Abstract
The quantum state of matter of a two-dimensional Dirac material with a buckled honeycomb structure can be tuned by an electric field. In the absence of an external electric field the material is a topological insulator owing to the spin-orbit coupling, which opens a band gap at the K and K ’ points of the Brillouin zone. The size of this band gap decreases with increasing electric field until eventually the band gap completely closes at a critical electric field E c and the material becomes a semi-metal. For electric fields exceeding E c the band gaps reopens again and the material undergoes a topological phase transition from a semi-metal to a normal band insulator. The electric field in a tunnel junction depends on the applied voltage bias across the junction as well as the difference in work function of the two electrodes. Here we show how scanning tunneling microscopy can be employed to simultaneously apply an electric field and study the electronic structure of a two-dimensional Dirac material with a buckled honeycomb structure. The electric field applied by the scanning tunneling microscope offers the possibility to locally alter the quantum state of matter of two-dimensional topological insulator to a semi-metal or normal band insulator. This results in the development of topologically protected spin polarized edge states within the material. We present a spectroscopic method to probe these topologically protected edge states. • Electric field induces topological phase transitions in 2D materials. •A method to probe topologically protected edge modes in a 2D Dirac material is proposed. • The band gap in a 2D Dirac material with a buckled honeycomb lattice can be tuned by an electric field.
Highlights
The successful isolation of graphene [1,2], i.e. a single layer of sp2 hybridized carbon atoms arranged in a honeycomb structure, has resulted into the opening of a new research field
If spin-orbit coupling is not taken into account, graphene has no band gap and a vanishing density of states at the Fermi level
Spin-orbit coupling is taken into account a band gap at the K and K’ points of the Brillouin zone is present
Summary
The successful isolation of graphene [1,2], i.e. a single layer of sp hybridized carbon atoms arranged in a honeycomb structure, has resulted into the opening of a new research field. Theoretical studies have revealed that the graphene-like allotropes of silicon, germanium and tin referred to as silicene, germanene and stanene respectively, can exist These two-dimensional materials share many properties with their carbon counterpart [17,18,19,20,21]. With increasing electric field silicene, germanene and stanene undergo a topological phase transition from a topological insulator to a semi-metal and subsequently to a normal band insulator [23,24,30,31] It has been pointed out by Ezawa {24] that the applica tion of an inhomogeneous electric field, for instance by using a scanning tunneling microscope, can result in the development of topologically protected and spin polarized edge states anywhere within the two-dimensional material [24]. The topo logically protected edge states act as barriers for incoming electron waves resulting in standing wave patterns, which will show up as peaks in the scanning tunneling spectroscopy spectra
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