Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

Recent experiments by Gutiérrez et al (2016 Nat. Phys. 12 950) on a graphene–copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice—a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called ‘Kek-Y’ texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field B, the valley degeneracy of the B-dependent Landau levels is removed by the valley-momentum locking but a B-independent and valley-degenerate zero-mode remains.

[1]  Jiwoong Park,et al.  Imaging chiral symmetry breaking from Kekulé bond order in graphene , 2016, Nature Physics.

[2]  C. Mudry.  Two-dimensional materials: Heavy going , 2016, 1610.09135.

[3]  J. Wang,et al.  Valley precession in graphene superlattices , 2015 .

[4]  C. Zeng,et al.  Single-Valley Engineering in Graphene Superlattices , 2015, 1501.05553.

[5]  J. Brink,et al.  Kekule textures, pseudo-spin one Dirac cones and quadratic band crossings in a graphene-hexagonal indium chalcogenide bilayer. , 2014, 1412.8072.

[6]  C. Gutiérrez.  Visualizing Ordered Electronic States in Epitaxial Graphene , 2015 .

[7]  T. Kuschel,et al.  Spin orbitronics: Charges ride the spin wave. , 2015, Nature nanotechnology.

[8]  M. Wimmer,et al.  Kwant: a software package for quantum transport , 2013, 1309.2926.

[9]  Francisco Guinea,et al.  Artificial honeycomb lattices for electrons, atoms and photons. , 2013, Nature nanotechnology.

[10]  D. Pesin,et al.  Spintronics and pseudospintronics in graphene and topological insulators. , 2012, Nature materials.

[11]  Francisco Guinea,et al.  Designer Dirac fermions and topological phases in molecular graphene , 2012, Nature.

[12]  W. Marsden.  I and J , 2012 .

[13]  P. Recher,et al.  A defect controls transport in graphene , 2011 .

[14]  V. Fal’ko,et al.  Ordered states of adatoms on graphene , 2009, 0909.2988.

[15]  V. Fal’ko,et al.  Hidden Kekule ordering of adatoms on graphene , 2009, 0906.5174.

[16]  Nitin Samarth,et al.  Spintronics without magnetism , 2009 .

[17]  J. Kailasvuori.  Pedestrian index theorem à la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene , 2009, 0904.3807.

[18]  F. Guinea,et al.  The electronic properties of graphene , 2007, Reviews of Modern Physics.

[19]  A. Fert.  The origin, development and future of spintronics , 2008 .

[20]  Albert Fert,et al.  Origin, development, and future of spintronics (Nobel Lecture). , 2008, Angewandte Chemie.

[21]  M. Katsnelson,et al.  Zero-energy states in corrugated bilayer graphene , 2008, 0802.1409.

[22]  C. Beenakker.  Andreev reflection and Klein tunneling in graphene , 2007, 0710.3848.

[23]  Jeroen van den Brink,et al.  Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations , 2007 .

[24]  J. Brink,et al.  Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations , 2007, 0704.1994.

[25]  G. Burkard,et al.  Spin qubits in graphene quantum dots , 2006, cond-mat/0611252.

[26]  Christopher Mudry,et al.  Electron fractionalization in two-dimensional graphenelike structures. , 2006, Physical review letters.

[27]  O. Ogurisu,et al.  Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field , 2001 .

[28]  C. Chamon.  Solitons in carbon nanotubes , 1998, cond-mat/9810233.

[29]  W. Fulton.  The Winding Number , 1995 .

[30]  A. Zee,et al.  Winding number, family index theorem, and electron hopping in a magnetic field , 1989 .

[31]  Y. Aharonov,et al.  Ground state of a spin-½ charged particle in a two-dimensional magnetic field , 1979 .

[32]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[33]  John W. Bruce.  HEAVY GOING , 1959 .

[34]  E. H. Wilson.  Origin , 1927, Bulletin of popular information - Arnold Arboretum, Harvard University..