scholarly journals Topological Edge States of a Majorana BBH Model

2021 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Alfonso Maiellaro ◽  
Roberta Citro
Keyword(s):  
2D Materials ◽  
Finite Size ◽  
Majorana Fermions ◽  
Topological Phase ◽  
Two Dimensional ◽  
Edge States ◽  
Finite Size Scaling ◽  
Topological Properties ◽  
Berry Curvature ◽  
Topological Superconductors

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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