Ferrotronics for the creation of band gaps in graphene

We experimentally demonstrate a simple graphene/ferrolectric device, termed ferrotronic (electronic effect from ferroelectric) device in which the band structure of single-layer graphene is modified. The device architecture consists of graphene deposited on a ferroelectric substrate which encodes a periodic surface potential achieved through domain engineering. This structure takes advantage of the nature of conduction through graphene to modulate the Fermi velocity of the charge carriers by the variations in surface potential, leading to the emergence of energy minibands and a band gap at the superlattice Brillouin zone boundary. Our work represents a simple route to building circuits whose functionality is controlled by the underlying substrate.

Figure 1

Hybrid graphene/ferroelectric GFET device configuration. (a) Device schematic showing graphene strip on periodically poled ferroelectric substrate, and with source, drain, and backgate connections. (b) PFM phase image showing ferroelectric domains between source and drain contacts (which are at the top and bottom of the imaged strip, respectively). (c) SEM image of device showing electrical contacts on top of graphene strip. (d) Variation of surface potential difference between alternately polarized domains as a function of time.

Figure 2

Conductance measurements demonstrating existence of a band gap. (a) Conductance vs relative gate voltage of a graphene/ferroelectric device (Device A) at 10 K, where a flattened region of width $\sim 340$ meV can be seen around the Dirac point. (b) Conductance vs relative gate voltage as a function of temperature for a second device (Device B), where a series of miniband gaps are apparent up to 20 K, but not above that. (c) Data at 10 K for a reference device with no periodic domains, and which displays no evidence of any band gap.

Figure 3

Location of superlattice Brillouin zones (SBZs). (a) Band structure of graphene, whereby the locations of the SBZ are indicated on the $x$ ($k$) axis showing wave vector, on the basis of the harmonics associated with the square-wave potential. On this basis, we can determine the values of energy (related to gate voltage) where band gaps should appear; (b) mapping the locations of these band gaps onto a conductance measurement. The expected width of the band gaps decreases with increasing harmonic as expected for a square wave.

Figure 4

(a) Mapping of expected locations of miniband gaps associated with SBZ, from Fig. 3. Zones 1–6 correspond to SBZ band gaps 1–6, respectively. The proximity of these band gaps to each other and their partial overlap is what gives rise to the flattened region around the Dirac point in the conductance-relative gate voltage characteristics. Data from additional devices where the same analysis has been applied to pinpoint the positions of the SBZ, with potential parameters of (b) period 60 nm, height 200 meV and (c) period 100 nm, height 30 meV. In all cases, the zone numbers in shaded boxes are those for which the point at which the conductance drops is in good agreement with the model. For the case of the weaker potential with longer period, more deviations can be seen due to noise and incoherence issues.