Brillouin zone

About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.

An Aharonov-Bohm interferometer for determining Bloch band topology

Abstract: The geometric structure of a single-particle energy band in a solid is fundamental for a wide range of many-body phenomena and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. We realize an atomic interferometer to measure Berry flux in momentum space, in analogy to an Aharonov-Bohm interferometer that measures magnetic flux in real space. We demonstrate the interferometer for a graphene-type hexagonal optical lattice loaded with bosonic atoms. By detecting the singular π Berry flux localized at each Dirac point, we establish the high momentum resolution of this interferometric technique. Our work forms the basis for a general framework to fully characterize topological band structures.

Superfluidity of Bose–Einstein condensate in an optical lattice: Landau–Zener tunnelling and dynamical instability

Abstract: Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

Origin of doping in quasi-free-standing graphene on silicon carbide.

Abstract: We explain the robust p-type doping observed for quasi-free-standing graphene on hexagonal silicon carbide by the spontaneous polarization of the substrate. This mechanism is based on a bulk property of SiC, unavoidable for any hexagonal polytype of the material and independent of any details of the interface formation. We show that sign and magnitude of the polarization are in perfect agreement with the doping level observed in the graphene layer. With this mechanism, models based on hypothetical acceptor-type defects as they are discussed so far are obsolete. The n-type doping of epitaxial graphene is explained conventionally by donorlike states associated with the buffer layer and its interface to the substrate that overcompensate the polarization doping. The basis for the unique electronic and optical properties of graphene is the linear dispersion relation of the � electrons, which is responsible for Dirac-type quasiparticles with many unusual properties. The band structure in the relevant energy range is made up by double cones in the corners of the two-dimensional hexagonal Brillouin zone; their opening angle is determined by the slope vF ¼ d! dk of the dispersion relation called the Fermi velocity, which is an intrinsic material parameter. The origin of these so-called Dirac cones defines the Fermi energy in an isolated and intrinsic graphene layer. At finite temperatures, the reservoir of mobile charge carriers is due to thermal excitation of equal concentrations n0 and p0 of electrons and holes. Evaluation of the Fermi statistics yields a value of n0 ¼ �k 2 B

Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures

Abstract: Monolayers of transition-metal dichalcogenides feature exceptional optical properties that are dominated by tightly bound electron–hole pairs, called excitons. Creating van der Waals heterostructures by deterministically stacking individual monolayers can tune various properties via the choice of materials1 and the relative orientation of the layers2,3. In these structures, a new type of exciton emerges where the electron and hole are spatially separated into different layers. These interlayer excitons4–6 allow exploration of many-body quantum phenomena7,8 and are ideally suited for valleytronic applications9. A basic model of a fully spatially separated electron and hole stemming from the K valleys of the monolayer Brillouin zones is usually applied to describe such excitons. Here, we combine photoluminescence spectroscopy and first-principles calculations to expand the concept of interlayer excitons. We identify a partially charge-separated electron–hole pair in MoS2/WSe2 heterostructures where the hole resides at the Γ point and the electron is located in a K valley. We control the emission energy of this new type of momentum-space indirect, yet strongly bound exciton by variation of the relative orientation of the layers. These findings represent a crucial step towards the understanding and control of excitonic effects in van der Waals heterostructures and devices. A new type of exciton is observed in transition-metal dichalcogenide heterobilayers that is indirect in both real space and momentum space. It consists of a paired electron in MoS2 at the K point and hole spread across MoS2 and WSe2 at the Γ point.

Dipolar Sums in the Primitive Cubic Lattices

Abstract: Dipole-wave sums, important in many magnetic and electric problems involving dipole-dipole interactions, are defined, and numerical values are given at sets of independent points in k-space equivalent to a 512-fold sampling of the first Brillouin zone of each of the three primitive cubic lattices. Strong size, shape, and position dependence of these sums is shown to occur in a pathological region about the origin in k-space. The dipole-wave sums are shown to be related to dipole-field factors at points within the unit cell. The dipolar anisotropy energy in the antiferromagnet MnO is discussed as an illustration of the use of dipole-wave sums.