triple points
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2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungjoon Park ◽  
Yoonseok Hwang ◽  
Hong Chul Choi ◽  
Bohm-Jung Yang

AbstractAcoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu–Goldstone theorem. Here, we show that this triple point can carry a topological charge $${\mathfrak{q}}$$ q that is a property of three-band systems with space-time-inversion symmetry. The charge $${\mathfrak{q}}$$ q can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial $${\mathfrak{q}}$$ q the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when Oh or Th groups protect it. The charge $${\mathfrak{q}}$$ q constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu–Goldstone theorem form a new platform to study the topology of band degeneracies.


2021 ◽  
Author(s):  
Vladimir Y. Gotsulsky ◽  
Salvatore Magazù ◽  
Nikolay P. Malomuzh

Abstract A new approach to the physical nature of the water density maximum at 4°C is proposed. The main attention is focused on the role of H-bonds in the formation of the specific volume and thermal expansion coefficients for ordinary and heavy water. It is shown that the minimum of the specific volume for water is connected with the amplification of H-bonds (D-bonds) role at approaching their triple points.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anupam Bhattacharya ◽  
Vishal Bhardwaj ◽  
Brajesh K Mani ◽  
Jayanta K Dutt ◽  
Ratnamala Chatterjee

AbstractTopologically non-trivial electronic structure is a feature of many rare-earth half-Heusler alloys, which host atoms with high spin-orbit coupling bringing in the non-triviality. In this article, using the first-principles simulations, rare-earth half-Heusler YPdBi, ScPdBi, LaPdBi, LuPdBi, YPtBi and LuPtBi alloys are studied under strain to reveal multiple band inversions associated with topological phase transitions. From our simulations we find that, as a result of first band-inversion, the Brillouin zone of the diamagnetic half-Heusler alloys hosts eight triple points whereas, the second band inversion causes the emergence of sixteen more triple points. These band-inversions are observed to be independent of the spin-orbit coupling and are the reason behind increasing occupation of bismuth 7s orbitals as volume of the unit cell increases. The surface electronic transport in different triple point semi-metallic phases is found to evolve under strain, as the number of Fermi arcs change due to multiple band inversions. Once the second band inversion occurs, further application of tensile strain does not increase the number of triple points and Fermi arcs. However, increasing tensile strain (or decreasing compressive strain) pushes the triple point crossing to higher momenta, making them more effective as source of highly mobile electrons. These observations make a pathway to tune the bulk as well as surface transport through these semi-metals by application of tensile or compressive strain depending on the unstrained relative band-inversion strength of the material.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sławomir Cynk

Abstract We give a formula for the Hodge numbers of a three-dimensional hypersurface in a weighted projective space with only ordinary triple points as singularities.


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yu Liu ◽  
Baoguo Xiao ◽  
Lan Wang ◽  
Chao Wang

The stability of oblique detonation waves (ODWs) is a fundamental problem, and resistance of ODWs against disturbances is crucial for oblique detonation engines in high-speed propulsion. In this work, numerical studies on ODW stability in disturbed flows are conducted using the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model. Two kinds of flow disturbances are, respectively, introduced into the steady flow field to assess ODW stability, including upstream transient high-pressure disturbance (UTHD) and downstream jet flow disturbance (DJFD) with different durations. Generally, an ODW is susceptible to disturbances at larger wedge angles and stable at smaller wedge angles. In the unstable wedge angle range, different ODW structures and transition patterns are obtained after disturbances, including different locations of the primary triple points, different numbers of the steady triple points on the wave surface, and different transition patterns from the leading oblique shock wave to the ODW. It is found that the primary triple point tends to move upstream for the disturbances that can form a local strong detached bow shock wave near the wedge tip. In contrast, the wave surface and the transition pattern are susceptible to all of the disturbances introduced in this study. Despite the unstable responses of the ODWs to the disturbances, the ODWs can keep standing stability after disturbances, which is beneficial to the propulsion application of ODWs.


Materials ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 4321
Author(s):  
Yang Li ◽  
Jihong Xia ◽  
Rabah Khenata ◽  
Minquan Kuang

Topological materials with band-crossing points exhibit interesting electronic characteristics and have special applications in electronic devices. However, to further facilitate the experimental detection of the signatures of these band crossings, topological materials with a large linear energy range around the band-crossing points need to be found, which is challenging. Here, via first-principle approaches, we report that the previously prepared P6/mmm-type CrB2 material is a topological metal with one pair of 1D band-crossing points, that is, nodal lines, in the kz= 0 plane, and one pair of 0D band-crossing points, that is, triple points, along the A–Γ–A’ paths. Remarkably, around these band-crossing points, a large linear energy range (larger than 1 eV) was found and the value was much larger than that found in previously studied materials with a similar linear crossing. The pair of nodal lines showed obvious surface states, which show promise for experimental detection. The effect of the spin–orbit coupling on the band-crossing points was examined and the gaps induced by spin–orbit coupling were found to be up to 69 meV. This material was shown to be phase stable in theory and was synthesized in experiments, and is therefore a potential material for use in investigating nodal lines and triple points.


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