i> to <i>Z</i> path<i>,</i> respectively. Thus, the –1% in-plane compression strain makes the system transit from the quadratic contact point semimetal to a Dirac semimetal. When 1% in-plane expansion strain is applied and the SOC is neglected, there exists one band intersection along <i>Y→</i><i>Γ</i>. When the SOC is taken into consideration, the gap is opened. Therefore, the 1% in-plane expansion strain drives Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub> into a strong topological insulator. In addition, the system is also expected to have strong correlation effect and superconductivity due to the possible flat band. This work can guide the study of topological phase transitions in three-dimensional materials and provide a good material platform for the design of low-dissipation electronic devices.

Quantum layertronics in van der Waals systems

In van der Waals system, the interlayer van der Waals coupling between adjacent atomically thin layers makes the electronic wave function spread on more than one specific layer, turning spatial discrete layer degree of freedom into a quantum mechanical degree of freedom. The coupling of layer degree of freedom with the in-plane center-of-mass motion of electrons forms a nontrivial layer pseudospin structure in momentum space, resulting in various new quantum geometric properties in an extended parameter space, which is unique to the lattice mismatched van der Waals systems. They trigger off a plenty of novel transport and optical effects, linear and nonlinear responses, and offer new pathways towards device applications, becoming the research frontiers of quantum layertronics. This article briefly reviews this emerging research direction, and discusses possible development in the near future based on its crossing with other intensive research fields such as nonlinear electronics, twistronics and chiral electronics.

On the Quantization of AB Phase in Nonlinear Systems.

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

Momentum-space structure of dineutrons in Borromean nuclei

A comparative study is made of the momentum-space structure of dineutrons in the Borromean nuclei $^{11}\mathrm{Li}$, $^{6}\mathrm{He}$, $^{22}\mathrm{C}$, and $^{19}\mathrm{B}$. The ground-state properties of these nuclei are well described by a three-body model using a newly constructed finite-range $nn$ interaction in momentum space. I clarify how the mean opening angle between momenta of valence neutrons and the opening-angle distribution reflect the two-neutron density of the Borromean nuclei. By indicating the similarities to the distributions for the correlation angle in the knockout-reaction experiments, I show that the angular correlations of halo neutrons can provide rich information for the characteristic structure of dineutrons in the Borromean nuclei.

Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets

The stability of a magnetic skyrmion crystal in a centrosymmetric orthorhombic lattice system is numerically investigated. By performing the simulated annealing for an effective spin model with the momentum-resolved interaction on a uniaxially distorted triangular lattice, we find that the skyrmion crystal is robustly realized when dominant interaction channels consist of the double-Q structure in momentum space. Moreover, we show that an anti-type skyrmion crystal with the opposite skyrmion number is obtained by tuning the sign of the bond-dependent anisotropic exchange interaction that originates from the relativistic spin–orbit coupling.

Observation of a Flat and Extended Surface State in a Topological Semimetal.

A flat band structure in momentum space is considered key for the realization of novel phenomena. A topological flat band, also known as a drumhead state, is an ideal platform to drive new exotic topological quantum phases. Using angle-resolved photoemission spectroscopy experiments, we reveal the emergence of a highly localized surface state in a topological semimetal BaAl and provide its full energy and momentum space topology. We find that the observed surface state is localized in momentum, inside a square-shaped bulk Dirac nodal loop, and in energy, leading to a flat band and a peak in the density of state. These results imply this class of materials as an experimental realization of drumhead surface states and provide an important reference for future studies of the fundamental physics of correlated quantum effects in topological materials.

Nucleon momentum distribution of 56Fe from the axially deformed relativistic mean-field model with nucleon-nucleon correlations

Nucleon momentum distribution (NMD), particularly its high-momentum components, is essential for understanding the nucleon--nucleon ($ NN $) correlations in nuclei. Herein, we develop the studies of NMD of $^{56}\text{Fe}$ from the axially deformed relativistic mean-field (RMF) model. Moreover, we introduce the effects of $ NN $ correlation into the RMF model from phenomenological models based on deuteron and nuclear matter. For the region $ k<k_{\text{F}} $, the effects of deformation on the NMD of the RMF model are investigated using the total and single-particle NMDs. For the region $ k>k_{\text{F}} $, the high-momentum components of the RMF model are modified by the effects of $ NN $ correlation, which agree with the experimental data. Comparing the NMD of relativistic and non-relativistic mean-field models, the relativistic effects on nuclear structures in momentum space are analyzed. Finally, by analogizing the tensor correlations in deuteron and Jastrow-type correlations in nuclear matter, the behaviors and contributions of $ NN $ correlations in $^{56}\text{Fe}$ are further analyzed, which helps clarify the effects of the tensor force on the NMD of heavy nuclei.

Observation of Dresselhaus type spin splitting of zinc blende structure semiconductors by circular dichroic photoemission study

Material family of zinc blende structure semiconductors (ZBSSs) is important for novel technique such as spintronics. A study of the ZBSS spin-splitting structure in momentum space is essential when seeking to understand the exotic properties of the material. The Dresselhaus field predominates in the bulk, but the Rashba field plays important roles in states near the surface. Here, we used circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES) to explore the spin-splitting structure of bulk ZBSS in momentum space. The observed structure was well-explained by a Dresselhaus field attributable to the lack of inversion symmetry in ZBSS crystals. We show that CD-ARPES usefully reveals spin-splitting in momentum space. CD-ARPES combined with hard x-ray incident-beam would be useful to investigate the spin-splitting structures of the interface states in the ZBSS heterostructure.

Realizing Hopf Insulators in Dipolar Spin Systems.

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In an accompanying paper [T. Schuster etal., Phys. Rev. A 103, AW11986 (2021)PLRAAN2469-9926] we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of ^{40}K^{87}Rb.

Angle-resolved photoemission studies of quantum materials

The physics of quantum materials is dictated by many-body interactions and mathematical concepts such as symmetry and topology that have transformed our understanding of matter. Angle-resolved photoemission spectroscopy (ARPES), which directly probes the electronic structure in momentum space, has played a central role in the discovery, characterization, and understanding of quantum materials ranging from strongly-correlated states of matter to those exhibiting non-trivial topology. Over the past two decades, ARPES as a technique has matured dramatically with ever-improving resolution and continued expansion into the space-, time-, and spin-domains. Simultaneously, the capability to synthesize new materials and apply non-thermal tuning parameters \emph{in-situ} has unlocked new dimensions in the study of all quantum materials. We review these developments, and survey the scientific contributions they have enabled in contemporary quantum materials research.

Flatness and boundness of photonic drumhead surface state in a metallic lattice

Nodal chain (NC) semi-metals have the degeneracy of interlacing rings in their band structure in momentum space. With the projection of degenerate rings towards crystal boundaries, there is a special type of surface dispersion appearing at surface Brillouin zone and termed drumhead surface state (DSS). Previously, experimental investigations on photonic NC and DSS have been done on metallic photonic crystals at microwave frequencies. However, far-field detection of DSS and its coupling to radiative modes in free space have not been studied. In the work, we analyze the photonic DSS in a metallic lattice by angle-resolved far-field reflection measurement and numerical simulation at terahertz (THz) frequencies, and reveal its flatness and boundness in band structure, even in the radiation continuum. Particularly, the DSS band can be tuned being from negatively dispersive via flat to positively dispersive by a single surface parameter, and the DSS at Γ point in surface Brillouin zone is in fact a symmetry-protected bound state in the continuum. Our results might have some potential applications towards THz photonics.

Exotic pairing structures in population-imbalanced fermionic systems: dynamics as a probe

We investigate a population-imbalanced two-species fermionic system where the resonantly paired fermions combine to form bosonic molecules via Feshbach interaction. We study the dynamics of the intrinsic quantum fluctuations of the system. It is shown that the natural fluctuations of the condensate fraction consist of a fixed number of periodic components: indicating that these oscillations do not die out, and are sustained in the mean field dynamics of the system. These frequency components bear distinct signatures of the nature of pairing present in the system. We describe how a time-dependent external magnetic field can be used to locate these oscillation frequencies, and thus to explore the momentum space structure of the population imbalanced system. We propose that this method can be used as an indirect experimental probe for detecting exotic phases like the breached-pair state, FFLO state, and a phase-separated state comprising of BCS and normal regions.

Nematic-Orbit Coupling and Nematic Density Waves in Spin-1 Condensates.

We propose the creation of artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates, in analogy with spin-orbit coupling. Using a suitably designed microwave chip, the quadratic Zeeman shift, normally uniform in space, can be made to be spatiotemporally varying, leading to a coupling between spatial and nematic degrees of freedom. A phase diagram is explored where three quantum phases with the nematic order emerge: easy axis, easy plane with single-well structure, and easy plane with double-well structure in momentum space. By including spin-dependent and spin-independent interactions, we also obtain the low energy excitation spectra in these three phases. Last, we show that the nematic-orbit coupling leads to a periodic nematic density modulation in relation to the period λ_{T} of the cosinusoidal quadratic Zeeman term. Our results point to the rich possibilities for manipulation of tensorial degrees of freedom in ultracold gases without requiring Raman lasers, and therefore, obviating light-scattering induced heating.