Related Experiment Video
Updated: Aug 9, 2025
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
9.7K
Realization of a Hopf Insulator in Circuit Systems.
Zhu Wang1,2, Xu-Tao Zeng2,3, Yuanchuan Biao1,2
1Wuhan Institute of Quantum Technology, Wuhan 430206, China.
Physical Review Letters
|February 17, 2023
Summary
Researchers have experimentally realized the first three-dimensional (3D) Hopf insulator using a novel circuit system. This breakthrough achieves a topological phase previously only theorized, opening new avenues for exploring exotic quantum materials.
Area of Science:
- Condensed Matter Physics
- Topological Matter
- Quantum Materials
Background:
- Three-dimensional (3D) two-band Hopf insulators represent a unique topological phase of matter, distinct from classifications based on K theory and symmetry indicators.
- Theoretically proposed in 2008, Hopf insulators offer conceptual novelty, connections to knot theory, and intriguing physical properties.
- Previous experimental realization in 3D systems was hindered by the requirement for specific long-range spin-orbit coupling.
Purpose of the Study:
- To report the first experimental realization of a 3D Hopf insulator.
- To demonstrate a practical method for creating Hopf insulators in a controllable system.
- To verify the bulk-boundary correspondence of the realized topological phase.
Main Methods:
- Construction of basic pseudospin and connection modules to realize 2x2 matrix elements.
- Design of a circuit network based on a tight-binding Hopf insulator Hamiltonian derived from the Hopf map.
- Simulation of band structure and calculation of the Hopf invariant.
- Experimental measurement of the band structure on a printed circuit board.
Main Results:
- The designed circuit system successfully realizes a Hopf insulator with a measured Hopf invariant of 4.
- Experimental measurements of bulk bands and topological surface states align with theoretical predictions.
- The bulk-boundary correspondence of the Hopf insulator is experimentally verified.
Conclusions:
- This work presents the first experimental realization of a 3D Hopf insulator in a circuit system.
- The developed scheme provides a platform for studying Hopf insulators and exploring novel topological phases.
- This achievement paves the way for investigating topological phases beyond current classification schemes.
Related Concept Videos
01:15First-Order Circuits
1.5K
First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
1.5K
01:17Second-Order Circuits
1.5K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
1.5K
01:16Equipotential Surfaces and Conductors
3.5K
For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic...
3.5K
01:25Network Function of a Circuit
340
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
340
01:26Linear Approximation in Frequency Domain
121
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
121
01:17Linear Circuits
446
A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
446