Effect of magnetic field on Goos-Hänchen shifts in gaped graphene triangular barrier

Abstract We study the effect of a magnetic field on Goos-Hanchen shifts in gaped graphene subjected to a double triangular barrier. Solving the wave equation separately in each region composing our system and using the required boundary conditions, we then compute explicitly the transmission probability for scattered fermions. These wavefunctions are then used to derive the Goos-Hanchen shifts in terms of different physical parameters such as energy, electrostatic potential strength and magnetic field. Our numerical results show that the Goos-Hanchen shifts are affected by the presence of the magnetic field and depend on the geometrical structure of the triangular barrier.

[1]  A. Jellal,et al.  Tunneling for Dirac Fermions in Constant Magnetic Field , 2009, 0906.0097.

[2]  Edouard Sonin.  Effect of Klein tunneling on conductance and shot noise in ballistic graphene , 2009, 0902.3622.

[3]  Yu Song,et al.  Giant Goos-Hänchen shift in graphene double-barrier structures , 2012, 1208.2395.

[4]  F. Goos,et al.  Ein neuer und fundamentaler Versuch zur Totalreflexion , 1947 .

[5]  H. Bahlouli,et al.  Goos–Hänchen like shifts in graphene double barriers , 2013, 1306.5679.

[6]  S. Yelin,et al.  Proposal for graphene-based coherent buffers and memories , 2010 .

[7]  P. Wallace.  The Band Theory of Graphite , 1947 .

[8]  X. Dai,et al.  Enhancement and control of the Goos—Hänchen shift by nonlinear surface plasmon resonance in graphene , 2018, Chinese Physics B.

[9]  H. S. Allen.  The Quantum Theory , 1928, Nature.

[10]  M. I. Katsnelson,et al.  Chiral tunnelling and the Klein paradox in graphene , 2006 .

[11]  H. Bahlouli,et al.  Tunneling of Graphene Massive Dirac Fermions Through a Double Barrier , 2011, 1110.0826.

[12]  H. Bahlouli,et al.  Transmission through biased graphene strip , 2011, 1105.5279.

[13]  L. Dell'Anna,et al.  Multiple magnetic barriers in graphene , 2008, 0810.1236.

[14]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[15]  Yuanjiang Xiang,et al.  Giant and controllable Goos-Hänchen shifts based on surface plasmon resonance with graphene-MoS2 heterostructure , 2018, Optical Materials Express.

[16]  A. Jellal,et al.  Dirac fermions in an inhomogeneous magnetic field , 2010, 1010.5574.

[17]  F. Peeters,et al.  Magnetic Kronig–Penney model for Dirac electrons in single-layer graphene , 2009, 0907.3871.

[18]  X. Dai,et al.  Comparison of Goos–Hänchen shifts of the reflected beam from graphene on dielectrics and metals , 2014 .

[19]  Xi Chen,et al.  Giant negative and positive lateral shifts in graphene superlattices , 2013 .

[20]  Xi Chen,et al.  Goos-Hänchen-like shifts for Dirac fermions in monolayer graphene barrier , 2010, 1004.0350.

[21]  C. Sinha,et al.  Resonant tunnelling in a Fibonacci bilayer graphene superlattice , 2010 .

[22]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[23]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[24]  A. Jellal,et al.  Zero, positive and negative quantum Goos–Hänchen shifts in graphene barrier with vertical magnetic field , 2015 .

[25]  Resonances in the one-dimensional Dirac equation in the presence of a point interaction and a constant electric field , 2005, hep-th/0512073.

[26]  A Selectable Multiband Bandpass Microwave Photonic Filter , 2013, IEEE Photonics Journal.

[27]  F. Goos,et al.  Neumessung des Strahlversetzungseffektes bei Totalreflexion , 1949 .

[28]  C. Beenakker,et al.  Quantum Goos-Hänchen effect in graphene. , 2008, Physical review letters.

[29]  Controllable Goos-Hänchen shift in graphene triangular double barrier , 2016, 1604.08906.

[30]  Andrew G. Glen,et al.  APPL , 2001 .

[31]  Cheol-Hwan Park,et al.  New generation of massless Dirac fermions in graphene under external periodic potentials. , 2008, Physical review letters.

[32]  D. Goldhaber-Gordon,et al.  Evidence for Klein tunneling in graphene p-n junctions. , 2008, Physical review letters.

[33]  Daniel W. Wilson,et al.  Quantum interference effects in semiconductors: a bibliography , 1991, Proc. IEEE.

[34]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[35]  Zach DeVito,et al.  Opt , 2017 .

[36]  Weiping Zhang,et al.  Goos-Hänchen-like shifts in atom optics , 2008, 0802.2149.

[37]  Sankalpa Ghosh,et al.  Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[38]  H. Sevinçli,et al.  Superlattice structures of graphene-based armchair nanoribbons , 2007, 0711.2414.