Abstract
Image potential states (IPSs) are electronic states localized in front of a surface in a potential well, formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid, a double Rydberg series of IPSs has been predicted, which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunneling spectroscopy and the results are compared with ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.
Highlights
The highly oriented pyrolitic graphite (HOPG) crystal used was cleaved in situ under ultrahigh vacuum (UHV) conditions (1 × 10−10 mbar)
The samples were imaged at 4.2 K in constant current mode in the scanning tunneling microscope (STM)
Self-consistent density functional calculations of the electronic structure of the isolated ML and BL graphene sheets were performed using the plane-wave basis set with a cut-off of 50 Ryd and a 36 × 36 k grid for the density within a local density approximation (LDA) with exchangecorrelation potential of [16]
Summary
The image potential states (IPSs) have been measured using a home-built scanning tunneling microscope under ultrahigh vacuum (UHV) conditions. The samples were imaged at 4.2 K in constant current mode in the scanning tunneling microscope (STM). Scanning tunneling spectroscopic (STS) measurements of the IPSs were performed with constant current in a closed feedback loop where the distance–voltage (z(V )) characteristics and the dI /dV signal were simultaneously recorded [9, 10, 12]. All spectroscopic measurements have been measured with the modulation technique using a lock-in amplifier, where the voltage modulation to the sample bias voltage was 20 mV at a frequency of 1 kHz. The lock-in signal (dI /dV ) shows peaks corresponding to the Stark shifted IPSs
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