Search

The low-frequency conductivity of a disordered Fermi gas in one spatial dimension is governed by the Mott-Berezinskii law $\sigma(\omega) \propto \omega^2 \ln \omega^2$. In a recent Letter [Phys. Rev. Lett. 84, 1760 (2000)] A. O. Gogolin claimed that this law is invalid, challenging our basic understanding of disordered systems and a massive amount of previous theoretical work. We point out two calculational errors in Gogolin's paper. Once we correct them, the Mott-Berezinskii formula is fully recovered. We also present numerical results supporting the Mott-Berezinskii formula but ruling out that of Gogolin., Comment: 1 page, 1 figure, RevTeX 4

We show that a quantum Hall bilayer with the total filling $\nu = 1$ should exhibit a dynamical regime similar to the flux-flow in large Josephson junctions. This analogy may explain a conspicuous peak in the interlayer tunneling conductance [\prl {\bf 84}, 5808 (2000)]. The flux-flow is likely to be spatiotemporally chaotic at low bias voltage, which will manifest itself through broad-band noise. The peak position can be controlled by an in-plane magnetic field., Comment: Published version + one bonus figure; 5 pages, 3 figures total

We propose a dynamical theory of the stripe phase arising in a two-dimensional electron liquid near half-integral fillings of high Landau levels. The system is modelled as a novel type of a smectic liquid crystal with the Lorentz force dominated dynamics. We calculate the structure factor, the dispersion relation of the collective modes (magnetophonons), and their intrinsic attenuation rate. We find strong power-law renormalizations of the elastic and dissipative coefficients by thermal fluctuations familiar from the conventional smectics but with different dynamical scaling exponents., Comment: Replaced with the published version

The two-dimensional motion of a charged particle in a random potential and a transverse magnetic field is believed to be delocalized only at discrete energies $E_N$. In strong fields there is a small positive deviation of $E_N$ from the center of the $N$th Landau level, which is referred to as the ``weak levitation'' of the extended state. I calculate the size of the weak levitation effect for the case of a smooth random potential re-deriving earlier results of Haldane and Yang [PRL 78, 298 (1997)] and extending their approach to lower magnetic fields. I find that as the magnetic field decreases, this effect remains weak down to the lowest field $B_{min}$ where such a quasiclassical approach is still justified. Moreover, in the immediate vicinity of $B_{min}$ the weak levitation becomes additionally suppressed. This indicates that the ``strong levitation'' expected at yet even lower magnetic fields must be of a completely different origin., Comment: RevTeX, 4 pages, 1 figure

The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $\xi$ of such states at even filling factors $\nu = 2 N$. The calculation is done for several models of disorder (``white-noise,'' short-range, and long-range random potentials). We find that the localization length has a power-law dependence on the Landau level index, $\xi \propto N^\alpha$ with the exponent $\alpha$ between one and ${10/3}$, depending on the model. In particular, for a ``white-noise'' random potential $\xi$ roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples., Comment: moderate changes in Sec.IV and VI

We show by a meta-analysis of the available Quantum Monte-Carlo (QMC) results that two-dimensional fermions with repulsive interactions exhibit universal behavior in the strongly-correlated regime, and that their freezing transition can be described using a quantum generalization of the classical Hansen-Verlet freezing criterion. We calculate the liquid-state energy and the freezing point of the 2D dipolar Fermi gas (2DDFG) using a variational method by taking ground state wave functions of 2D electron gas (2DEG) as trial states. A comparison with the recent fixed-node diffusion Monte-Carlo analysis of the 2DDFG shows that our simple variational technique captures more than 95% of the correlation energy, and predicts the freezing transition within the uncertainty bounds of QMC. Finally, we utilize the ground state wave functions of 2DDFG as trial states and provide a variational account of the effects of finite 2D confinement width. Our results indicate significant beyond mean-field effects. We calculate the frequency of collective monopole oscillations of the quasi-2D dipolar gas as an experimental demonstration of correlation effects., Comment: 6 pages, 4 figures + supplemental materials (3 pages, 1 figure)

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of the order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$., REVTeX, 21 pages + 12 figures in PostScript. Uses amsfonts.sty, multicol.sty, and psfig.sty

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$., Several errors corrected

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors., Comment: 14 pages, compressed Postscript file

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of finding a two-dimensional charge distribution on the interface of a semiconductor heterostructure under the influence of a split gate., 4 pages, postscript

We use scanning near-field optical microscopy to study the response of hexagonal boron nitride nanocones at infrared frequencies, where this material behaves as a hyperbolic medium. The obtained images are dominated by a series of hot rings that occur on the sloped sidewalls of the nanocones. The ring positions depend on the incident laser frequency and the nanocone shape. Both dependences are consistent with directional propagation of hyperbolic phonon polariton rays that are launched at the edges and zigzag through the interior of the nanocones, sustaining multiple internal reflections off the sidewalls. Additionally, we observe a strong overall enhancement of the near-field signal at discrete resonance frequencies. These resonances attest to low dielectric losses that permit coherent standing waves of the sub-diffractional polaritons to form. We comment on potential applications of such shape-dependent resonances and the field concentration at the hot rings., Accepted for publication in Nano Letters

We report an implementation of a 2-dimensional electrostatic lattice potential for indirect excitons. We present electrode designs for square, triangular, and honeycomb lattices, and exciton photoluminescence measurements in a square lattice.

We present a method for determining correlations in a gas of indirect excitons in a semiconductor quantum well structure. The method involves subjecting the excitons to a periodic electrostatic potential that causes modulations of the exciton density and photoluminescence (PL). Experimentally measured amplitudes of energy and intensity modulations of exciton PL serve as an input to a theoretical estimate of the exciton correlation parameter and temperature. We also present a proof-of-principle demonstration of the method for determining the correlation parameter and discuss how its accuracy can be improved., 10 pages, 11 figures

We have performed combined studies of the charge compressibility and resistance of high‐mobility 2D electron and hole systems in the region where dρ/dT changes its sign with decreasing carrier concentration — the apparent Metal‐Insulator Transition. Despite the large difference in rs, inverse compressibility in both electron and hole systems can be quantitatively explained by a nonlinear screening of disorder by the carriers. In addition, we have shown that the resistance exhibits a scaling characteristic of the percolation transition. The resistance percolation threshold, which agrees with the percolation point obtained from the analysis of the compressibility, is found to be at a lower concentration than the MIT.

BACKGROUND Light trapped at the nanoscale, deep below the optical wavelength, exhibits an increase in the associated electric field strength, which results in enhanced light-matter interaction. This leads to strong nonlinearities, large photonic forces, and enhanced emission and absorption probabilities. A practical approach toward nanoscale light trapping and manipulation is offered by interfaces separating media with permittivities of opposite signs. Such interfaces sustain hybrid light-matter modes involving collective oscillations of polarization charges in matter, hence the term polaritons. Surface plasmon polaritons, supported by electrons in metals, constitute a most-studied prominent example. Yet there are many other varieties of polaritons, including those formed by atomic vibrations in polar insulators, excitons in semiconductors, Cooper pairs in superconductors, and spin resonances in (anti)ferromagnets. Together, they span a broad region of the electromagnetic spectrum, ranging from microwave to ultraviolet wavelengths. We discuss polaritons in van der Waals (vdW) materials: layered systems in which individual atomic planes are bonded by weak vdW attraction (see the figure). This class of quantum materials includes graphene and other two-dimensional crystals. In artificial structures assembled from dissimilar vdW atomic layers, polaritons associated with different constituents can interact to produce unique optical effects by design. ADVANCES vdW materials host a full suite of different polaritonic modes with the highest degree of confinement among all known materials. Advanced near-field imaging methods allow the polaritonic waves to be launched and visualized as they travel along vdW layers or through multilayered heterostructures. Spectroscopic and nanoimaging experiments have identified multiple routes toward manipulation of nano-optical phenomena endowed by polaritons. A virtue of polaritons in vdW systems is their electrical tunability. Furthermore, in heterostructures assembled from dissimilar vdW layers, different brands of polaritons interact with each other, thus enabling unparalleled control of polaritonic response at the level of single atomic planes. New optoelectronic device concepts aimed at the detection, harvesting, emission, propagation, and modulation of light are becoming feasible as a result of combined synthesis, nanofabrication, and modeling of vdW systems. The extreme anisotropy of vdW systems leading to opposite signs of the in-plane and out-of-plane permittivities of the same layered crystal enables efficient polaritonic waveguides, which are instrumental for subdiffractional focusing and imaging. In addition to near-field optical probes facilitating nanoimaging, coupling to polaritons can be accomplished via electrical excitation and nonlinear wave mixing. OUTLOOK Potential outcomes of polariton exploration in vdW heterostructures go beyond nano-optical technologies. In particular, images of polaritonic standing and traveling waves contain rich insights into quantum phenomena occurring in the host material supporting polaritons. This line of inquiry into fundamental physics through polaritonic observations constitutes an approach toward optics-based materials research. In particular, the strong spatial confinement exhibited by vdW polaritons involves large optical-field gradients—or equivalently, large momenta—which allows regions of the dispersion relations of electrons, phonons, and other condensed-matter excitations to be accessed beyond what is currently possible with conventional optics. Additionally, polaritons created by short and intense laser pulses add femtosecond resolution to the study of these phenomena. Alongside future advances in the understanding of the physics and interactions of vdW polaritons, solutions to application challenges may be anticipated in areas such as loss compensation, nanoscale lasing, quantum optics, and nanomanipulation. The field of vdW polaritonics is ripe for exploring genuinely unique physical scenarios and exploiting these new phenomena in technology. van der Waals (vdW) materials consist of individual atomic planes bonded by weak vdW attraction. They display nearly all optical phenomena found in solids, including plasmonic oscillations of free electrons characteristic of metals, light emission/lasing and excitons encountered in semiconductors, and intense phonon resonances typical of insulators. These phenomena are embodied in confined light-matter hybrid modes termed polaritons—excitations of polarizable media, which are classified according to the origin of the polarization. The most studied varieties are plasmon, phonon, and exciton polaritons. In vdW materials, polaritons exhibit extraordinary properties that are directly affected by dimensionality and topology, as revealed by state-of-the-art imaging of polaritonic waves. vdW heterostructures provide unprecedented control over the polaritonic response, enabling new quantum phenomena and nanophotonics applications.