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Action potential generation underlies some of the most consequential dynamical systems on Earth, from brains to hearts. It is therefore interesting to develop synthetic cell-free systems, based on the same molecular mechanisms, which may allow for the exploration of parameter regions and phenomena not attainable, or not apparent, in the live cell. We previously constructed such a synthetic system, based on biological components, which fires action potentials. We call it "Artificial Axon". The system is minimal in that it relies on a single ion channel species for its dynamics. Here we characterize the Artificial Axon as a dynamical system in time, using a simplified Hodgkin-Huxley model adapted to our experimental context. We construct a phase diagram in parameter space identifying regions corresponding to different temporal behavior, such as Action Potential (AP) trains, single shot APs, or damped oscillations. The main new result is the finding that our system with a single ion channel species, with inactivation, is dynamically equivalent to the system of two channel species without inactivation (the Morris-Lecar system), which exists in nature. We discuss the transitions and bifurcations occurring crossing phase boundaries in the phase diagram, and obtain criteria for the channels' properties necessary to obtain the desired dynamical behavior. In the second part of the paper we present new experimental results obtained with a system of two AAs connected by excitatory and/or inhibitory electronic "synapses". We discuss the feasibility of constructing an autonomous oscillator with this system., Comment: 14 pages, 21 figures

The Artificial Axon is a unique synthetic system, based on biomolecular components, which supports action potentials. Here we examine, experimentally and theoretically, the properties of the threshold for firing in this system. As in real neurons, this threshold corresponds to the critical point of a saddle-node bifurcation. We measure the delay time for firing as a function of the distance to threshold, recovering the expected scaling exponent of $- 1/2$. We introduce a minimal model of the Morris-Lecar type, validate it on the experiments, and use it to extend analytical results obtained in the limit of "fast" ion channel dynamics. In particular, we discuss the dependence of the firing threshold on the number of channels. The Artificial Axon is a simplified system, an Ur-neuron, relying on only one ion channel species for functioning. Nonetheless, universal properties such as the action potential behavior near threshold are the same as in real neurons. Thus we may think of the Artificial Axon as a cell-free breadboard for electrophysiology research., Comment: 11 pages, 14 figures

The celebrated phenomenon of quantum Hall effect has recently been generalized from transport of conserved charges to that of other approximately conserved state variables, including spin and valley, which are characterized by spin- or valley-polarized boundary states with different chiralities. Here, we report a new class of quantum Hall effect in ABA-stacked graphene trilayers (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the systems mirror reflection symmetry. At the charge neutrality point and a small perpendicular magnetic field $B_{\perp}$, the longitudinal conductance $\sigma_{xx}$ is first quantized to $4e^2/h$, establishing the presence of four edge channels. As $B_{\perp}$ increases, $\sigma_{xx}$ first decreases to $2e^2/h$, indicating spin-polarized counter-propagating edge states, and then to approximately $0$. These behaviors arise from level crossings between even and odd parity bulk Landau levels, driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong $B_{\perp}$ limit, and a spin-polarized state at intermediate fields. The transitions between spin-polarized and unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

The use of relative twist angle between adjacent atomic layers in a van der Waals heterostructure, has emerged as a new degree of freedom to tune electronic and optoelectronic properties of devices based on 2D materials. Using ABA-stacked trilayer (TLG) graphene as the model system, we show that, contrary to conventional wisdom, the band structures of 2D materials are systematically tunable depending on their relative alignment angle between hexagonal BN (hBN), even at very large twist angles. Moreover, addition or removal of the hBN substrate results in an inversion of the K and K' valley in TLG's lowest Landau level (LL). Our work illustrates the critical role played by substrates in van der Waals heterostructures and opens the door towards band structure modification and valley control via substrate and twist angle engineering.

As the Fermi level and band structure of two-dimensional materials are readily tunable, they constitute an ideal platform for exploring Lifshitz transition, a change in the topology of a material's Fermi surface. Using tetralayer graphene that host two intersecting massive Dirac bands, we demonstrate multiple Lifshitz transitions and multiband transport, which manifest as non-monotonic dependence of conductivity on charge density n and out-of-plane electric fieldD, anomalous quantum Hall sequences and Landau level crossings that evolve with n, D and B., Comment: accepted to PRL

Owing to the spin, valley, and orbital symmetries, the lowest Landau level (LL) in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall states in bilayer graphene with controlled layer polarization. The state at filling factor {\nu}=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the {\nu}=2/3 quantum Hall state and a feature at {\nu}=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.