Topic
Brillouin zone
About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.
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TL;DR: In this article, a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone is presented. But it does not specify gauge-fixing conditions.
Abstract: We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.
177 citations
TL;DR: In this paper, the phonons in boron nitride nanotubes using density functional perturbation theory in the local density approximation were evaluated based on the nonsymmorphic rod-group symmetry of the tubes, the Raman and infrared-active modes at the G point of the one-dimensional Brillouin zone were evaluated.
Abstract: We present an extensive first-principles study of the phonons in boron nitride nanotubes using density functional perturbation theory in the local density approximation. Based on the nonsymmorphic rod-group symmetry of the tubes, the Raman- and infrared-active modes at the G point of the one-dimensional Brillouin zone are evaluated. For zigzag and chiral nanotubes, the set of infrared-active modes is a subset of the Raman-active modes. In particular, the radial breathing mode is not only Raman but also infrared active. However, for armchair tubes, the sets of infrared- and Raman-active modes are disjoint. This may serve to spectroscopically distinguish between macroscopic samples of zigzag-chiral and armchair nanotubes. We present the frequencies of the active modes of zigzag, chiral, and armchair tubes as a function of the tube diameter and compare the results with the frequencies obtained by the zone-folding method, i.e., the rolling of a single hexagonal BN sheet into a tube. Except for the high-frequency tangential modes, the zone-folding results are in very good agreement with the ab initio calculations. The radial breathing mode frequency can be derived by folding a sheet of finite width. Finally, we show that the effects of bundling on the phonon frequencies are small. This demonstrates that the obtained results for isolated BN tubes may serve as a basis for an accurate assignment of phonon modes in spectroscopic measurements.
177 citations
TL;DR: In this paper, a general model for a semiconductor-to-metal transition is discussed, in which the energy gap between the valence and conduction bands decreases linearly with the number of electrons excited across the gap.
Abstract: This paper discusses a general model for a semiconductor-to-metal transition, in which the energy gap between the valence and conduction bands decreases linearly with the number of electrons excited across the gap. It is shown that this model results in a rapid disappearance of the forbidden gap with rising temperature according to either a first-order or a second-order phase transition, depending on the magnitude of the relative change in gap with the number of excited carriers. Two possible physical models are treated in detail. In one the energy gap results from the splitting of the first Brillouin zone by an antiferromagnetic exchange interaction, and in the other it results from a crystalline-structure distortion to lower symmetry. The latter model is considered in detail in terms of the pairing of ions in a one-dimensional crystal. With these models, using plausible values of the parameters, the explicit relationship between energy gap and freecarrier concentration is estimated. The thermodynamic theory is worked out for the limiting cases of band width large and small compared to the zero-temperature gap. In the narrow-band limit it is found that the parameters of the model are such as to give a second-order transition for the antiferromagnetic case and a first-order transition in the crystalline-distortion model. Using these models, the transition temperature can be evaluated explicitly in terms of the zero-temperature gap. A number of results relating experimentally measurable quantities such as the pressure coefficient of the transition temperature and the energy gap can be derived.
176 citations
TL;DR: In this article, the Brillouin optical microscopy was used to characterize material acoustic properties at GHz frequency and measure the longitudinal elastic moduli of lenses, which showed biomechanical heterogeneity in the cortex and nucleus of the lens with high spatial resolution.
175 citations
TL;DR: A novel method, based on stimulated Brillouin scattering (SBS), is presented, for the simultaneous distributed measurement of fast strain variations along the entire length of the sensing fiber.
Abstract: We present a novel method, based on stimulated Brillouin scattering (SBS), for the simultaneous distributed measurement of fast strain variations along the entire length of the sensing fiber. A specially synthesized and adaptable probe wave is used to place the Brillouin interaction always on the slope of the local Brillouin gain spectrum, allowing a single pump pulse to sample fast strain variations along the full length of a fiber with an arbitrary distribution of the Brillouin frequency shift. In this early demonstration of the method, strain vibrations of a few hundred Hz are demonstrated, simultaneously measured on two different sections of an 85m long fiber, having different static Brillouin shifts and with a spatial resolution of 1.5m.
173 citations