Tunneling theory for a bilayer graphene quantum dot’s single- and two-electron states

Abstract

The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states' orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot's spin and valley multiplets induced by interactions and magnetic field (the latter splittings being a consequence of bilayer graphene's Berry curvature). Our results elucidate spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.

Automated Reconstruction of Bound States in Bilayer Graphene Quantum Dots

“…For future considerations, one can analyze the role of the nondimer atom sites tunneling, causing trigonal warping or electron-electron exchange interactions [43,44], both neglected in our theory assumptions. In fact, it would be very interesting to combine the most recent available experimental data [44,45] with the most advanced theory description [43,46], through the algorithmic methodology introduced here.…”

Gate‐Controlled Quantum Dots Based on 2D Materials

“…In addition, two‐particle states in bilayer graphene quantum dots, [ 186 ] which are more complicated, have also been studied. For both spin and valley wavefunction components, there are three symmetric (triplet state $$|T_{S,V}^{0, \pm }\rangle $$) and one anti‐symmetric (singlet state $$|{S_{S,V}}\rangle $$) two‐particle states, where S ( V ) indicates spin (valley) degree of freedom.…”

Probing two-electron multiplets in bilayer graphene quantum dots

“…This is all the more true since the spin and valley (K + , K − ) degrees of freedom in BLG yield a total of 16 twoparticle states where the wavefunction-dependent valley g-factors give rise to a rich level spectrum. The total two-particle wavefunction in BLG can be factorized into an orbital, a spin and a valley term [16,17], resulting in 6 states with an anti-symmetric spin-valley and a symmetric orbital wavefunction, and 10 states with a symmetric spin-valley and an anti-symmetric orbital wavefunction. This gives rise to the symmetric and anti-symmetric multiplet structure of the two-electron spectrum in BLG.…”

“…Additionally, orbitally symmetric two-particle states are affected by short-range symmetry breaking interactions induced by fluctuations [18][19][20], since their orbital wavefunctions have non-zero density at the relevant short inter-particle distances. Such short-range interactions break the symmetries in sublattice and valley space, introducing splittings δ 1,2 proportional to the strength of the corresponding short-range interactions [17]. The energy of the spinand valley-dependent part is determined by the coupling to the magnetic field and the spin-orbit coupling.…”

“…3(c) allow conclusions about the microscopic short-range interaction constants in BLG. We can relate the multiplet splittings δ 1,2 to the short-range coupling constants [17][18][19], g ⊥ , (quantifying inter-valley scattering) and, g z0 , g 0z , (generated by "current-current" interactions): δ 1 + δ 2 = 8|g ⊥ J| and δ 2 − δ 1 = 4|(g z0 + g 0z )J|, where J captures the wavefunction overlap of the specific QD state [16,17]. Consequently, our experimental observation of near-vanishing δ 1 indicates that inter-valley scattering and "current-current" interactions are of the same magnitude in our system, i.e., 2|g ⊥ | ≈ |g z0 + g 0z |.…”