Supermoir\'e low-energy effective theory of twisted trilayer graphene

Stacking three monolayers of graphene with a twist generally produces two moir\'e patterns. A moir\'e of moir\'e structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moir\'e lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\bf \Gamma}_M$ point of the moir\'e Brillouin zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The velocities and small gaps exhibit a spatial dependence in the moir\'e-of-moir\'e unit cell, entailing a non-abelian connection potential which ensures gauge invariance. The resulting model is numerically solved and a fully connected spectrum is obtained, which is protected by the combination of time-reversal and twofold-rotation symmetries.Comment: 17 pages, 15 figure

Chern mosaic and ideal flat bands in equal-twist trilayer graphene

We study trilayer graphene arranged in a staircase stacking configuration with equal consecutive twist angle. On top of the moir\'e cristalline pattern, a supermoir\'e long-wavelength modulation emerges that we treat adiabatically. For each valley, we find that the two central bands are topological with Chern numbers $C=\pm 1$ forming a Chern mosaic at the supermoir\'e scale. The Chern domains are centered around the high-symmetry stacking points ABA or BAB and they are separated by gapless lines connecting the AAA points, where the spectrum is fully connected. In the chiral limit and at a magic angle of $\theta \sim 1.69^\circ$, we prove that the central bands are exactly flat with ideal quantum curvature at ABA and BAB. Furthermore, we decompose them analytically as a superposition of an intrinsic color-entangled state with $\pm 2$ and a Landau level state with Chern number $\mp 1$. To connect with experimental configurations, we also explore the non-chiral limit with finite corrugation and find that the topological Chern mosaic pattern is indeed robust and the central bands are still well separated from remote bands.Comment: 7+7 pages, 5 figure

Mechanical damage characteristics of CR/PPA composite modified asphalt pavement under multi-factor coupling effect in the seasonally frozen region

Asphalt pavements are inevitably affected by coupled effects of dry-wet/freeze-thaw cycles, UV radiation, temperature, and loading during service, resulting in degradation of their road performance and reduced service life. Therefore, this study used crumb rubber (CR) and polyphosphoric acid (PPA) as modifiers to prepare CR/PPA composite modified asphalt mixtures for testing. To investigate the mechanical properties of the composite modified asphalt mixtures under the action of multi-factor coupling. Meanwhile, the performance analysis of matrix asphalt and SBS modified asphalt mixtures were carried out as a comparison. Density and water penetration tests, splitting tests, beam bending tests, and four-point bending fatigue tests reveal the evolution of asphalt mixture road performance. Finally, regression fitting was performed on the test data to establish the mechanical damage model of each type of asphalt mixture. The results show that with the increase of wet-dry/freeze-thaw cycles and the increase of UV radiation time, the void ratio and water permeability coefficient increase and the splitting strength, bending and tensile strain, and fatigue life decrease for all types of asphalt mixtures. When the number of wet-dry/freeze-thaw cycles reached 8, the mechanical properties of the asphalt mixture decreased significantly, while the changes leveled off after the number of cycles reached 15. When the UV radiation time is less than 4 months, the mechanical properties of the asphalt mixture decay more slowly. However, with a further increase in radiation time, the mechanical properties decay rapidly. The water-saturated specimens have a more significant effect on the mechanical damage of each type of asphalt mixture. Compared with the other two mixtures, the composite modified asphalt mixtures have superior mechanical properties and fatigue life. The mixture performance damage model based on the least squares Levenberg-Marquardt method (L-M method) was able to simulate the experimental data well, with a minimum correlation coefficient R2 of 0.9285. In summary, the road performance of all types of asphalt mixtures under the coupling of multiple factors has deteriorated, while the composite modified asphalt mixtures have better anti-damage characteristics, with good prospects for promotion

Behavior of Lime-Stabilized Red Bed Soil after Cyclic Wetting-Drying in Triaxial Tests and SEM Analysis

Most red beds demonstrate inferior geotechnical properties in natural conditions and need to be improved when used as construction material. In this study, a serious of triaxial tests, permeability tests, and scanning electron microscopy (SEM) analysis were carried out on lime-stabilized and untreated red bed soil after experiencing different wetting-drying (W-D) cycles. The test results showed that, with the increase in the added lime, the shear strength, strength parameters (including the cohesion and the internal friction angle), and the shear modulus of red bed soil increased gradually. For the untreated specimens, the four parameters decreased considerably after experiencing W-D cycles, while for the lime-stabilized specimens, they generally increased with an increase in the W-D cycles. Without experiencing the W-D cycles, the permeability coefficient increased by two times after it was stabilized with 10% lime. But with an increase in the W-D cycles, the permeability coefficient of the untreated and lime-stabilized specimens continuously increased and significantly decreased, respectively. Finally, variations in microstructure of the red bed soil under the effects of the lime stabilization and W-D cycles were discussed based on the SEM analysis. The results may contribute to improvement of red bed soil when used as roadbed and airfield fillings

Experimental Study on Electric Resistivity Characteristics of Compacted Loess under Different Loads and Drying-Wetting Cycles

Densely compacted loess foundations of many man-made infrastructures are often exposed to various loads and extreme weathering processes (e.g., drying-wetting cycles), which significantly deteriorate their mechanical properties. Traditional methods applied to characterize soil engineering properties are primarily based on visual inspections, point sensors, or destructive approaches, the results of which often have relatively high costs and cannot provide large-area coverage. The electrical resistivity method is a reasonable alternative that provides a nondestructive, sensitive, and continuous evaluation of the soil physical properties. Thus, the relationships between electrical resistivity and soil strength should be understood, particularly for scenarios in which soils undergo significant loads and cycles of drying and wetting. In this study, a suite of laboratory tests simulating loads (consolidation tests, unconfined compression tests, and uniaxial cyclic unloading-reloading tests) and seasonal field conditions (drying-wetting cycle tests) were conducted to quantitatively assess their deterioration effects on the geophysical and geotechnical properties of compacted loess. The experimental results indicated that electric resistivity decreases with the increase in stress and then approaches a stable value after the stress becomes 200 kPa. During the uniaxial compression process, the electric resistivity corresponds to both the stress and strain of loess in real-time. The electrical resistivity of loess reflects plastic damage under uniaxial unloading-reloading tests, but it is deficient in representing the dissipated energy of loess. The electrical resistivity of loess samples increases as the number of drying-wetting cycles increases but decreases with increasing cycle numbers after stabilization under consolidation load. The electrical resistivity can effectively characterize the mechanical and deformation characteristics of loess samples under loads and drying-wetting cycles, exhibiting a certain potential for long-term monitoring of soil engineering properties

Bibliometric Analysis of the Permafrost Research: Developments, Impacts, and Trends

Permafrost is a significant part of the cryosphere, which has gained increasing attention from scientists, policy-makers, and the general public due to global warming, environmental degradation, water shortages, and intense human activities. Although many permafrost research review articles have been published, these studies were predominantly limited to either one subject or one field, while systematic studies about permafrost based on bibliometric analysis methods remain limited. We aim to fill this gap by conducting a bibliometric analysis of 13,697 articles in the field of permafrost research from 1942 to 2021, collected from the Web of Science core collection database. The results indicate that permafrost research is a typically multi-author, multi-country, and multi-institution cooperative field, involved in many research fields. The cumulative number of publications has presented an exponential increase over the past 80 years, with an average annual growth rate of 10.40%. Since 2000, China has seen a rapid growth in the number of publications per year, surpassing the USA in 2016 and leading in the years since then. In addition, the authors from China have great contributions in publications, and there is good room for permafrost development in the future according to the authors’ M-index ranking. After the analysis of authors’ keywords, we found that, compared to the conventional methods, machine learning and interferometric synthetic aperture radar (InSAR) are new technological approaches introduced in recent years, and the Qinghai–Tibet Plateau has become a popular study area. The results presented here can help related researchers, scholars, and students in the field to better understand the past developments, current status, and future trends of permafrost research. Furthermore, this paper presents and expands the general process of the bibliometric method used in permafrost studies, which can provide researchers with new inspirations and improve discipline research approach

Dynamic variations in thermal regime and surface deformation along the drainage channel for an expanding lake on the Tibetan Plateau

The outburst of Zonag Lake in 2011 triggered a series of floods in the continuous permafrost region of the hinterland of the Qinghai-Tibet Plateau. This re-distributed the surface water in the basin and caused rapid expansion of the tail lake (Salt Lake). To avoid potential overflow of the expanding Salt Lake, a channel was excavated to drain the lake water into a downstream river. In this study, to investigate the permafrost thermal regime and the surface deformation around the expanding Salt Lake and the channel, in-situ monitoring sections were settled from Salt Lake to the downstream of the channel to obtain the permafrost temperature. Additionally, using small baseline subset interferometric synthetic aperture radar (SBAS-InSAR), the surface deformation around Salt Lake and the channel was measured. The data showed that the ground temperature at the channel was 0.6°C higher than the natural field and the mean subsidence rate around the channel was 1.5 mm/yr higher than that at Salt Lake. These results show that the permafrost temperature in the study area changed considerably with variations in the distance from the lake/channel, and the deformation in the study area was dominated by subsidence.</p