Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Three-dimensional Dirac-like fermions in an optical lattice

Mou Yang, Shi-Liang Zhu

Published Dec 23, 2010• 11 citations
Publisher

Abstract

We present a scheme to realize three-dimensional Dirac-like fermions with an edge-centered cubic optical lattice. We propose a method to construct the optical edge-centered cubic crystals and then determine the parameters required for the description of the systems with a tight-binding model. Interestingly, we show that the low-energy quasiparticles are three-dimensional massive or massless Dirac-like fermions determined by the parameters of the system. In addition, two three-dimensional degenerate flat bands lie between the upper and the lower branches of the Dirac dispersion. Furthermore, we demonstrate that the Dirac dispersion relation and the flat bands can be verified by the density profile measurement.

DOI
10.1103/physreva.82.064102

Related papers

Single Dirac cone with a flat band touching on line-centered-square optical lattices

R. Shen, L. B. Shao, Baigeng Wang +1 more

Using ultracold atoms trapped in an optical lattice, we form a line-centered-square lattice in the condensed-matter physics, where a crossover from massive to massless Dirac fermion behavior can be easily achieved by tuning the laser intensities. The present Dirac fermions satisfy a three-component quantum equation for pseudospin-1 fermions, resulting in a single Dirac cone in the energy spectrum, a flat band touching at the Dirac point, and a vanishing Berry's phase. Interestingly, the massless Dirac fermions here may exhibit an all-angle Klein tunneling; i.e., the barrier is completely transparent for all incident angles.

Physical Review B•Jan 14, 2010•298 citations

Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice

Sheng-Tao Wang, Dong-Ling Deng, Luming Duan

We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.

arXiv:1402.1204•Physical Review Letters•Jul 16, 2014•50 citations

Ultracold fermions in a graphene-type optical lattice

Kean Loon Lee, Benoît Grémaud, Rui Han +2 more

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter ${t}_{0}$ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.

arXiv:0906.4158•Physical Review A•Oct 19, 2009•132 citations

Massless Dirac fermions in a square optical lattice

Jing-Min Hou, Wen‐Xing Yang, Xiong-Jun Liu

We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.

arXiv:0902.4746•Physical Review A•Apr 21, 2009•63 citations

Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices

Zhihao Lan, Nathan Goldman, A. Bermúdez +2 more

Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the $(2s+1)$-dimensional representations of the $\mathfrak{su}$(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin $s$. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer $s$, and a metallic phase that contains a flat zero-energy band at integer $s$. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.

arXiv:1102.5283•Physical Review B•Oct 14, 2011•119 citations

Simulation and Detection of Dirac Fermions with Cold Atoms in an Optical Lattice

Shi-Liang Zhu, Baigeng Wang, L.-M. Duan

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.

arXiv:cond-mat/0703454•Physical Review Letters•Jun 25, 2007•306 citations
We present a scheme to realize three-dimensional Dirac-like fermions with an edge-centered cubic optical lattice. We propose a method to construct the optical edge-centered cubic crystals and then determine the parameters required for the description of the systems with a tight-binding model. Interestingly, we show that the low-energy quasiparticles are three-dimensional massive or massless Dirac-like fermions determined by the parameters of the system. In addition, two three-dimensional degenerate flat bands lie between the upper and the lower branches of the Dirac dispersion. Furthermore, we demonstrate that the Dirac dispersion relation and the flat bands can be verified by the density profile measurement.
Using ultracold atoms trapped in an optical lattice, we form a line-centered-square lattice in the condensed-matter physics, where a crossover from massive to massless Dirac fermion behavior can be easily achieved by tuning the laser intensities. The present Dirac fermions satisfy a three-component quantum equation for pseudospin-1 fermions, resulting in a single Dirac cone in the energy spectrum, a flat band touching at the Dirac point, and a vanishing Berry's phase. Interestingly, the massless Dirac fermions here may exhibit an all-angle Klein tunneling; i.e., the barrier is completely transparent for all incident angles.
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter t0{t}_{0}t0​ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.
We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.
Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the (2s+1)(2s+1)(2s+1)-dimensional representations of the su\mathfrak{su}su(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin sss. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer sss, and a metallic phase that contains a flat zero-energy band at integer sss. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.