Topological circuit based on non-reciprocal Aubry-Ander (AA) model and implementation method thereof

Abstract

The invention discloses a topology circuit based on a non-reciprocal Aubry-Andrie (AA) model and an implementation method of the topology circuit, and particularly constructs a passive RLC non-Hermite topology circuit based on the non-reciprocal AA model, the passive RLC non-Hermite topology circuit is composed of a chip resistor, a chip inductor, a chip capacitor, a coaxial connector, a copper-clad epoxy resin glass fiber cloth dielectric substrate and a BNC coaxial connector, and the chip resistor, the chip inductor, the chip capacitor, the coaxial connector, the copper-clad epoxy resin glass fiber cloth dielectric substrate and the BNC coaxial connector are connected in series. The non-reciprocal AA model has a non-Hermite skin state and an Anderson local state, the characteristic voltage distribution of the non-Hermite skin state and the Anderson local state can be observed by adjusting the value of a component, and the competitive relation between Anderson localization and the non-Hermite skin effect embodied in the non-reciprocal AA model is achieved.

Description

Technical Field This invention belongs to the field of topological research, specifically to a non-Hermitian topological circuit and its implementation method. This circuit can realize the competitive relationship between the non-Hermitian skin effect and Anderson localization embodied in the nonreciprocal Aubry-André (AA) model. The topological circuit of this invention has important scientific significance and research value for studying the complex phase transition behavior, topological properties, and Anderson localization of non-Hermitian systems, and provides an efficient and flexible implementation approach for the development of non-Hermitian topological sensors and topological electronic devices. Background Art With the development of physics, materials science, information technology, etc., topological phase transitions and non-Hermitian systems have become cutting-edge research fields. The concept of non-Hermitian originates from quantum mechanics. It is generally believed that open non-Hermitian quantum systems have no measurable intrinsic energy with physical significance, that is, no real eigenstates. However, if the system satisfies parity-time symmetry, the non-Hermitian Hamiltonian may also have real eigenvalues. This pioneering work has changed people's traditional understanding of the criteria for judging the conservation of energy in non-Hermitian open systems and greatly expanded the research scope of non-Hermitian systems. Studying the synergistic effect between non-Hermitian and topology, and studying its near-field local enhancement, will help further explore new physical phenomena in non-Hermitian topological systems and provide ideas for the research and development of new optoelectronic devices.

[0001] Physical phenomena such as singular points and non-Hermitian skin effects in non-Hermitian systems provide new design ideas for new electronic components, optical devices, and high-sensitivity sensors. Currently, research in the non-Hermitian field mainly focuses on the steady-state properties of topological materials and their behavior in disordered environments. The non-reciprocal AA model is a typical representative of non-Hermitian systems. The non-reciprocal AA model refers to the addition of a quasi-periodic potential Δ to the non-reciprocal Hatono-Nelson (HN) model. n This model provides a new approach to studying topological phase transitions and localization phenomena, and it can achieve localization through quasi-periodic potentials even in the absence of disorder. Anderson localization (AL) refers to the phenomenon that after the electron wave function is subjected to random perturbations, multiple scattering of electrons / light, etc., leads to coherence, which prevents its propagation, so the wave function will be confined to a certain range. Unlike Anderson localization, the non-Hermitian skin effect (NHSE) in non-Hermitian systems describes the accumulation behavior of the eigenstates of the wave function toward a certain boundary. Based on the non-reciprocal AA model, the competition between Anderson localization and non-Hermitian skin effect and their topological phase transitions are studied, which has broad prospects in the fields of sensing and signal transmission. It can be used for the design of high-sensitivity sensors, the development of anti-interference topological materials, etc., to achieve low-loss and high-robustness signal transmission, and provide a design reference for intelligent sensing technology and new electronic devices. Summary of the Invention To address the challenges of constructing non-Hermitian topological circuits, including their high cost and measurement difficulties, this paper proposes a circuit design and implementation method based on the non-reciprocal AA model. The circuit is composed of passive components (resistors, inductors, capacitors, etc.). By designing non-reciprocal coupling and quasi-periodic potentials within the circuit system, competition and conversion between the NHSE and AL are achieved. The goal of this invention is to establish a simple, stable, and efficient topological circuit system that realizes complex phase transitions with non-Hermitian topological effects and localization, providing new insights for experimental research on non-Hermitian topological physical phenomena and the development of topological electronic devices.

[0002] The topological circuit of the present invention consists of chip resistors, chip inductors, chip capacitors, a coaxial connector, an epoxy resin glass fiber cloth dielectric substrate, and a BNC coaxial connector. Passive RLC asymmetry is introduced into the circuit to adjust the numerical proportional relationship between the components to construct a one-dimensional nonreciprocal topological circuit system. This circuit exhibits abnormal voltage localization (NHSE) and AL phenomena at specific frequencies. By adjusting the values ​​of each component, the circuit can also achieve conversion between NHSE and AL. This circuit design offers the advantages of flexible parameter adjustment and simple design and implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0003] Figure 1 A schematic diagram of the structure of a non-reciprocal AA model circuit unit provided by an embodiment of the present invention;

[0004] Figure 2 Schematic diagram of a non-reciprocal AA circuit with n=13 nodes provided by an embodiment of the present invention;

[0005] Figure 3 A schematic diagram of specific component values ​​provided by an embodiment of the present invention;

[0006] Figure 4 Voltage response distribution diagram under non-Hermitian skin state provided by an embodiment of the present invention;

[0007] Figure 5 Schematic diagram of a non-reciprocal AA model topology phase change circuit with n=13 nodes provided in an embodiment of the present invention;

[0008] Figure 6 An embodiment of the present invention provides a graph showing the change in disorder intensity of the Inverse Participation Ratio (IPR) in a circuit system. DETAILED DESCRIPTION

[0009] like Figure 1This is a schematic diagram of the unit structure of the non-reciprocal AA model circuit of the present invention. The topological circuit of the present invention adopts circuit board etching technology, and selects an epoxy resin glass fiber cloth dielectric substrate with a thickness of 4mm. Each component is connected by a copper wire with a width of 0.381mm. A solder mask window design is performed on the substrate to facilitate the subsequent soldering of electronic components. Three components, chip resistors, chip inductors, and chip capacitors, are selected and soldered on the reserved pads. At the same time, a BNC coaxial connector is added at each node as a transmission interface for signal transmission. The operating frequency range of the topological circuit designed by the present invention is 500~1500kHz. The topological circuit can be regarded as a number of unit cells composed of resistors, capacitors, and inductors. The number of unit cells is equal to the number of nodes n. The value of n can be: 8, 13, 21... and other Fibonacci series values. The circuit is divided into a main line item and a grounding item. The main line item is composed of an inductor L n The grounding item is composed of capacitor C n , inductance l n , resistor R n The number of inductors in the main circuit is n+1, and the number of capacitors, inductors, and resistors in the grounding term is equal to n. The numerical units of each component are: Inductance L n (uH), C n (nF), l n (uH), R n (kΩ), the specific value is calculated by formula (1):

[0010] L n =L0g -n ,R n =R0g -n ,C n =C0g n ,l n =L0g -n [2Δ(cos2πβn+1)] -1 (1)

[0011] Where n is the number of nodes, L n 、R n 、C n They represent the inductance, resistance, and capacitance of the nth node respectively; β is a constant defined by the Fibonacci sequence: β = F n+1 / F n , F n is the Fibonacci sequence; g is the strength of the non-reciprocal coupling in the model, which is given by g = e |a| where a is the nonreciprocal transition strength, ranging from 0.1 to 0.5. Δ is the quasi-periodic potential in the model. According to formula (1), adjusting g and Δ changes the values ​​of the components, causing the circuit to exhibit abnormal NHSE or AL at a specific frequency.

[0012] The circuit connection method is: main line inductance L n The left and right sides are connected to the main line inductor L n-1 and L n+1 A ground loop unit is connected between two adjacent main line inductors. All three components are connected in parallel and grounded simultaneously. A BNC coaxial connector serves as a signal transmission interface at the junction of the main inductor and the RLC loop.

[0013] Specific implementation cases

[0014] The following describes the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. The described embodiments are only part of the embodiments of the present invention. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0015] Example 1: Left-skin-state circuit based on non-reciprocal AA model

[0016] Figure 2 The figure shows a left-skin-state non-reciprocal AA model circuit with n=13 nodes provided by an embodiment of the present invention, with a non-reciprocal transition strength a=0.2, g=e | a | ≈1.221, disorder Δ / J=0.2. Select C0=10nF, R0=100kΩ, L0=10μH, and calculate by formula (1): L n 、R n 、C n 、l n When the number of nodes n = 13, the number of main line inductors is 14, and the number of grounding RLC loops is 13. The specific component values ​​are as follows: Figure 3 As shown. Figure 3 The components are packaged according to the component values ​​in the figure. The components selected in this embodiment are SMD components with package types of 0805 and 1210. Figure 2 Specifically, the right side of the inductor L1 is connected to the resistor R1, capacitor C1, and inductor l1 to form unit cell 1. The left side of the inductor L1 is directly grounded. This unit cell is located on the left side of the circuit. The left side of the inductor L2 is connected to the right side of the inductor L1 and the grounding items R1, C1, and l1 to form the first node 1 in the circuit. The subsequent components are arranged in order from left to right, just like the design of unit cell 1. When arranged to unit cell 13, the inductor L 13 Connect inductor L on the right 14 , and the inductor L 14The right side is directly grounded, and a BNC coaxial connector is connected at each node as a signal transmission interface. The substrate selected in the embodiment of the present invention is an epoxy resin glass fiber cloth dielectric substrate with a thickness of 4mm. The width of the copper wire connecting the components is 0.381mm, and the BNC interface selects a straight-in 5-hole type. By opening a solder mask window on the substrate to add a layer of solder mask to facilitate patch soldering, the patch components and BNC interface are soldered to the pads of the substrate, and finally a left-skin state non-reciprocal AA model circuit with n=13 nodes is obtained. An AC current source with a frequency of f=588.2kHz is connected to the BNC interface to measure the voltage response. The results show that the voltage value at the left node is large, and an abnormal voltage response is obtained, that is, the left-skin state. The voltage measurement results are shown in the attached figure. Figure 4 shown.

[0017] Example 2 Topological Phase Change Circuit Based on Non-reciprocal AA Model

[0018] Figure 5 The figure shows a non-reciprocal AA model topology phase change circuit with n=13 nodes provided by an embodiment of the present invention, with a non-reciprocal jump strength a=0.2, g=e |a| ≈1.221, disorder Δ / J is a variable parameter, and its value range is 0.1~2.5. Select C0=10nF, R0=100kΩ, L0=10μH, and calculate by formula (1), we can determine L n 、R n 、C n 、l n For a topology circuit with n=13 nodes, the number of main line inductors is 14 and the number of grounding RLC loops is 13, where L n 、C n 、R n The value of is the same as that in Example 1, n The value of can be divided into 25 groups with 13 values ​​in each group as the disorder degree Δ / J changes. Component package selection is performed based on the calculated component values. The components selected in this embodiment are SMD components with package types of 0805 and 1210. Figure 5 Specifically, the right side of the inductor L1 is connected to the resistor R1, capacitor C1, and inductor l1 to form a unit cell 1. An additional empty package pad with a different package from l1 is added at the ground inductor l1 to facilitate the replacement of the ground item l1 of a different package. The left side of the inductor L1 is directly grounded, and the unit cell is located at the leftmost side of the circuit. The left side of the inductor L2 is connected to the right side of the inductor L1 and the ground items R1, C1, and l1 to form the first node 1 in the circuit. The subsequent components are arranged in order from left to right, just like the design of unit cell 1. When arranged to unit cell 13, the inductor L 13Connect inductor L on the right 14 , inductance L 14 The right side is directly grounded. This design can obtain a topological circuit with 13 nodes, and an additional BNC coaxial connector is connected at each node as a signal transmission interface. The embodiment of the present invention uses an epoxy resin glass fiber cloth dielectric substrate with a thickness of 4mm, the copper wire width connecting the components is 0.381mm, and the BNC interface selects a straight-in 5-hole type. The dielectric substrate is subjected to a solder mask window operation to add a layer of solder mask to facilitate manual patch welding, and the patch components and BNC interfaces are soldered on the reserved pads to finally obtain a topological phase change circuit. An AC current source with a frequency range f of 500kHz to 1500kHz is connected to the BNC interface on the right node. At the same time, the grounding inductance l is adjusted by the number of groups. n By performing desoldering and replacement measurements, it can be found that as Δ / J increases, the IPR value decreases first and then increases sharply. The turning point occurs when Δ / J = e | a | At ≈1.221, a topological phase transition of the non-reciprocal AA model was observed, from the left-skin state to the Anderson localized state. The results are as follows Figure 6 The inverse participation rate (IPR) is mainly used to characterize the localization degree of the wave function. Here, it is used to observe the topological phase transition. The specific calculation method is shown in formula (2).

[0019]

[0020] Among them, V n is the magnitude of the node voltage.

Claims

1. A topological circuit based on the nonreciprocal Aubry-André (AA) model, characterized by: The circuit is composed of chip capacitors, chip inductors, chip resistors, an epoxy resin fiberglass cloth dielectric substrate, and a BNC coaxial connector. Passive RLC asymmetry is introduced into the circuit to adjust the numerical proportional relationship between linear components. The circuit exhibits non-Hermitian skin effect (abnormal voltage localization) and Anderson localization (quasi-insulator) at specific frequencies.

2. A topological circuit based on the non-reciprocal Aubry-André (AA) model as claimed in claim 1, characterized in that The reciprocal Aubry-André (AA) model is a classical physical model in condensed matter physics. Specifically, it adds a quasi-periodic potential Δ to the non-reciprocal Hatono-Nelson model. n The non-reciprocal Aubry-André (AA) model in condensed matter physics is realized using topological circuits.

3. A topological circuit based on the non-reciprocal Aubry-André (AA) model as claimed in claim 1, characterized in that The circuit is divided into the main line part and the grounding part. The main line part consists of the inductor L n The grounding part is composed of capacitor C n 、Inductor n , resistor R n The RLC circuit is composed of the number of inductors in the main line equal to the number of nodes n plus 1, and the number of capacitors, inductors, and resistors in the grounding part equals the number of nodes n. The circuit connection method is: the main line inductor L n Connect the main line inductor L on the left and right sides respectively n-1 , L n+1 , a ground loop unit is connected between two adjacent main line inductors, and the three components are connected in parallel and grounded at the same time.

4. A topological circuit based on the non-reciprocal Aubry-André (AA) model as claimed in claim 1, characterized in that The main implementation process of the circuit is as follows: 1) Select the value of the components according to formula (1), and select the components according to the obtained values. L n =L0g -n ,R n =R0g -n ,C n =C0g n ,l n =L0g -n [2Δ(cos2πβn+1)] -1 (1) n is the number of nodes in the circuit, g is the non-reciprocal transition strength, Δ is the amplitude of disorder, and β is a constant defined by the Fibonacci sequence: β = F n+1 / F n , F n is the Fibonacci sequence. 2) Using circuit etching technology, a copper wire with a width of 0.381 mm is etched on the dielectric substrate, and the chip inductor, chip capacitor, and chip resistor are soldered to the reserved pads.

5. A topological circuit based on the non-reciprocal Aubry-André (AA) model as claimed in claim 1, characterized in that The Hermite skin effect is manifested as the voltage amplitude accumulated at the leftmost node of the circuit and the amplitude is large, while the Anderson localization is manifested as the voltage localized at the rightmost node of the circuit and the amplitude is comparable to the feed voltage.

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