rotation symmetry
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2021 ◽  
Author(s):  
Andrew T. Pierce ◽  
Yonglong Xie ◽  
Seung Hwan Lee ◽  
Patrick R. Forrester ◽  
Di S. Wei ◽  
...  

AbstractSymmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at specific filling factors that spontaneously breaks the spin-rotation symmetry1–3. This ferromagnet has been shown to support spin-wave excitations known as magnons that can be electrically generated and detected4,5. Although long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations—including the magnon chemical potential and density—have not been measured. Here we present local measurements of electron compressibility under the influence of magnons, which reveal a reduction in the gap associated with the ν = 1 quantum Hall state by up to 20%. Combining these measurements with the estimates of temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables the extraction of free magnon density, magnon chemical potential and average skyrmion spin. Our methods provide a means of probing the thermodynamic properties of charge-neutral excitations that are applicable to other symmetry-broken electronic phases.


2021 ◽  
pp. 12-24
Author(s):  
Ming He, Teng Zhao

In this paper, A retrospective review was performed for all the patients who underwent surgery with the Goldman technique by the senior author from 2004 to 2009 for correction of the broad nasal tip. The clinical and pathologic findings of these patients were reviewed, and an independent observer evaluated the pre- and postoperative photos of the patients using five parameters: projection, rotation, symmetry, shape, and distance of the tip-defining points. The evaluation was performed using a scale of -1 to +1 for each of the five parameters. Of the 205 patients who underwent the technique, 115 (56%) were patients with broad tips, and 90 (44%) were patients with broad (boxy) tips. A total of 189 cases (92.2%) involved primary rhinoplasties, and 16 cases (7.8%) involved revision. During this period, complications were observed in five patients (2.4%), who underwent revision rhinoplasty with a successful result. The average score for the five parameters already mentioned for primary rhinoplasties according to the scale of -5 to +5 showed a significant postoperative improvement (score, +4.3). It implied that the cartilage rhinoplasty with Goldman technique is safe when performed by experienced surgeons and according to specific indications. This conclusion is indicated by the low rate of complications in the large series of patients in this study.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chang-geun Oh ◽  
Sang-Hoon Han ◽  
Sangmo Cheon

AbstractWe investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw–Rebbi (JR) models. We show that time-reversal (T), charge-conjugation (C), parity (P), and discrete internal field rotation ($$Z_n$$ Z n ) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the $$Z_2$$ Z 2 rotation symmetry, whereas it shows chiral solitons with the broken $$Z_2$$ Z 2 rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only $$Z_2$$ Z 2 rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced $$Z_4$$ Z 4 rotation symmetry. Moreover, we find that the nonchiral solitons have C, P symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that T, C, P symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.


2021 ◽  
Author(s):  
Jinrun Zhang ◽  
Jinwei Zeng ◽  
Yangjie Liu ◽  
Yajuan Dong ◽  
Jian Wang

2021 ◽  
Author(s):  
Huaqing Huang ◽  
Feng Liu

ABSTRACT The higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry preserves in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled $\beta $-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.


2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Helene Spring ◽  
Anton Akhmerov ◽  
Daniel Varjas

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.


2021 ◽  
Vol 103 (23) ◽  
Author(s):  
Rafael González-Hernández ◽  
Erick Tuiran ◽  
Bernardo Uribe

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