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The recently discovered flat electronic bands and strongly correlated and superconducting phases in magic-angle twisted bilayer graphene (MATBG)(1,2) crucially depend on the interlayer twist angle, theta. Although control of the global theta with a precision of about 0.1 degrees has been demonstrated(1-7), little information is available on the distribution of the local twist angles. Here we use a nanoscale on-tip scanning superconducting quantum interference device (SQUID-on-tip)(8) to obtain tomographic images of the Landau levels in the quantum Hall state(9) and to map the local theta variations in hexagonal boron nitride (hBN)-encapsulated MATBG devices with relative precision better than 0.002 degrees and a spatial resolution of a few moire periods. We find a correlation between the degree of theta disorder and the quality of the MATBG transport characteristics and show that even state-of-the-art devices-which exhibit correlated states, Landau fans and superconductivity-display considerable local variation in theta of up to 0.1 degrees, exhibiting substantial gradients and networks of jumps, and may contain areas with no local MATBG behaviour. We observe that the correlated states in MATBG are particularly fragile with respect to the twist-angle disorder. We also show that the gradients of theta generate large gate-tunable in-plane electric fields, unscreened even in the metallic regions, which profoundly alter the quantum Hall state by forming edge channels in the bulk of the sample and may affect the phase diagram of the correlated and superconducting states. We thus establish the importance of theta disorder as an unconventional type of disorder enabling the use of twist-angle gradients for bandstructure engineering, for realization of correlated phenomena and for gate-tunable built-in planar electric fields for device applications.

SQUID-on-tip tomographic imaging of Landau levels in magic-angle graphene provides nanoscale maps of local twist-angle disorder and shows that its properties are fundamentally different from common types of disorder.

Solid-state lithium metal batteries require accommodation of electrochemically generated mechanical stress inside the lithium: this stress can be(1,2) up to 1 gigapascal for an overpotential of 135 millivolts. Maintaining the mechanical and electrochemical stability of the solid structure despite physical contact with moving corrosive lithium metal is a demanding requirement. Using in situ transmission electron microscopy, we investigated the deposition and stripping of metallic lithium or sodium held within a large number of parallel hollow tubules made of a mixed ionic-electronic conductor (MIEC). Here we show that these alkali metals-as single crystals-can grow out of and retract inside the tubules via mainly diffusional Coble creep along the MIEC/metal phase boundary. Unlike solid electrolytes, many MIECs are electrochemically stable in contact with lithium (that is, there is a direct tie-line to metallic lithium on the equilibrium phase diagram), so this Coble creep mechanism can effectively relieve stress, maintain electronic and ionic contacts, eliminate solid-electrolyte interphase debris, and allow the reversible deposition/stripping of lithium across a distance of 10 micrometres for 100 cycles. A centimetre-wide full cell-consisting of approximately 10(10) MIEC cylinders/solid electrolyte/LiFePO4-shows a high capacity of about 164 milliampere hours per gram of LiFePO4, and almost no degradation for over 50 cycles, starting with a 1x excess of Li. Modelling shows that the design is insensitive to MIEC material choice with channels about 100 nanometres wide and 10-100 micrometres deep. The behaviour of lithium metal within the MIEC channels suggests that the chemical and mechanical stability issues with the metal-electrolyte interface in solid-state lithium metal batteries can be overcome using this architecture.

By containing lithium metal within oriented tubes of a mixed ionic-electronic conductor, a 3D anode for lithium metal batteries is produced that overcomes chemomechanical stability issues at the electrolyte interface.