Robust Quantum Oscillation of Dirac Fermions in a Single-Defect Resonant Transistor

Abstract

The massless nature of Dirac Fermions produces large energy gaps between Landau levels (LLs), which is promising for topological devices. While the energy gap between the zeroth and first LLs reaches 36 meV in a magnetic field of 1 T in graphene, exploiting the quantum Hall effect at room temperature requires large magnetic fields (∼30 T) to overcome the energy level broadening induced by charge inhomogeneities in the device. Here, we report a way to use the robust quantum oscillations of Dirac Fermions in a single-defect resonant transistor, which is based on local tunneling through a thin (∼1.4 nm) hexagonal boron nitride (h-BN) between lattice-orientation-aligned graphene layers. A single point defect in the h-BN, selected by the orientation-tuned graphene layers, probes local LLs in its proximity, minimizing the energy broadening of the LLs by charge inhomogeneity at a moderate magnetic field and ambient conditions. Thus, the resonant tunneling between lattice-orientation-aligned graphene layers highlights the potential to spectroscopically locate the atomic defects in the h-BN, which contributes to the study on electrically tunable single photon source via defect states in h-BN.

A magnetically-induced Coulomb gap in graphene due to electron-electron interactions

“…Figure 4a shows in more detail the B field-dependence of the tunnel current I(B) using a small but finite bias V b = 0.6 mV, V g = 1.65 V and at three different temperatures, 0.3, 2 and 7 K. The 3 peaks labelled p = 1, 2 and 3 in Fig. 4a occur at magnetic fields B p , B 1 = 3.85 ± 0.02 T, B 2 = 1.97 ± 0.02 T and B 3 = 1.30 ± 0.02 T. These magneto-oscillations are periodic in 1/B with a frequency 1/B F = 1/(3.9 ± 0.05) T −1 , see inset, where B F = pB p and B p is the magnetic field value of the peak with index p. They are superficially similar in form to Shubnikov-de-Haas magnetooscillations 24 but have a different physical origin. The sharp resonant peaks in the tunnel current occur at zero bias when the Landau levels in each graphene layer are aligned energetically with each other and with the defect energy level in the hBN layer, E 1 , which is measured with respect to the Dirac point of the bottom graphene layer:…”

“…When the lattices of the graphene layers are aligned so that their relative angular misorientation (twist angle) is small, ≲3°, electrons can tunnel coherently between the Dirac cones of the two layers with the conservation of momentum [8][9][10][11][12][13][14][15] . When the twist angle is large, an electron must scatter in order to tunnel between the misaligned Dirac cones; in this case, tunnelling can occur by phonon-assisted electron tunnelling [16][17][18] or by hopping via defects or impurities within the tunnel barrier [18][19][20][21][22][23][24][25][26] . The large twist angle of ≈30°between the two graphene layers in our devices ensures that direct band-to-band tunnelling with conservation of in-plane momentum is suppressed.…”

“…A high quality hBN tunnel barrier typically contains within its band gap only a small number of strongly localised defect states, each with a sharply-defined energy level. Such a quantised state can provide a channel through which electrons can tunnel resonantly from one graphene layer to the other [18][19][20][21][22][23][24][25][26] . We have selected a device with a single active localised state within the tunnel barrier.…”

Phase Engineering of 2D Materials

“…130 Hydrogenation and passivation have been often used to preserve the pristine nature of subtle 2D materials. 131,132 Such phase engineering has been supported by many theoretical studies with various aspects and influences of ion intercalations. 130,133−137 Intercalation critically modulates the interlayer coupling strength between layers in 2D materials.…”

“…Another way to stabilize the metastable 1T phase of MoS 2 was suggested by Yazdani et al They reported that encapsulating Li-MoS 2 with top and bottom h-BN layers can optimize the thermodynamic energy barrier for the phase transition between 2H and 1T′ . Hydrogenation and passivation have been often used to preserve the pristine nature of subtle 2D materials. , Such phase engineering has been supported by many theoretical studies with various aspects and influences of ion intercalations. ,− …”