Chemical potential and compressibility of quantum Hall bilayer excitons

This paper considers a system of two parallel quantum Hall layers with total filling factor $0$ or $1$. When the distance between the layers is small enough, electrons and holes in opposite layers form inter-layer excitons, which have a finite effective mass and interact via a dipole-dipole potential. Results are presented for the chemical potential $\mu$ of the resulting bosonic system as a function of the exciton concentration $n$ and the interlayer separation $d$. Both $\mu$ and the interlayer capacitance have an unusual nonmonotonic dependence on $d$, owing to the interplay between an increasing dipole moment and an increasing effective mass with increasing $d$. A phase transition between superfluid and Wigner crystal phases is shown to occur at $d \propto n^{-1/10}$. Results are derived first via simple intuitive arguments, and then verified with more careful analytic derivations and numeric calculations.Comment: 7 pages, 5 figures; improved discussion and references; published versio

The price of anarchy in basketball

Optimizing the performance of a basketball offense may be viewed as a network problem, wherein each play represents a "pathway" through which the ball and players may move from origin (the in-bounds pass) to goal (the basket). Effective field goal percentages from the resulting shot attempts can be used to characterize the efficiency of each pathway. Inspired by recent discussions of the "price of anarchy" in traffic networks, this paper makes a formal analogy between a basketball offense and a simplified traffic network. The analysis suggests that there may be a significant difference between taking the highest-percentage shot each time down the court and playing the most efficient possible game. There may also be an analogue of Braess's Paradox in basketball, such that removing a key player from a team can result in the improvement of the team's offensive efficiency.Comment: 9 pages, 6 figures; extra example and some discussion added; formatting errors fixed; typo in Sec. IIID fixe

Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites

Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription breaks down in situations where a large and long-ranged random potential develops. In particular, we examine a canonical model of a completely compensated semiconductor, and we show that at low temperatures hopping proceeds along self-organized, low-dimensional subspaces having fractal dimension $d = 2$. We derive and study numerically the spatial structure of these subspaces, as well as the conductivity and density of states that result from them. One of our prominent findings is that fractal ordering of low energy sites greatly enhances the hopping conductivity, and allows Efros-Shklovskii type conductivity to persist up to unexpectedly high temperatures.Comment: 9 pages, 6 figures; published version with added references and discussio

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.Comment: 24 pages, 2 figures; Final published versio

Large, nonsaturating thermopower in a quantizing magnetic field

The thermoelectric effect is the generation of an electrical voltage from a temperature gradient in a solid material due to the diffusion of free charge carriers from hot to cold. Identifying materials with large thermoelectric response is crucial for the development of novel electric generators and coolers. In this paper we consider theoretically the thermopower of Dirac/Weyl semimetals subjected to a quantizing magnetic field. We contrast their thermoelectric properties with those of traditional heavily-doped semiconductors and we show that, under a sufficiently large magnetic field, the thermopower of Dirac/Weyl semimetals grows linearly with the field without saturation and can reach extremely high values. Our results suggest an immediate pathway for achieving record-high thermopower and thermoelectric figure of merit, and they compare well with a recent experiment on Pb$_{1-x}$Sn$_x$Se.Comment: 6+3 pages, 4 figures; update discussion of experiments and device performanc

Effect of magnetization on the tunneling anomaly in compressible quantum Hall states

Tunneling of electrons into a two-dimensional electron system is known to exhibit an anomaly at low bias, in which the tunneling conductance vanishes due to a many-body interaction effect. Recent experiments have measured this anomaly between two copies of the half-filled Landau level as a function of in-plane magnetic field, and they suggest that increasing spin polarization drives a deeper suppression of tunneling. Here we present a theory of the tunneling anomaly between two copies of the partially spin-polarized Halperin-Lee-Read state, and we show that the conventional description of the tunneling anomaly, based on the Coulomb self-energy of the injected charge packet, is inconsistent with the experimental observation. We propose that the experiment is operating in a different regime, not previously considered, in which the charge-spreading action is determined by the compressibility of the composite fermions.Comment: (5+1) pages, 1 figure; (v2) minor changes and added reference to our accompanying paper arXiv:1712.02357; (v3) Final published versio