Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene

Abstract

Energy spectroscopy of strongly interacting phases requires probes which minimize screening while retaining spectral resolution and local sensitivity. Here, we demonstrate that such probes can be realized using atomic sized quantum dots bound to defects in hexagonal Boron Nitride tunnel barriers, placed at nanometric distance from graphene. With dot energies capacitively tuned by a planar graphite electrode, dot-assisted tunneling becomes highly sensitive to the graphene excitation spectrum. The spectra track the onset of degeneracy lifting with magnetic field at the ground state, and at unoccupied excited states, revealing symmetry-broken gaps which develop steeply with magnetic field - corresponding to Landé g factors as high as 160. Measured up to B = 33 T, spectra exhibit a primary energy split between spin-polarized excited states, and a secondary spin-dependent valley-split. Our results show that defect dots probe the spectra while minimizing local screening, and are thus exceptionally sensitive to interacting states.

Spectroscopy of NbSe2 Using Energy-Tunable Defect-Embedded Quantum Dots

“…Such high charging energies, associated with a very small volume of the QD, are consistent with previous reports [14][15][16] . We also notice that at these high biases, the QD transport features exhibit finite curvature -due to the change in QD-Gate capacitance associated with a change in the graphene DOS 16 . To interpret this result we recall from Equation (1) that the total conductance G is a sum of the direct tunneling G t and QD assisted tunneling G d .…”

“…We find that even when scanning V BG over a range of ±90 V, no evidence of a successive Coulomb diamond appears 16 , setting a lower limit for the charging energy of E C > 50 meV. Such high charging energies, associated with a very small volume of the QD, are consistent with previous reports [14][15][16] . We also notice that at these high biases, the QD transport features exhibit finite curvature -due to the change in QD-Gate capacitance associated with a change in the graphene DOS 16 .…”

“…Van der Waals barriers host atomic point defects [8][9][10][11][12] associated with localized energy states addressable in electrical transport measurements [13][14][15][16] . A recent study from our group by Dvir et al 17 , showed that when these barrier-bound defects are placed in proximity to a vdW superconductor, the heterostructure emulates the quantum dot (QD) -superconductor (SC) systems often studied in nanowires (NW) [18][19][20][21] .…”

“…For electrodes on NbSe 2 , a pre-evaporation ion milling step using Argon ions is carried out for obtaining oxide-free low resistance contacts. The schematics in Figure 1(c) show how a graphene electrode permits the penetration of electric field exerted by an external gate [14][15][16] , by tracking the evolution of the dot potential µ dot with the application of back gate voltage V BG . The left panel depicts the potential map assuming the electrochemical potential φ (z) is constant at V BG = 0 with graphene at zero density.…”

Energy spectra of graphene quantum dots induced between Landau levels

“…This property offers a superior control over the dot states compared to dot states formed in nano-sheets of graphene. 6 The results are relevant to other confined systems formed in two-dimensional materials by external fields, [16][17][18][19][20][21][22][23][24][25] as well as to general hybrid graphene-based systems including defects and heterostructures. [26][27][28][29][30][31][32][33] Section II presents the physical model of the graphene quantum dot and explains with some qualitative arguments how the discrete levels of the dot emerge from the bulk Lan-dau levels.…”