Wave-function geometry of band crossing points in two-dimensions

Geometry of the wave function is a central pillar of modern solid state physics. In this work, we unveil the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs). We show that the Berry phase of BCPs are governed by the quantum metric describing the infinitesimal distance between quantum states. For generic linear BCPs, we show that the corresponding Berry phase is determined either by an angular integral of the quantum metric, or equivalently, by the maximum quantum distance of Bloch states. This naturally explains the origin of the $\pi$-Berry phase of a linear BCP. In the case of quadratic BCPs, the Berry phase can take an arbitrary value between 0 and $2\pi$. We find simple relations between the Berry phase, maximum quantum distance, and the quantum metric in two cases: (i) when one of the two crossing bands is flat; (ii) when the system has rotation and/or time-reversal symmetries. To demonstrate the implication of the continuum model analysis in lattice systems, we study tight-binding Hamiltonians describing quadratic BCPs. We show that, when the Berry curvature is absent, a quadratic BCP with an arbitrary Berry phase always accompanies another quadratic BCP so that the total Berry phase of the periodic system becomes zero. This work demonstrates that the quantum metric plays a critical role in understanding the geometric properties of topological semimetals.Comment: 7+9 pages, 4+1 figures, published versio

Geometric characterization of anomalous Landau levels of isolated flat bands

According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.Comment: 10+8 pages, 5+3 figure

Effect of accumulated vs continuous exercise on excess post-exercise oxygen consumption

Background: A continuous aerobic exercise program is an effective method of improving calorie consumption on the metabolism of skeletal muscle. However, studies report that accumulated exercise of 30 minutes divided into three sessions of 10 minutes is as effective as one continuous exercise session for 30 minutes. As yet, no study has compared the excess post-exercise oxygen consumption associated with accumulated exercise and continuous exercise over these timeframes. Objective: The primary purpose of this study was to compare the excess post-exercise oxygen consumption associated with performing continuous exercise for 30 minutes and three sessions of accumulated exercise for 10 minutes at the same intensity of 60% VO2max. Method: Posters about the study were posted on the February 2019 Konkuk university homepage and bulletin board, and a total of 34 college students (males, n=18; females, n=16) volunteered to participate. Using a balanced repeated-measures crossover design, the subjects randomly took two exercises: continuous exercise (1 x 30 minutes) or accumulated exercise (3 x 10 minutes), and the washout period between the two exercises was a week. All exercises were performed using an ergometer at 60% maximal oxygen consumption. Oxygen consumption and heart rate were monitored and measured during exercise and after exercise. Lipid profile and lactate acid were measured at rest, exercise end, exercise end plus 30 minutes, and exercise end plus 60 minutes. IBM SPSS Statistics 23 was used to perform a paired t-test, and the statistically significant difference was set at <.05. Results: Excess post-exercise oxygen consumption parameters (e.g., total oxygen consumption, total calorie, and summation of heart rate) were higher in accumulated exercise than in continuous exercise (p<.05). No significant difference in the calorie during exercise between CEx and AEx (p = .140). No significant difference was observed in the lipid profile between accumulated exercise and continuous exercise (p>.05). No significant differences were observed at rest, exercise end plus 30 minutes, exercise end plus 60 minutes in lactic acid in the blood (p <.05). However, at exercise end, it was significantly higher in the accumulated exercise (p<.01). Conclusions: This study confirmed that after equalizing energy expenditure for continuous exercise and accumulated exercise in participants in their 20s, accumulated exercise results in higher excess post-exercise oxygen consumption than continuous exercise. The data suggests that accumulated exercise may be more effective in reducing body fat than continuous exercise for a given amount of energy expenditure. [Ethiop.J. Health Dev. 2020;34(Special issue-3):84-90] Keywords: Continuous exercise, accumulated exercise, excess post-exercise oxygen consumptio