We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not ...for ν = 1, clearly inconsistent with Mott insulation. We compute r s = E U/E K, where E U and E K are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of ν. We find that, for ν = 1, r s fails to cross the threshold (r s = 37) for the triangular lattice, and metallic transport ensues. However, for ν = 2 and ν = 3, the thresholds r s = 22 and r s = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (ν = 2) and a kagome (ν = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.
The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic ...two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the rs parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃ 38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.
The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the E_8 lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in the sense that they ...minimize the total pair interaction energy of infinite point configurations for all completely monotone functions of the squared distance. This conjecture was recently proved by Cohn-Kumar-Miller-Radchenko-Viazovska in dimensions 8 and 24. We explain in this note how the conjecture implies the minimality of the same lattices for the Coulomb and Riesz renormalized energies as well as jellium and periodic jellium energies, hence settling the question of their minimization in dimensions 8 and 24.
The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative ...fixed-phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.
The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors (ν≲1/6) has long been a topic of interest and controversy in condensed matter. Following the recent ...breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n=6.1×10^{10}/cm^{2} and mobility μ=25×10^{6} cm^{2}/V s, we find a deep minimum in the longitudinal magnetoresistance (R_{xx}) at ν=1/7 when T≃104 mK. There is also a clear sign of a developing minimum in R_{xx} at ν=2/13. While insulating phases are still predominant when ν≲1/6, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν=p/(2mp±1) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R_{xx}∝e^{E_{A}/2kT} corroborate this view and imply the presence of pinned Wigner solid states when ν≠p/(2mp±1). Similar results are seen in another sample with a lower density, further generalizing our observations.
Abstract
We examine a charge lattice coupled to a one-dimensional asymmetric potential in the presence of an applied magnetic field, which induces gyrotropic effects in the charge motion. This system ...could be realized for Wigner crystals in nanostructured samples, dusty plasmas, or other classical charge-ordered states where gyrotropic motion and damping can arise. For zero magnetic field, an applied external ac drive can produce a ratchet effect in which the particles move along the easy flow direction of the substrate asymmetry. The zero field ratchet effect can only occur when the ac drive is aligned with the substrate asymmetry direction; however, when a magnetic field is added, the gyrotropic forces generate a Hall effect that leads to a variety of new behaviors, including a transverse ratchet motion that occurs when the ac drive is perpendicular to the substrate asymmetry direction. We show that this system exhibits commensuration effects as well as reversals in the ratchet effect and the Hall angle of the motion. The magnetic field also produces a nonmonotonic ratchet efficiency when the particles become localized at high fields.
The conductivity of a neodymium-based arti ficial honeycomb lattice undergoes dramatic changes upon application of magnetic fi elds and currents. We attribute these changes to a redistribution of ...magnetic charges that are formed at the vertices of the honeycomb due to the nonvanishing net flux of magnetization from adjacent magnetic elements. We suggest that the application of a large magnetic fi eld or a current causes a transition from a disordered state, in which magnetic charges are distributed at random, to an ordered state, in which they are regularly arranged on the sites of two interpenetrating triangular Wigner crystals. The field and current tuning of electrical properties are greatly desirable functionalities for spintronics applications. As a result, a new spintronics research platform can be envisaged in arti cial magnetic honeycomb lattice.
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