Kavli Affiliate: Alessandra Lanzara
| First 5 Authors: Samuel T. Ciocys, Quentin Marsal, Paul Corbae, Daniel Varjas, Ellis Kennedy
| Summary:
In our understanding of solids, the formation of highly spatially coherent
electronic states, fundamental to command the quantum behavior of materials,
relies on the existence of discrete translational symmetry of the crystalline
lattice. In contrast, in the absence of long-range order, as in the case of
non-crystalline materials, the electronic states are localized and electronic
coherence does not develop. This brings forward the fundamental question
whether long range order is necessary condition to establish coherence and
structured momentum-dependent electronic state, and how to characterize it in
the presence of short-range order. Here we study Bi$_2$Se$_3$, a material that
exists in its crystalline form with long range order, in amorphous form, with
short and medium range order, and in its nanocrystalline form, with reduced
short range order. By using angle resolved photoemission spectroscopy to
directly access the electronic states in a momentum resolved manner, we reveal
that, even in the absence of long-range order, a well-defined real-space length
scale is sufficient to produce dispersive band structures. Moreover, we observe
for the first time a repeated Fermi surface structure of duplicated annuli,
reminiscent of Brillouin zone-like repetitions. These results, together with
our simulations using amorphous Hamiltonians, reveal that the typical momentum
scale where coherence occurs is the inverse average nearest-neighbor distance,
the direct fingerprint of the local order of the underlying atomic structure.
These results, not only lead the way to a new understanding of electronic
coherence in solids, but also open the way to the realization of novel
momentum-dependent quantum phenomena such as momentum pairing and spin-orbit
coupling, in a much broader class of materials than the currently studied ones,
lacking long range crystalline translational symmetry.
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