Topologically Protected Edge State in Two-Dimensional Su–Schrieffer–Heeger Circuit
Shuo Liu,
Wenlong Gao,
Qian Zhang,
Shaojie Ma,
Lei Zhang,
Changxu Liu,
Yuan Jiang Xiang,
Tie Jun Cui,
Shuang Zhang
Affiliations
Shuo Liu
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK; Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Wenlong Gao
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
Qian Zhang
State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
Shaojie Ma
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK; Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Lei Zhang
State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
Changxu Liu
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
Yuan Jiang Xiang
Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Tie Jun Cui
State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
Shuang Zhang
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
Topological circuits, an exciting field just emerged over the last two years, have become a very accessible platform for realizing and exploring topological physics, with many of their physical phenomena and potential applications as yet to be discovered. In this work, we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit, which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions, in analogy to the Su–Schrieffer–Heeger model. We take full control of the topological invariant (i.e., Zak phase) as well as the gap width of the band structure by simply tuning the circuit parameters. Excellent agreement is found between the experimental and simulation results, both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects. The demonstration of topological properties in circuits provides a convenient and flexible platform for studying topological materials and the possibility for developing flexible circuits with highly robust circuit performance.
