One-way signal amplification topology circuit heterojunction based on non-Hermite skin effect

Abstract

The invention relates to the technical field of circuits, in particular to a unidirectional signal amplification topological circuit heterojunction based on a non-Hermite skin effect, which is formed by connecting a topological non-trivial region and a topological trivial region at an interface, every two adjacent nodes are connected through a first coupling element, every two secondary adjacent nodes are connected through a negative impedance converter, and each node is connected with a grounding capacitor or a grounding inductor; the topological trivial area is a rectangular circuit lattice, and every two adjacent nodes are connected through a second coupling element; and the boundary nodes of the topological non-trivial region are connected with the boundary nodes of the topological trivial region through third coupling elements, so that the problems of complex circuit structure, poor stability and easy noise interference caused by introduction of additional gain or loss terms for realizing the non-Hermi topology phenomenon are solved; the device has the advantages of simple structure, high stability and low noise.

Description

Technical Field

[0001] This application relates to the field of circuit technology, and in particular to a heterojunction of a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect. Background Technology

[0002] Topological insulators are a cutting-edge field of physics research in recent years. These materials have the property of "bulk state insulation and edge state conduction". Their boundary states are topologically protected, robust to local defects and disturbances, and can realize unidirectional transmission of signals (such as electrons or photons).

[0003] As research has deepened, the concept of topology has been extended to classical wave systems. For example, topological circuits composed of lumped elements such as inductors and capacitors provide a convenient way to realize and study novel topological physical phenomena on a controllable experimental platform. Meanwhile, the development of non-Hermitian physics has greatly expanded the scope of topological states of matter. Unlike energy-conserving Hermitian systems, non-Hermitian systems describe energy exchange with the environment by introducing gain or loss. Non-Hermitian topological systems exhibit many unique physical effects, the most famous of which is the non-Hermitian skin effect (where all bulk wave functions in the system are localized at the system's boundaries), which provides potential applications for non-reciprocal control and unidirectional amplification of signals.

[0004] like Figure 1 As shown, in order to achieve the non-Hermitian skin effect in circuit systems, related technologies typically rely on the explicit introduction of gain and loss elements (such as active elements or resistor networks) in each node or coupling of the circuit lattice.

[0005] However, solutions relying on complex active gain and loss components distributed throughout the system lead to problems such as complex circuit structures, high manufacturing costs, reduced system stability, and susceptibility to noise, hindering practical applications and expansion. Furthermore, explicit non-Hermitian designs struggle to achieve efficient control in wave-like systems (such as acoustics and optics). Summary of the Invention

[0006] This application provides a heterojunction unidirectional signal amplification topology circuit based on the non-Hermitian skin effect to solve the problems of complex circuit structure, poor stability and susceptibility to noise interference caused by the introduction of additional gain or loss terms to realize the non-Hermitian topology phenomenon. It has the advantages of simple structure, high stability and low noise.

[0007] The first aspect of this application provides a heterojunction for a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect. The heterojunction is formed by connecting topologically nontrivial regions and topologically trivial regions at an interface. The non-trivial region of the topology is a regular hexagonal circuit lattice. In the regular hexagonal circuit lattice, each adjacent node is connected through a first coupling element, each next adjacent node is connected through a negative impedance transformer, and each node is connected to a grounding capacitor or a grounding inductor. The topological trivial region is a rectangular circuit lattice, in which each adjacent node is connected by a second coupling element; The boundary nodes of the non-trivial region of the topology are connected to the boundary nodes of the trivial region of the topology through a third coupling element.

[0008] Optionally, in some embodiments, the negative impedance transformer includes: A first resistor, one end of which is connected to any node; A second resistor, one end of which is connected to the other end of the first resistor, has an impedance equal to that of the first resistor; A third resistor, one end of which is connected to the other end of the second resistor, and the other end of which is connected to the next adjacent node of any node; An operational amplifier, wherein the positive input terminal of the operational amplifier is connected to any of the nodes, the inverting input terminal of the operational amplifier is connected to the connection point between the second resistor and the third resistor, and the output terminal of the operational amplifier is connected to the connection point between the first resistor and the second resistor.

[0009] Optionally, in some embodiments, the first coupling element and the third resistor satisfy a first preset relationship, wherein the first preset relationship is: ; in, The impedance of the third resistor is... Let be the impedance of the first coupling element. The coupling strength between adjacent nodes. The coupling strength between the next adjacent nodes.

[0010] Optionally, in some embodiments, in the regular hexagonal circuit lattice, each adjacent node has a first Hermitian reciprocal coupling relationship and each adjacent node has a second Hermitian non-reciprocal coupling relationship.

[0011] Optionally, in some embodiments, the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect described above further includes: adjusting the admittance of the grounding capacitor or grounding inductor connection to adjust the equivalent in-situ potential energy of the non-trivial region of the topology, so that the zero level is located in the band gap of the non-trivial region of the topology.

[0012] Optionally, in some embodiments, it includes: The equivalent Hamiltonian of the non-trivial region of the topology is: ; in, The equivalent Hamiltonian of the heterojunction is given by [reference to value]. For wave vector, The coupling strength between adjacent nodes. It is the imaginary unit.

[0013] Optionally, in some embodiments, the zero level of the rectangular circuit lattice in the topologically trivial region is located in the conduction band.

[0014] Optionally, in some embodiments, the coupling strength between the boundary nodes of the topologically non-trivial region and the boundary nodes of the topologically trivial region satisfies a second preset relationship with the coupling strength between adjacent nodes, wherein the second preset relationship is: ; in, The coupling strength between adjacent nodes. The coupling strength between the boundary nodes of the non-trivial region of the topology and the boundary nodes of the trivial region of the topology.

[0015] Optionally, in some embodiments, the third coupling element and the first coupling element satisfy a third preset relationship, wherein the third preset relationship is: 2 ; in, The impedance of the first coupling element is... The impedance of the third coupling element.

[0016] Optionally, in some embodiments, the coupling element is a capacitor or an inductor.

[0017] Therefore, the embodiments of this application have the following beneficial effects: (1) This application implicitly introduces non-Hermitian terms through energy exchange between topological non-trivial regions and topological trivial regions, transforms the topological boundary state into a non-Hermitian skin effect, realizes asymmetric transmission of signals along the heterojunction interface direction, does not require explicit gain or loss components, and the system has the advantages of simple structure, high stability and low noise.

[0018] (2) This application can be used for unidirectional signal amplification and can be extended to acoustic, optical and other wave systems, and has good application value.

[0019] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0020] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a schematic diagram illustrating the principle of a scheme for implementing non-Hermitian topological phenomena in related technologies. Figure 2 This is a schematic diagram of a heterojunction in a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect, according to an embodiment of this application. Figure 3 This is a complete circuit schematic diagram of a regular hexagonal lattice cell according to an embodiment of this application; Figure 4 This is a schematic diagram of the circuit structure of a negative impedance converter according to an embodiment of this application; Figure 5 This is a schematic diagram showing a rectangular lattice unit connected to a topologically nontrivial region according to an embodiment of this application; Figure 6 This is a schematic diagram of a voltage response curve provided according to an embodiment of this application; Figure 7 This is a schematic diagram of a pulse excitation response curve provided according to an embodiment of this application. Detailed Implementation

[0021] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0022] The following description, with reference to the accompanying drawings, describes a heterojunction of a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect, according to embodiments of this application. Addressing the problems mentioned in the background art, such as the need to introduce additional gain or loss terms to achieve the non-Hermitian topology, which leads to complex circuit structures, poor stability, and susceptibility to noise interference, this application provides a heterojunction of a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect. This heterojunction is formed by connecting topologically nontrivial regions and topologically trivial regions at their interfaces. The topologically nontrivial region is a regular hexagonal circuit lattice, in which each adjacent node is connected through a first coupling element, each next adjacent node is connected through a negative impedance transformer, and each node is connected to a ground capacitor or ground inductor. The topologically trivial region is a rectangular circuit lattice, in which each adjacent node is connected through a second coupling element. The boundary nodes of the topologically nontrivial region and the boundary nodes of the topologically trivial region are connected through a third coupling element. This solves the problems of complex circuit structures, poor stability, and susceptibility to noise interference caused by introducing additional gain or loss terms to achieve the non-Hermitian topology, and offers advantages such as simple structure, high stability, and low noise.

[0023] Specifically, Figure 2 This is a schematic diagram of a heterojunction of a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect, provided as an embodiment of this application.

[0024] like Figure 2 As shown, the heterojunction 1 of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect is formed by connecting a topologically nontrivial region 11 and a topologically trivial region 12 at the interface. The topologically nontrivial region 11 is a regular hexagonal circuit lattice. In the regular hexagonal circuit lattice, each adjacent node is connected through a first coupling element, each next adjacent node is connected through a negative impedance transformer, and each node is connected to a ground capacitor or a ground inductor. The topologically trivial region 12 is a rectangular circuit lattice. In the rectangular circuit lattice, each adjacent node is connected through a second coupling element. The boundary nodes of the topologically nontrivial region 11 and the boundary nodes of the topologically trivial region 12 are connected through a third coupling element.

[0025] The coupling element is either a capacitor or an inductor. In the regular hexagonal circuit lattice, each adjacent node has a first coupling relationship of Hermitian reciprocity and a second coupling relationship of Hermitian non-reciprocity.

[0026] It should be noted that the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect proposed in this application realizes the equivalent behavior of a topological insulator through the topological non-trivial region and the equivalent behavior of a topological conductor through the topological trivial region. Based on the unidirectional topological boundary states of the topological non-trivial region (topological insulator), the non-Hermitian term is implicitly introduced through the energy exchange between the topological trivial region (topological conductor) and the topological non-trivial region to realize the non-Hermitian skin effect without the need for additional gain or loss terms.

[0027] Combination Figures 2 to 5 As shown, the heterojunction 1 of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect in this embodiment is composed of two interconnected parts, including an equivalent circuit topology insulator region 11 and a conductor region 12. The circuit topology insulator region 11 has a regular hexagonal lattice, where nearest-neighbor coupling can be achieved by a capacitor (or inductor) 111, second-nearest-neighbor coupling can be achieved by a negative impedance transformer 112, and node in-situ potential energy can be achieved by a grounded inductor (or capacitor) 113. The circuit conductor region 12 has a rectangular lattice, where x-direction coupling can be achieved by a capacitor (or inductor) 121, and y-direction coupling can be achieved by a capacitor (or inductor) 122. The circuit topology insulator region 11 and conductor region 12 can be connected by a capacitor (or inductor) 13.

[0028] In the embodiments of this application, such as Figure 2 As shown, a structure is established along the interface direction of the heterojunction. y An axis is established in its vertical direction. x The axis is constructed with one of the lattice points on the interface between the topologically nontrivial region 11 and the topologically trivial region 12 as the origin. xy Coordinate system.

[0029] The core of the topological nontrivial region 11 is to construct a regular hexagonal circuit lattice equivalent to the Haldane topological model, such as... Figure 3 As shown, nearest neighbor coupling corresponds to each node in the lattice being connected to its three nearest neighbors, which is the first coupling relationship of Hermitian reciprocity, and the coupling strength is... In this embodiment, the first coupling relationship is achieved through a lumped element 111, for example, by connecting adjacent nodes with a capacitance value of... The capacitance, its impedance magnitude ,in, This is the circuit's operating angular frequency.

[0030] The second nearest neighbor coupling corresponds to each node in the lattice being connected to its second six neighboring nodes. This is a Hermitian non-reciprocal second coupling relationship, with a coupling strength of... The second coupling relationship is used to break the time-reversal symmetry of the system, transforming the ordinary regular hexagonal lattice model into a Haldane model with topological boundary states. This coupling is achieved through a negative impedance transformer.

[0031] Optionally, in some embodiments, the negative impedance transformer includes: a first resistor, one end of which is connected to any node; a second resistor, one end of which is connected to the other end of the first resistor, the impedance of the second resistor being equal to the impedance of the first resistor; a third resistor, one end of which is connected to the other end of the second resistor, the other end of which is connected to the next adjacent node of any node; and an operational amplifier, the positive input terminal of which is connected to any node, the inverting input terminal of which is connected to the connection point between the second and third resistors, and the output terminal of which is connected to the connection point between the first and second resistors.

[0032] The first coupling element and the third resistor satisfy a first preset relationship, which is: ; in, The impedance of the third resistor. The impedance of the first coupling element is... The coupling strength between adjacent nodes. The coupling strength between the next adjacent nodes.

[0033] like Figure 4 As shown, Figure 4 A specific circuit schematic of a negative impedance converter is provided, which includes an operational amplifier (Op-Amp) and two feedback resistors of equal value. and a working resistor In this configuration, due to the virtual short-circuit and virtual open-circuit operating characteristics of the operational amplifier, the current flowing into node ① is... The current flowing into node ② is Therefore, this negative impedance transformer behaves as a "negative resistor" for node ①. Node ②, however, behaves as a typical resistor. This breaks the symmetry between the two nodes.

[0034] Optionally, in some embodiments, the heterojunction 1 of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect described above further includes: adjusting the admittance of the grounding capacitor or grounding inductor connection to adjust the equivalent in-situ potential energy of the topological nontrivial region 11, so that the zero level is located in the band gap of the topological nontrivial region 11.

[0035] Specifically, the in-situ potential energy of each node is realized by connecting a grounding capacitor or a grounding inductor (i.e., grounding element 113) to each node, and a grounding inductor is connected to each node. At that time, its impedance satisfies the following at the operating frequency: ; This impedance is used to control the position of the Bloch band of the insulator in the circuit topology. Under this configuration, the self-admittance of each node is: ; The corresponding zero level is located in the band gap of the Haldane model. Therefore, the bulk states of the circuit topology insulator region 11 are insulating, but the topological boundary states that support unidirectional signal conduction at their boundaries are given by:

[0036] in, For the equivalent Hamiltonian of the heterojunction, For wave vector, The coupling strength between adjacent nodes. It is the imaginary unit.

[0037] Optionally, in some embodiments, the zero level of the rectangular circuit lattice of the topological trivial region 12 is located in the conduction band.

[0038] The coupling strength between the boundary nodes of the topologically nontrivial region 11 and the boundary nodes of the topologically trivial region 12 satisfies a second preset relationship with the coupling strength between adjacent nodes. The second preset relationship is as follows: ; in, The coupling strength between adjacent nodes. Let be the coupling strength between the boundary nodes of the topologically nontrivial region 11 and the boundary nodes of the topologically trivial region 12. The third coupling element and the first coupling element satisfy a third preset relationship, wherein the third preset relationship is: 2 ; in, The impedance of the first coupling element is... The impedance of the third coupling element.

[0039] Specifically, the topological trivial region 12 is used to simulate the conductor region of the circuit, such as... Figure 5 As shown, the connection relationship of its components forms an equivalent rectangular circuit lattice, in which... x Directional coupling is achieved through a second coupling element 121 between adjacent nodes. In this embodiment, the second coupling element uses an inductance value of An inductor, whose impedance is ; y Directional coupling is achieved through a second coupling element 122 between adjacent nodes. In this embodiment, a capacitance value of [value missing] is used. A capacitor has an impedance of The zero level of the conductor region 12 in this circuit is located in its conduction band, therefore, when it passes through the third coupling element 13 (capacitance value in this embodiment), When a capacitor (capacitor) and a topologically nontrivial region 11 are connected at the boundary, energy exchange can occur between them. The impedance is Its value must meet the following requirements. 2 At this time, its corresponding coupling strength satisfy .

[0040] According to one embodiment of the present invention, both the topological nontrivial region 11 and the topological trivial region 12 are Hermitian systems, and therefore the heterojunction 1 of the topological circuit formed by their connection is also a Hermitian system. However, at the interface between the two, energy exchange occurs between the topological nontrivial region 11 and the topological trivial region 12. This energy exchange is physically equivalent to the topological boundary state of the topological nontrivial region 11 being implicitly introduced into the topological trivial region 12, transforming the topological boundary state, which can only propagate in a single direction along the interface, into a non-Hermitian skin effect with asymmetric propagation characteristics in both directions. Therefore, the non-Hermitian topological phenomenon implemented in the embodiments of this application does not require the explicit addition of any additional gain and loss components to the system.

[0041] In summary, the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect proposed in this invention is formed by connecting two regions at the interface, including a topologically nontrivial region one and a topologically trivial region two. The topological relationships of the circuit element connections in region one constitute an equivalent regular hexagonal circuit lattice, corresponding to a topological insulator. The element topology in region two constitutes an equivalent rectangular circuit lattice, corresponding to a conductor. Each node in the regular hexagonal lattice of region one has a Hermitian reciprocal coupling relationship with its three nearest neighbors, with a coupling strength of [value missing]. Each node in the crystal lattice has a Hermitian non-reciprocal coupling relationship with its next six nearest neighbors, and the coupling strength is... , The imaginary unit, This represents the non-reciprocal property, specifically manifested from the center of the regular hexagonal element containing the coupling relationship, when the coupling direction is clockwise. Counterclockwise .

[0042] By adjusting the self-admittance of the circuit nodes, the in-situ potential energy of the lattice points can be changed, controlling the position of the Bloch band of the topological insulator and thus achieving the modulation of the supported zero-energy mode. When the zero level is located in the band gap of the topological insulator, the model is insulated internally while supporting unidirectional boundary states at the boundary.

[0043] Each node in the region two rectangular lattice and its x The coupling strength between adjacent nodes in the direction is , y The coupling strength between adjacent nodes in the direction is Region 1 connects to Region 2 on its boundary. The energy exchange between the two at the interface will introduce non-Hermitian interaction terms into the boundary states of the topological insulator, transforming the boundary states into non-Hermitian skin effects.

[0044] It should be noted that, in the embodiments of this application, nearest neighbor coupling... This is achieved by connecting a capacitor (or inductor) between adjacent nodes, where the impedance of the connected capacitor (or inductor) is... Second nearest neighbor coupling This is achieved through a negative impedance transformer, and Each negative impedance transformer contains an operational amplifier and two feedback resistors with equal impedance. and working resistance ; The in-situ potential energy at the lattice points is realized by connecting a grounded inductor (or capacitor) to the node, and the impedance of the connected inductor (or capacitor) is... Region Two x Directional coupling and y Directional coupling This is achieved by connecting capacitors (or inductors) between adjacent nodes, with the impedances of the connected capacitors (or inductors) being respectively... and Region 2 is only connected to nodes on the boundary of Region 1, and the zero level of the equivalent conductor lattice of Region 2 is located in the conduction band; the coupling strength between nodes on the boundary of Region 1 and nodes on the boundary of Region 2 is... And satisfy This coupling is achieved by connecting a capacitor (or inductor), the impedance of which is... , 2 .

[0045] This application also provides a method for fabricating a heterojunction of a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect, the method comprising the following steps: S1, using methods including but not limited to printed circuit boards, direct wire connections, etc., to connect the above-mentioned circuit lumped components that meet the parameter requirements according to... Figure 3 and Figure 5 The connection relationships shown are processed into corresponding circuits for the topological insulator region 11 and the conductor region 12.

[0046] S2, using a capacitor or inductor as a connecting element 13, the topological insulator region 11 and the conductor region 12 are connected at the boundary. Figure 5 Connect them as shown to obtain the heterojunction 1 of the topology circuit.

[0047] To enable those skilled in the art to further understand the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect of the embodiments of this application, a detailed description is provided below in conjunction with specific embodiments.

[0048] First, the lumped elements used in the heterojunction are selected, including the nearest-neighbor coupling capacitor 111 of the topological insulator region 11, the operational amplifier, feedback resistor, and operating resistor of the second-nearest-neighbor coupling negative impedance transformer 112, and the node grounding inductor 113; the conductor region 12 x Directional coupling is achieved by inductor 121. y Directional coupling capacitor 122. Then, using printed circuit boards and surface mount technology, these are fabricated into circuit boards corresponding to the topological insulator region 11 and conductor region 12, respectively. Connecting capacitor 13 is selected and used to connect specific boundary nodes of the two types of circuit boards, resulting in the topological circuit heterojunction 1.

[0049] In actual implementation, such as Figure 6 As shown, the heterojunction topology of this embodiment enables signals input to its one-dimensional interface to exhibit different transmission characteristics in two directions away from the excitation source. This indicates that energy (voltage amplitude) tends to be localized at one end of the interface, a characteristic typical of the non-Hermitian skin effect. Utilizing this asymmetry, the embodiments of this application can be used to achieve unidirectional signal amplification. Figure 7 As shown, if a circuit gain is introduced at the node of the heterojunction interface (e.g., through a negative impedance transformer that behaves as a "negative resistance" by grounding), the original direction can be reduced. A signal that decays in a specific direction becomes exponentially amplified, while The directional signal still decays rapidly, thus achieving a highly efficient unidirectional signal amplifier.

[0050] According to the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect proposed in the embodiments of this application, the circuit admittance matrix of region one at the operating frequency is equivalent to the Hamiltonian matrix of a Haldane topological insulator. Therefore, its voltage distribution characteristics exhibit chiral topological boundary states locally at the boundary, that is, the voltage signal cannot propagate inside the region one, but can only be transmitted unidirectionally along the boundary of region one, for example, only along... Directional transmission. The circuit structure of region two is equivalent to a conductor in a rectangular lattice. When it is connected to region one, there is an energy exchange between them. This can be considered as region two introducing a non-Hermitian action term to the boundary of the connected region one. On the boundary of region one, the original chiral topological boundary states cause the voltage signal to only propagate in the direction of transmission. Directional transmission, Directional transmission is impossible. However, after introducing non-Hermitian characteristics in connection region two, the voltage signal can be transmitted in both directions, but an asymmetry exists, i.e., in the direction of transmission... The attenuation rate of directional transmission is greater than that of directional transmission. The attenuation rate of directional transmission is a typical non-Hermitian skin effect. This method does not require distributed gain / loss throughout the system, has a simple structure, and high stability, providing a novel technical path for realizing non-Hermitian topology control in wave systems such as circuits, acoustics, and optics.

[0051] Therefore, the heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect in this embodiment constructs a regular hexagonal lattice in the topological insulator region using passive lumped elements such as capacitors and inductors. By connecting negative impedance transformers between the next nearest neighbor nodes to achieve Hermitian non-reciprocal coupling, the time-reversal symmetry is broken, resulting in non-trivial topological invariants in the Bloch band of this lattice, leading to the generation of unidirectional propagating topological boundary states in the bandgap. Furthermore, the boundary nodes of the topological insulator are connected to a conductor region. Both regions are Hermitian, but at the interface, energy exchange occurs between the topological insulator and the conductor. Therefore, physically, the conductor exerts a non-Hermitian effect on the topological insulator boundary. When the zero level of the topological insulator lattice is located in the bandgap, since only topological boundary states exist there, the model can be described by the equivalent Hamiltonian of the boundary states, while the influence of the conductor on the boundary states can be described by its self-energy. Specifically, the self-energy of the conductor transforms the boundary state into a non-Hermitian skin effect, causing waves entering the heterojunction interface to exhibit asymmetric propagation characteristics in different directions. Based on the non-Hermitian skin effect, it is possible to unidirectionally amplify the input voltage signal at the heterojunction interface.

[0052] The heterojunction of the unidirectional signal amplification topology circuit based on the non-Hermitian skin effect proposed in the embodiments of this application is formed by connecting a topologically nontrivial region and a topologically trivial region at the interface. The topologically nontrivial region is a regular hexagonal circuit lattice. In the regular hexagonal circuit lattice, each adjacent node is connected through a first coupling element, each next adjacent node is connected through a negative impedance transformer, and each node is connected to a ground capacitor or a ground inductor. The topologically trivial region is a rectangular circuit lattice. In the rectangular circuit lattice, each adjacent node is connected through a second coupling element. The boundary nodes of the topologically nontrivial region and the boundary nodes of the topologically trivial region are connected through a third coupling element. Thus, the problems of complex circuit structure, poor stability, and susceptibility to noise interference caused by the introduction of additional gain or loss terms to realize the non-Hermitian topology phenomenon are solved. It has the advantages of simple structure, high stability, and low noise.

[0053] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0054] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0055] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0056] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0057] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0058] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A heterojunction for a unidirectional signal amplification topology circuit based on the non-Hermitian skin effect, characterized in that, The heterojunction is formed by connecting topologically nontrivial regions and topologically trivial regions at the interface, wherein, The non-trivial region of the topology is a regular hexagonal circuit lattice. In the regular hexagonal circuit lattice, each adjacent node is connected through a first coupling element, each next adjacent node is connected through a negative impedance transformer, and each node is connected to a grounding capacitor or a grounding inductor. The topological trivial region is a rectangular circuit lattice, in which each adjacent node is connected by a second coupling element; The boundary nodes of the non-trivial region of the topology are connected to the boundary nodes of the trivial region of the topology through a third coupling element.

2. The heterojunction according to claim 1, characterized in that, The negative impedance converter includes: A first resistor, one end of which is connected to any node; A second resistor, one end of which is connected to the other end of the first resistor, has an impedance equal to that of the first resistor; A third resistor, one end of which is connected to the other end of the second resistor, and the other end of which is connected to the next adjacent node of any node; An operational amplifier, wherein the positive input terminal of the operational amplifier is connected to any of the nodes, the inverting input terminal of the operational amplifier is connected to the connection point between the second resistor and the third resistor, and the output terminal of the operational amplifier is connected to the connection point between the first resistor and the second resistor.

3. The heterojunction according to claim 2, characterized in that, The first coupling element and the third resistor satisfy a first preset relationship, which is: ； in, The impedance of the third resistor is... Let be the impedance of the first coupling element. The coupling strength between adjacent nodes. The coupling strength between the next adjacent nodes.

4. The heterojunction according to claim 1, characterized in that, In the hexagonal circuit lattice, each adjacent node has a first Hermitian reciprocal coupling relationship and a second Hermitian non-reciprocal coupling relationship.

5. The heterojunction according to claim 1, characterized in that, include: Adjust the admittance of the grounding capacitor or grounding inductor connection to adjust the equivalent in-situ potential energy of the topological nontrivial region, so that the zero level is located in the band gap of the topological nontrivial region.

6. The heterojunction according to claim 4, characterized in that, include: The equivalent Hamiltonian of the non-trivial region of the topology is: ； in, The equivalent Hamiltonian of the heterojunction is given by [reference to value]. For wave vector, The coupling strength between adjacent nodes. It is the imaginary unit.

7. The heterojunction according to claim 1, characterized in that, The zero level of the rectangular circuit lattice in the topologically trivial region is located in the conduction band.

8. The heterojunction according to claim 1, characterized in that, The coupling strength between the boundary nodes of the non-trivial region and the boundary nodes of the trivial region satisfies a second preset relationship with the coupling strength between adjacent nodes. The second preset relationship is as follows: ； in, The coupling strength between adjacent nodes. The coupling strength between the boundary nodes of the non-trivial region of the topology and the boundary nodes of the trivial region of the topology.

9. The heterojunction according to claim 1, characterized in that, The third coupling element and the first coupling element satisfy a third preset relationship, wherein the third preset relationship is: 2 ； in, The impedance of the first coupling element is... The impedance of the third coupling element.

10. The heterojunction according to claim 1, characterized in that, The coupling element is a capacitor or an inductor.

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