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Beurling densities of regular spectra of self-similar spectral measure with consecutive digit sets
Beurling density plays a key role in the study of frame-spectrality of
normalized Lebesgue measure restricted to a set. Accordingly, in this paper,
the authors study the -Beurling densities of regular maximal orthogonal sets
of a class of self-similar spectral measures, where is the Hausdorff
dimension of its support and obtain their exact upper bound of the densities
Gate-Tunable Tunneling Resistance in Graphene/Topological Insulator Vertical Junctions
Graphene-based vertical heterostructures, particularly stacks incorporated
with other layered materials, are promising for nanoelectronics. The stacking
of two model Dirac materials, graphene and topological insulator, can
considerably enlarge the family of van der Waals heterostructures. Despite well
understanding of the two individual materials, the electron transport
properties of a combined vertical heterojunction are still unknown. Here we
show the experimental realization of a vertical heterojunction between Bi2Se3
nanoplate and monolayer graphene. At low temperatures, the electron transport
through the vertical heterojunction is dominated by the tunneling process,
which can be effectively tuned by gate voltage to alter the density of states
near the Fermi surface. In the presence of a magnetic field, quantum
oscillations are observed due to the quantized Landau levels in both graphene
and the two-dimensional surface states of Bi2Se3. Furthermore, we observe an
exotic gate-tunable tunneling resistance under high magnetic field, which
displays resistance maxima when the underlying graphene becomes a quantum Hall
insulator
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