Abstract
We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted α − 𝒯3 quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-Büttiker approaches. Thereby the influence of a disordered environment is discussed as well.
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L. Yang, C.-H. Park, Y.W. Son, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 99, 186801 (2007)
S. Russo, J.B. Oostinga, D. Wehenkel, H.B. Heersche, S.S. Sobhani, L.M.K. Vandersypen, A.F. Morpurgo, Phys. Rev. B 77, 085413 (2008)
J.R. Williams, L. DiCarlo, C.M. Marcus, Science 317, 638 (2016)
L.A. Ponomarenko, F. Schedin, E.W.H.M.I. Katsnelson, R. Yang, K.S. Novoselov, A.K. Geim, Science 320, 356 (2008)
J.Y. Vaishnav, J.Q. Anderson, J.D. Walls, Phys. Rev. B 83, 165437 (2011)
J.M. Caridad, S. Connaughton, C. Ott, H.B. Weber, V. Krstic̀, Nat. Commun. 7, 12894 (2016)
D. Gunlycke, D.A. Areshkin, J. Li, J.W. Mintmire, C.T. White, Nano Lett. 7, 3608 (2007)
P. Zhao, J. Guo, J. Appl. Phys. 105, 034503 (2009)
J. Güttinger, F. Molitor, C. Stampfer, S. Schnez, A. Jacobsen, S. Dröscher, T. Ihn, K. Ensslin, Rep. Prog. Phys. 75, 126502 (2012)
R.V. Gorbachev, A.S. Mayorov, A.K. Savchenko, D.W. Horsell, F. Guinea, Nano Lett. 8, 1995 (2008)
O. Klein, Z. Phys. 53, 157 (1928)
M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)
B. Trauzettel, Y.M. Blanter, A.F. Morpurgo, Phys. Rev. B 75, 035305 (2007)
C. Wurl, H. Fehske, Phys. Rev. A 98, 063812 (2018)
J.H. Bardarson, M. Titov, P.W. Brouwer, Phys. Rev. Lett. 102, 226803 (2009)
H. Fehske, G. Hager, A. Pieper, Phys. Status Solidi B 252, 1868 (2015)
B. Brun, N. Moreau, S. Somanchi, V.H. Nguyen, K. Watanabe, T. Taniguchi, J.C. Charlier, C. Stampfer, B. Hackens, Phys. Rev. B 100, 041401 (2019)
R. Heinisch, F.X. Bronold, H. Fehske, Phys. Rev. Lett. 109, 243903 (2012)
J. Cserti, A. Pályi, C. Péterfalvi, Phys. Rev. Lett. 99, 246801 (2007)
R.L. Heinisch, F.X. Bronold, H. Fehske, Phys. Rev. B 87, 155409 (2013)
A. Pieper, R. Heinisch, H. Fehske, Europhys. Lett. 104, 47010 (2013)
M.M. Asmar, S.E. Ulloa, Phys. Rev. Lett. 112, 136602 (2014)
J.S. Wu, M.M. Fogler, Phys. Rev. B 90, 235402 (2014)
A. Filusch, C. Wurl, H. Fehske, Eur. Phys. J. B. 93, 59 (2020)
Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)
D. Smirnov, H. Schmidt, R.J. Haug, Appl. Phys. Lett. 100, 203114 (2008)
B. Sutherland, Phys. Rev. B 34, 5208 (1986)
J. Vidal, R. Mosseri, B. Dou çot, Phys. Rev. Lett. 81, 5888 (1998)
B. Dóra, J. Kailasvuori, R. Moessner, Phys. Rev. B 84, 195422 (2011)
A. Raoux, M. Morigi, J.N. Fuchs, F. Piéchon, G. Montambaux, Phys. Rev. Lett. 112, 026402 (2014)
R. Shen, L.B. Shao, B. Wang, D.Y. Xing, Phys. Rev. B 81, 041410 (2010)
D.F. Urban, D. Bercioux, M. Wimmer, W. Häusler, Phys. Rev. B 84, 115136 (2011)
S.K. Firoz Islam, P. Dutta, Phys. Rev. B 96, 045418 (2017)
Y.R. Chen, Y. Xu, J. Wang, J.F. Liu, Z. Ma, Phys. Rev. B 99, 045420 (2019)
M. Orlita, D.M. Basko, M.S. Zholudev, F. Teppe, W. Knap, V.I. Gavrilenko, N.N. Mikhailov, S.A. Dvoretskii, P. Neugebauer, C. Faugeras et al., Nat. Phys. 10, 233 (2015)
J.D. Malcolm, E.J. Nicol, Phys. Rev. B 92, 035118 (2015)
M. Rizzi, V. Cataudella, R. Fazio, Phys. Rev. B 73, 144511 (2006)
P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610 (1928)
S. Schnez, K. Ensslin, M. Sigrist, T. Ihn, Phys. Rev. B 78, 195427 (2008)
R. Jackiw, A.I. Milstein, S.Y. Pi, I.S. Terekhov, Phys. Rev. B 80, 033413 (2009)
D. Bercioux, D.F. Urban, H. Grabert, W. Häusler, Phys. Rev. A 80, 063603 (2009)
M. Vigh, L. Oroszlány, S. Vajna, P. San-Jose, G. Dávid, J. Cserti, B. Dóra, Phys. Rev. B 88, 161413 (2013)
Y. Betancur-Ocampo, G. Cordourier-Maruri, V. Gupta, R. de Coss, Phys. Rev. B 96, 024304 (2017)
H.Y. Xu, Y.C. Lai, Phys. Rev. B 94, 165405 (2016)
E.A. Stepanov, V.C. Zhukovsky, Phys. Rev. B 94, 094101 (2016)
E. Illes, E.J. Nicol, Phys. Rev. B 95, 235432 (2017)
M.R. Thomsen, T.G. Pedersen, Phys. Rev. B 95, 235427 (2017)
R. Zhu, C. Cai, J. Appl. Phys. 122, 124302 (2017)
C.Z. Wang, H.Y. Xu, L. Huang, Y.C. Lai, Phys. Rev. B 96, 115440 (2017)
O.V. Bugaiko, D.O. Oriekhov, J. Phys.: Condens. Matter 31, 325501 (2019)
D. Huang, A. Iurov, H.Y. Xu, Y.C. Lai, G. Gumbs, Phys. Rev. B 99, 245412 (2019)
H.Y. Xu, Y.C. Lai, Phys. Rev. Res. 2, 013062 (2020)
C.D. Han, H.Y. Xu, Y.C. Lai, Phys. Rev. Res. 2, 013116 (2020)
A.R. Akhmerov, C.W.J. Beenakker, Phys. Rev. B 77, 085423 (2008)
M. Grujić, M. Zarenia, A. Chaves, M. Tadić, G.A. Farias, F.M. Peeters, Phys. Rev. B 84, 205441 (2011)
J. Wurm, M. Wimmer, H.U. Baranger, K. Richter, Semicond. Sci. Technol. 25, 034003 (2010)
A. Filusch, C. Wurl, A. Pieper, H. Fehske, J. Low Temp. Phys. 191, 259 (2018)
M.V. Berry, R. Mondragon, Proc. R. Soc. Lond. A 412, 53 (1987)
M. Abramowitz, I.A. Stegun,Handbook of Mathematical Functions with formulas, graphs, and mathematical tables (Dover, New York, 1970)
A. Weiße, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006)
H.Y. Xu, Y.C. Lai, Phys. Rev. Res. 2, 023368 (2020)
P.S. Davids, Phys. Rev. B 52, 4146 (1995)
C.W. Groth, M. Wimmer, A.R. Akhmerov, X. Waintal, New J. Phys. 16, 063065 (2014)
G. Schubert, H. Fehske, Phys. Rev. Lett. 108, 066402 (2012)
A. Pieper, G. Schubert, G. Wellein, H. Fehske, Phys. Rev. B 88, 195409 (2013)
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
G. Schubert, J. Schleede, H. Fehske, Phys. Rev. B 79, 235116 (2009)
J. Schleede, G. Schubert, H. Fehske, Europhys. Lett. 90, 17002 (2010)
H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002)
J.H. Bardarson, J. Tworzydło, P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. Lett. 99, 106801 (2007)
G. Schubert, J. Schleede, K. Byczuk, H. Fehske, D. Vollhardt, Phys. Rev. B 81, 155106 (2010)
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Filusch, A., Fehske, H. Electronic properties of α − 𝒯3 quantum dots in magnetic fields. Eur. Phys. J. B 93, 169 (2020). https://doi.org/10.1140/epjb/e2020-10178-2
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DOI: https://doi.org/10.1140/epjb/e2020-10178-2