Investigation of the Bosonic Spectrum of Two-Dimensional Optical Graphene-Type Lattices. Normal Phase

Authors

  • I. V. Stasyuk Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
  • I. R. Dulepa Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
  • O. V. Velychko Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe59.09.0888

Keywords:

optical lattice, honeycomb lattice, phase transition, spectral density, hard-core bosons, Dirac points

Abstract

The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.

References

M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, Nature 415, 39 (2002).

https://doi.org/10.1038/415039a

M. Greiner, O. Mandel, T.W. H¨ansch, and I. Bloch, Nature 419, 51 (2002).

https://doi.org/10.1038/nature00968

I. Bloch, Nature Phys. 1, 23 (2005).

P. Soltau-Panahi, J. Struck, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, K. Sengstock, P. Hauke, and M. Lewenstein, Nature Phys. 7, 434 (2011).

D.-S. L¨uhmann, Phys. Rev. A 87, 043619 (2013).

https://doi.org/10.1103/PhysRevA.87.043619

Q.-Q. Lu and J.-M. Hou, Commun. Theor. Phys. 53, 861 (2010).

https://doi.org/10.1088/0253-6102/53/5/14

P. Soltau-Panahi, D.-S. L¨uhmann, J. Struck, P. Windpassinger, and K. Sengstock, Nature Phys. 8, 71 (2012).

E. Albus, X. Fernandez-Gonzalvo, J. Mur-Petit, J.J. Garcia-Ripoli, and J.K. Pachos, Ann. Phys. 328, 64 (2013).

https://doi.org/10.1016/j.aop.2012.10.005

Z. Chen and B. Wu, Phys. Rev. Lett. 107, 065301 (2011).

https://doi.org/10.1103/PhysRevLett.107.065301

S. Koghee, L.-K. Lim, M.O. Goerbig, and C. Morais-Smith, Phys. Rev. A 85, 023637 (2012).

https://doi.org/10.1103/PhysRevA.85.023637

M.P.A. Fisher, P.B. Weichman, G. Grinstein, and D.S. Fisher, Phys. Rev. B 40, 546 (1989).

https://doi.org/10.1103/PhysRevB.40.546

D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).

https://doi.org/10.1103/PhysRevLett.81.3108

R.T. Whitlock and P.R. Zilsel, Phys. Rev. 131, 2409 (1963).

https://doi.org/10.1103/PhysRev.131.2409

C.N. Varney, K. Sun, V. Galitski, and M. Rigol, New J. Phys. 14, 115028 (2012).

https://doi.org/10.1088/1367-2630/14/11/115028

T. Matsubara and H. Matsuda, Progr. Theor. Phys. 16, 569 (1956); 17, 19 (1957).

G.A. Czathy, J.D. Reppy, and M.H.W. Chan, Phys. Rev. Lett. 91, 235301 (2003).

https://doi.org/10.1103/PhysRevLett.91.235301

S. Robashkiewicz, R. Micnas, and K.A. Chao, Phys. Rev. B 23, 1447 (1981); 24, 1579 (1981).

G.D. Mahan, Phys. Rev. B 14, 780 (1976).

https://doi.org/10.1103/PhysRevB.14.780

M.J. Puska and R.M. Niemenen, Surf. Sci. 157, 413 (1985).

https://doi.org/10.1016/0039-6028(85)90683-1

W. Brenig, Surf. Sci. 291, 207 (1993).

https://doi.org/10.1016/0039-6028(93)91492-8

I.V. Stasyuk and I.R. Dulepa, Condens. Matter Phys. 10, 259 (2007).

https://doi.org/10.5488/CMP.10.2.259

I.V. Stasyuk and I.R. Dulepa, J. Phys. Studies 13, 2701 (2009).

I.V. Stasyuk, O. Vorobyov, and R.Ya. Stetsiv, Ferroelectrics 426, 6 (2012).

https://doi.org/10.1080/00150193.2012.671087

I.V. Stasyuk and O. Vorobyov, Condens. Matter Phys. 16, 23005 (2013).

https://doi.org/10.5488/CMP.16.23005

H.B. Roseustock, J. Chem. Phys. 16, 2064 (1953).

https://doi.org/10.1063/1.1698743

J.P. Hobson and W.A. Nierenberg, Phys. Rev. 89, 662 (1953).

https://doi.org/10.1103/PhysRev.89.662

P.T. Ernst, S. G¨otze, J.S. Krauser, K. Pyka, D.-S. L¨uhmann, D. Pfannkuche, and K. Sengstock, Nature Phys. 6, 56 (2010).

N. Fabbri, S.D. Huber, D. Cl’ement, L. Fallani, C. Fort, M. Inguscio, and E. Altman, Phys. Rev. Lett. 109, 055301 (2012).

https://doi.org/10.1103/PhysRevLett.109.055301

Y. Ohashi, M. Kitaura, and H. Matsumoto, Phys. Rev. A 73, 033617 (2006).

https://doi.org/10.1103/PhysRevA.73.033617

C. Menotti and N. Trivedi, Phys. Rev. B 77, 235120 (2008).

https://doi.org/10.1103/PhysRevB.77.235120

Published

2018-10-24

How to Cite

Stasyuk, I. V., Dulepa, I. R., & Velychko, O. V. (2018). Investigation of the Bosonic Spectrum of Two-Dimensional Optical Graphene-Type Lattices. Normal Phase. Ukrainian Journal of Physics, 59(9), 888. https://doi.org/10.15407/ujpe59.09.0888

Issue

Section

Solid matter