Highlights d Simultaneous recording of sequentially active premotor neurons during singing d Models suggest that network delays impact song-related population activity d Ultraslow axonal conduction within HVC generates substantial network delays d Local axonal delays shape spatial patterns of activity within a neural circuit

The E = 0 octet of bilayer graphene in the filling factor range of -4 <  < 4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.2 Bilayer graphene provides a fascinating platform to explore potentially new phenomena in the quantum Hall regime of a two-dimensional electron gas (2DEG). The existence of two spins, two valley indices K and Kʹ, and two isospins corresponding to the n = 0 and 1 orbital wave functions results in an eight-fold degeneracy of the singleparticle E = 0 Landau level (LL) in a perpendicular magnetic field B [1,2]. This SU (8) phase space provides ample opportunities for the emergence of broken-symmetry manybody ground states [3][4][5][6][7][8][9][10][11][12][13][14][15]. The application of a transverse electric field E drives valley polarization through their respective occupancy of the two constituent layers [1,2]. Coulomb exchange interactions, on the other hand, enhance spin ordering and promote isospin doublets [11,15,16]. As a result of these intricate competitions, the E = 0 octet of bilayer graphene (integer filling factor range -4 <  < 4) exhibits a far richer phase diagram than their semiconductor counterparts. Experiments have uncovered 4, 3, 2, 1 coincidence points for filing factors = 0, ±1, ±2 and ±3 respectively, where the crossing of two LLs leads to the closing of the gap and signals the phase transition of the ground state from one order to another [13,[15][16][17][18]. Their appearance provides key information to the energetics of the LLs and the nature of the ground states involved. Indeed, coincidence studies on semiconducting 2DEGs are used to probe the magnetization of quantum Hall states [19] and measure the many-body enhanced spin susceptibility [20]. In bilayer graphene, the valley and isospin degrees of freedom increase the number of potential many-body coherent ground states. Furthermore, the impact of actively controlling these degrees of freedom became evident in the recent observations of fractional and even-denominator fractional quantum Hall effects [17,[21][22][23][24][25].A good starting point of exploring this rich landscape would be a single-particle, or single-particlelike LL diagram, upon which interaction effects can be elucidated perturbatively. Indeed, even in the inherently strongly interacting fractional quantum Hall effect, effective single-particle models, e.g. the composite fermion model [26], can capture the bulk of the interaction effects and provide conceptually simple and elegant ways to understand complex many-body phenomena. In bilayer graphene, a LL ...

Charged plasma and Fermi liquid are two distinct states of electronic matter intrinsic to dilute two-dimensional electron systems at elevated and low temperatures, respectively. Probing their thermodynamics represents challenge because of lack of an adequate technique. Here, we report a thermodynamic method to measure the entropy per electron in gated structures. Our technique appears to be three orders of magnitude superior in sensitivity to a.c. calorimetry, allowing entropy measurements with only 10 8 electrons. This enables us to investigate the correlated plasma regime, previously inaccessible experimentally in twodimensional electron systems in semiconductors. In experiments with clean two-dimensional electron system in silicon-based structures, we traced entropy evolution from the plasma to Fermi liquid regime by varying electron density. We reveal that the correlated plasma regime can be mapped onto the ordinary non-degenerate Fermi gas with an interaction-enhanced temperature-dependent effective mass. Our method opens up new horizons in studies of low-dimensional electron systems.

SUMMARYSequential activation of neurons has been observed during various behavioral and cognitive processes and is thought to play a critical role in their generation. Here, we studied a circuit in the songbird forebrain that drives the performance of adult courtship song. In this region, known as HVC, neurons are sequentially active with millisecond precision in relation to behavior. Using large-scale network models, we found that HVC sequences could only be accurately produced if sequentially active neurons were linked with long and heterogeneous axonal conduction delays. Although such latencies are often thought to be negligible in local microcircuits, we empirically determined that HVC interconnections were surprisingly slow, generating delays up to 22 ms. An analysis of anatomical reconstructions suggests that similar processes may also occur in rat neocortex, supporting the notion that axonal conduction delays can sculpt the dynamical repertoire of a range of local circuits.

During development, neurons arrive at local brain areas in an extended period of time, but how they form local neural circuits is unknown. Here we computationally model the emergence of a network for precise timing in the premotor nucleus HVC in songbird. We show that new projection neurons, added to HVC post hatch at early stages of song development, are recruited to the end of a growing feedforward network. High spontaneous activity of the new neurons makes them the prime targets for recruitment in a self-organized process via synaptic plasticity. Once recruited, the new neurons fire readily at precise times, and they become mature. Neurons that are not recruited become silent and replaced by new immature neurons. Our model incorporates realistic HVC features such as interneurons, spatial distributions of neurons, and distributed axonal delays. The model predicts that the birth order of the projection neurons correlates with their burst timing during the song.

We report first thermodynamic measurements of the temperature derivative of chemical potential (∂µ/∂T ) in two-dimensional (2D) electron systems. In order to test the technique we have chosen Schottky gated GaAs/AlGaAs heterojunctions and detected experimentally in this 2D system quantum magnetooscillations of ∂µ/∂T . We also present a Lifshits-Kosevitch type theory for the ∂µ/∂T magnetooscillations in 2D systems and compare the theory with experimental data. The magnetic field dependence of the ∂µ/∂T value appears to be sensitive to the density of states shape of Landau levels. The data in low magnetic field domain demonstrate brilliant agreement with theory for non-interacting Fermi gas with Lorentzian Landau level shape.Quantum oscillations are known to be a universal tool to study the electron energy spectrum (Fermi surface cross-sections, electron effective mass and g-factor) in three-dimensional single crystals and two-dimensional (2D) systems. In contrast to the 3D-case, the 2D systems allow in-situ tuning the spectrum and the Fermi energy by various methods (including electric field effect in gated structures, illumination, uniaxial stress etc.), and, hence, allow comprehensive magnetooscillation studies. Quantum oscillations in 2D systems are most often studied in resistivity (Shubnikov-de Haas effect) [ functions µ 1,2 ), the charge of the plates is C(µ 1 − µ 2 )/e, where C is the electric capacitance. Correspondingly, when the two plates are connected electrically and an external parameter varies affecting one of the chemical potential values, a recharging current starts flowing between the plates. The recharging current is proportional to ∆µ (in case the capacitance C varies), ∝ ∂µ/∂n (in case one of the plates is a 2D gas of a density n varying with a gate voltage [6,7]), In our study we apply the technique of measuring ∂µ/∂T similar to that used by Nizhankovskii for bulk samples [10], to the 2D electron systems in magnetic field. We focus on ∂µ/∂T oscillations to compare them with semiclassical theory, and to determine the shape of the density of states of Landau levels. The advantage of the temperature modulation technique is the absence of eddy currents or a background signal (concomitant of many other techniques), and its pure thermodynamic origin.Qualitative discussion. -It is worthwhile to give a qualitative explanation why ∂µ/∂T oscillates with perpendicular magnetic field. For the bare quadratic energy spectrum, ε(p) = p 2 /2m, the single electron density of states is constant in two dimensions. At temperatures T ≪ E F the number of particle-like excitations above µ equals to the number of hole-like excitations below µ (hatched areas in Fig. 1a). Therefore, for a fixed electron density n the chemical potential is independent of temperature, ∂µ/∂T = 0, with exponential accuracy at low temperatures, T ≪ E F , where E F stands for the Fermi energy. In the case of energy dependent density of states (like e.g. in 3D systems, graphene or 2D systems in quantizing magnetic field), one can expand it...

1During development, neurons arrive at local brain areas in extended period of time, but how 2 they form local neural circuits is unknown. Here we computationally model the emergence of 3 a network for precise timing in the premotor nucleus HVC in songbird. We show that new 4 motor projection neurons, mostly added to HVC before and during song learning, are recruited 5 to the end of a growing feedforward network. High spontaneous activity of new neurons makes 6 them the prime targets for recruitment in a self-organized process via synaptic plasticity. Once 7 recruited, the new neurons fire readily at precise times, and they become mature. Neurons that 8 are not recruited become silent and replaced by new immature neurons. Our model incorporates 9 realistic HVC features such as interneurons, spatial distributions of neurons, and distributed 10 axonal delays. The model predicts that the birth order of the projection neurons correlates with 11 their burst timing during the song. 12 Significance Statement 13 Functions of local neural circuits depend on their specific network structures, but how the net-14 works are wired is unknown. We show that such structures can emerge during development 15 through a self-organized process, during which the network is wired by neuron-by-neuron re-16 cruitment. This growth is facilitated by steady supply of immature neurons, which are highly 17 excitable and plastic. We suggest that neuron maturation dynamics is an integral part of con-18 structing local neural circuits. 19 During development, the birth order of neurons plays a critical role in constructing the brain's 21 large-scale structures. In mammalian cortex, neurons that are destined to the deep cortical 22 layers are born earlier than those to the superficial layers [1, 2]. In rodent hippocampus, earlier 23 born neurons and late born neurons form distinctive parallel circuits through the hippocampal 24 pathway [3]. However, whether birth order is also important in constructing microcircuits in 25 local brain areas is unknown [4]. The premotor nucleus HVC (proper name) of the zebra finch 26 provides an excellent opportunity to investigate this issue. 27HVC is a premotor nucleus that drives singing of the courtship song in the zebra finch [5, 6]. 28 An adult zebra finch sings repetitions of a motif consisting of fixed sequence of syllables [7]. 29 Excitatory HVC neurons that project to the downstream premotor area RA (robust nucleus of 30 the arcopallium) encode the timing of acoustic features of the song [8]. Each HVCRA neuron 31 bursts once during the motif [8, 9]. As a population, HVCRA neurons sequentially burst through 32 the entire motif [10, 11]. 33 There is strong evidence that the sequential bursting of HVCRA neurons is generated within 34 HVC [12, 9, 13, 14]. Moreover, HVCRA neurons most likely form a feedforward synaptic chain 35 network, which supports propagation of burst spikes [15, 9]. Such a microcircuit in HVC acts as 36 an infrastructure for subsequent learning of the song, during whi...

Narrow HgTe quantum wells are remarkable by presence of poorly conductive two-dimensional heavy hole subband (located in the local valleys) states atop of well-conductive Dirac-like light holes at the Γ point. Here we propose and employ two methods to measure the density of states for these heavy holes. The first method uses the gate-recharging technique to measure thermodynamical entropy per particle. As the Fermi level is tuned with gate voltage from light to heavy subband, the entropy increases dramatically, and the value of this increase gives the estimate for the density of states. The second method determines the density of states for heavy holes indirectly from the gate voltage dependence of the period of the Shubnikov-de Haas oscillations for light holes. The results obtained by both methods are in the reasonable agreement with each other. Our approaches can be applied to measure large effective carrier masses in other two-dimensional gated systems.