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On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene

Carolien Castenmiller and Harold J. W. Zandvliet

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 Corresponding author: Harold J. W. Zandvliet, h.j.w.zandvliet@utwente.nl

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Abstract: Germanene, the germanium analogue of graphene, shares many properties with its carbon counterpart. Both materials are two-dimensional materials that host Dirac fermions. There are, however, also a few important differences between these two materials: (1) graphene has a planar honeycomb lattice, whereas germanene’s honeycomb lattice is buckled and (2) the spin-orbit gap in germanene is predicted to be about three orders of magnitude larger than the spin-orbit gap in graphene (24 meV for germanene versus 20 μeV for graphene). Surprisingly, scanning tunneling spectra recorded on germanene layers synthesized on different substrates do not show any sign of the presence of a spin-orbit gap. To date the exact origin of the absence of this spin-orbit gap in the scanning tunneling spectra of germanene has remained a mystery. In this work we show that the absence of the spin-orbit gap can be explained by germanene’s exceptionally low work function of only 3.8 eV. The difference in work function between germanene and the scanning tunneling microscopy tip (the work functions of most commonly used STM tips are in the range of 4.5 to 5.5 eV) gives rise to an electric field in the tunnel junction. This electric field results in a strong suppression of the size of the spin-orbit gap.

Key words: germanenespin-orbit couplingquantum spin Hall effecttwo-dimensional Dirac material



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Fig. 1.  (Color online) Buckled honeycomb lattice of germanene.

Fig. 2.  (Color online) Schematic diagram of the band structure of germanene near the K and K points of the surface Brillouin zone. From left to right: band structure without a spin-orbit gap, with a spin-orbit gap, applied electric field smaller than the critical value, applied electric field equal to the critical value and applied electric field larger than the critical value. Red and green refer to spin up and spin down bands, respectively.

[1]
Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306, 666 doi: 10.1126/science.1102896
[2]
Geim A K, Novoselov K S. The rise of graphene. Nat Mater, 2007, 6, 183 doi: 10.1038/nmat1849
[3]
Takeda K, Shiraishi K. Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Phys Rev B, 1994, 50, 14916 doi: 10.1103/PhysRevB.50.14916
[4]
Vogt P, de Padova P, Quaresima C, et al. Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys Rev Lett, 2012, 108, 155501 doi: 10.1103/PhysRevLett.108.155501
[5]
Bampoulis P, Zhang L, Safaei A, et al. Germanene termination of Ge2Pt crystals on Ge(110). J Phys Condens Matter, 2014, 26, 442001 doi: 10.1088/0953-8984/26/44/442001
[6]
Zhu F F, Chen W J, Xu Y, et al. Epitaxial growth of two-dimensional stanene. Nat Mater, 2015, 14, 1020 doi: 10.1038/nmat4384
[7]
Cahangirov S, Topsakal M, Aktürk E, et al. Two- and one-dimensional honeycomb structures of silicon and germanium. Phys Rev Lett, 2009, 102, 236804 doi: 10.1103/PhysRevLett.102.236804
[8]
Acun A, Zhang L, Bampoulis P, et al. Germanene: the germanium analogue of graphene. J Phys Condens Matter, 2015, 27, 443002 doi: 10.1088/0953-8984/27/44/443002
[9]
Kane C L, Mele E J. Z2 topological order and the quantum spin Hall effect. Phys Rev Lett, 2005, 95, 146802 doi: 10.1103/PhysRevLett.95.146802
[10]
Kane C L, Mele E J. Quantum spin Hall effect in graphene. Phys Rev Lett, 2005, 95, 226801 doi: 10.1103/PhysRevLett.95.226801
[11]
Liu C C, Feng W X, Yao Y G. Quantum spin Hall effect in silicene and two-dimensional germanium. Phys Rev Lett, 2011, 107, 076802 doi: 10.1103/PhysRevLett.107.076802
[12]
Borca B, Castenmiller C, Tsvetanova M, et al. Image potential states of germanene. 2D Mater, 2020, 7, 035021 doi: 10.1088/2053-1583/ab96cf
[13]
van Bremen R, Bampoulis P, Aprojanz J, et al. Ge2Pt hut clusters: A substrate for germanene. J Appl Phys, 2018, 124, 125301 doi: 10.1063/1.5046997
[14]
Zhang L, Bampoulis P, van Houselt A, et al. Two-dimensional Dirac signature of germanene. Appl Phys Lett, 2015, 107, 111605 doi: 10.1063/1.4931102
[15]
Walhout C J, Acun A, Zhang L, et al. Scanning tunneling spectroscopy study of the Dirac spectrum of germanene. J Phys Condens Matter, 2016, 28, 284006 doi: 10.1088/0953-8984/28/28/284006
[16]
Zhang L, Bampoulis P, Rudenko A, et al. Structural and electronic properties of germanene on MoS2. Phys Rev Lett, 2016, 116, 256804 doi: 10.1103/PhysRevLett.116.256804
[17]
Qin Z H, Pan J B, Lu S Z, et al. Direct evidence of Dirac signature in bilayer germanene Islands on Cu(111). Adv Mater, 2017, 29, 1606046 doi: 10.1002/adma.201606046
[18]
Ezawa M. A topological insulator and helical zero mode in silicene under an inhomogeneous electric field. New J Phys, 2012, 14, 033003 doi: 10.1088/1367-2630/14/3/033003
[19]
Liu C C, Jiang H, Yao Y G. Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys Rev B, 2011, 84, 195430 doi: 10.1103/PhysRevB.84.195430
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    Received: 01 July 2020 Revised: 09 July 2020 Online: Accepted Manuscript: 17 July 2020Uncorrected proof: 20 July 2020Published: 04 August 2020

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      Carolien Castenmiller, Harold J. W. Zandvliet. On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene[J]. Journal of Semiconductors, 2020, 41(8): 082003. doi: 10.1088/1674-4926/41/8/082003 C Castenmiller, H J W Zandvliet, On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene[J]. J. Semicond., 2020, 41(8): 082003. doi: 10.1088/1674-4926/41/8/082003.Export: BibTex EndNote
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      Carolien Castenmiller, Harold J. W. Zandvliet. On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene[J]. Journal of Semiconductors, 2020, 41(8): 082003. doi: 10.1088/1674-4926/41/8/082003

      C Castenmiller, H J W Zandvliet, On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene[J]. J. Semicond., 2020, 41(8): 082003. doi: 10.1088/1674-4926/41/8/082003.
      Export: BibTex EndNote

      On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene

      doi: 10.1088/1674-4926/41/8/082003
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