High-sensitivity non-Hermite sensing circuit system based on Mobius insulator

Abstract

The invention discloses a high-sensitivity non-Hermite sensing circuit system based on a Mobius insulator in the technical field of electronic circuits, and the system comprises at least one group of circuit nodes which comprise a first circuit node, a second circuit node, a third circuit node, a fourth circuit node and at least one group of non-reciprocal coupling assemblies, the group of non-reciprocal coupling components comprises two negative impedance converters, one negative impedance converter is arranged between the first circuit node and the third circuit node, and the other negative impedance converter is arranged between the second circuit node and the fourth circuit node; a non-Hermite element is introduced into a circuit, and parameters of the non-Hermite element are accurately adjusted, so that unidirectional aggregation and enhancement of current or signals in a specific direction, namely a non-Hermite skin effect is realized, and the effect enables the signals to be transmitted in a centralized manner along a specific path, so that the scattering loss of a system is effectively reduced, and the transmission efficiency and the direction selectivity are improved.

Description

Technical Field

[0001] The invention relates to the technical field of electronic circuits, and in particular to a highly sensitive non-Hermitian sensing circuit system based on a Mobius insulator. Background Art

[0002] With the in-depth development of topological physics in circuit systems, topological insulation and its realization in circuits have become cutting-edge research topics. However, traditional topological systems are mostly limited to the Hermitian framework, which makes it difficult to deal with non-equilibrium phenomena in actual systems. In recent years, non-Hermitian topological circuits have gradually attracted attention because they can describe and utilize novel phenomena such as non-reciprocity and singularities in the system.

[0003] In traditional Hermitian systems, by introducing the physical mechanisms of energy gain / loss or non-reciprocal energy coupling, the study of topological states has been further extended to non-Hermitian systems, greatly enriching the research direction of topological physics. The most distinctive physical phenomena in non-Hermitian systems include the destruction of body-boundary correspondence and the generation of skin effect. These new characteristics have also spawned a new topological classification. Since it is relatively difficult to introduce balanced gain and loss in cold atoms or photonics, the experimental verification of non-Hermitian topological systems has always been challenging. In recent years, thanks to the wide selectivity of active devices, circuit systems have gradually become an ideal experimental platform for studying various non-Hermitian topological systems. Based on previous theoretical studies, Liu et al. proposed a circuit experimental scheme for constructing non-Hermitian topological states using resistance gain and loss (Phys. Rev. Lett. 122, 233902 (2019)). In 2021, Liu et al. further experimentally proved the existence of the non-Hermitian skin effect in an improved non-reciprocal coupling Su-Schrieffer-Heeger (SSH) topological circuit (Phys. Rev. B 98, 205442 (2018)). In this experiment, the non-reciprocal coupling was realized through the unidirectional coupling characteristics of the voltage follower module. The results show that under periodic boundary conditions, all eigenstates oscillate with almost the same intensity in the circuit chain, while under open boundary conditions, the oscillation intensity decays exponentially from the edge of the circuit. In addition, Helbig et al. also experimentally confirmed the existence of a generalized body-edge correspondence in non-Hermitian topological circuits (Phys. Rev. Lett. 124, 056802 (2020)). In addition, many studies have also explored the realization of the skin effect and wave function clustering phenomenon in circuit systems, providing more experimental support for this field.

[0004] Therefore, non-Hermitian topological insulator circuits not only expand the application boundaries of topological physics, but also provide innovative ideas for the design of new generation electronic devices. Its application prospects are broad, covering communications, sensing, quantum information processing and other fields, and have significant technical and commercial value.

[0005] The Möbius insulator structure has a unique band gap and energy spectrum, which enables the system to exhibit unprecedented characteristics in energy transmission and signal processing, such as unidirectional transmission, enhanced robustness and fault tolerance. The present invention introduces this structure into a non-Hermitian framework to further give it non-reciprocity and dynamic adjustability, which is suitable for the development of high-performance electronic components such as isolators, circulators, and highly sensitive sensors. In addition, the circuit provides an experimental platform for simulating topological quantum states, which helps to explore potential quantum computing and communication technologies. Summary of the invention

[0006] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification summary and invention title of the present invention to avoid blurring the purpose of this section, specification summary and invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0007] Therefore, the purpose of the present invention is to provide a highly sensitive non-Hermitian sensing circuit system based on a Mobius insulator, which integrates non-reciprocal elements to achieve unidirectional transmission of signals and non-reciprocity enhancement. The non-Hermitian skin effect in the non-Hermitian circuit allows the signal to naturally gather in the direction of the boundary, improve transmission efficiency and reduce scattering losses. Its core technology is based on the simulation of non-Hermitian systems, supporting the construction of highly robust communication elements and highly sensitive sensors. The circuit design uses a negative impedance converter to achieve non-reciprocal coupling, and by precisely adjusting the capacitor and resistor elements, topological protection state transmission in different frequency bands is achieved. The system has a wide range of application value in the fields of modern communications, sensors and quantum information processing, and is particularly suitable for application scenarios with strict requirements on high performance and anti-interference capabilities.

[0008] In order to solve the above technical problems, the present invention provides a highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator, which adopts the following technical solution: comprising: at least one group of circuit nodes, one group of circuit nodes comprising a first circuit node, a second circuit node, a third circuit node, a fourth circuit node connected in sequence and at least one group of non-reciprocal coupling components, the group of non-reciprocal coupling components comprising two negative impedance converters, one of which is arranged between the first circuit node and the third circuit node, and the other negative impedance converter is arranged between the second circuit node and the fourth circuit node.

[0009] Optionally, a group of the circuit nodes further includes an inductor L1, which is arranged between the first circuit node and the third circuit node; and a capacitor C1, which is arranged between the second circuit node and the fourth circuit node.

[0010] Optionally, the negative impedance converter includes: an operational amplifier A; a resistor R a , the resistor Ra One end of the resistor R is connected to the positive input port of the operational amplifier A and the input voltage V1, and the other end is connected to the output port of the operational amplifier; b , the resistor R b One end of the operational amplifier is connected to the output port and the resistor R a The other end of the capacitor C g , the capacitor C g One end of the operational amplifier A is connected to the negative input port and the resistor R b The other end of the capacitor C g The other end is connected to the input voltage V2.

[0011] Optionally, the capacitor C g The negative impedance converter is adjustable by adjusting the capacitance C g The value of capacitor C g The ratio of capacitance C1 is used to adjust the frequency band structure of the sensing circuit system.

[0012] Optionally, a group of the circuit nodes further includes a capacitor c1, and the capacitor c1 is connected between the first circuit node and the second circuit node and between the third circuit node and the fourth circuit node.

[0013] Optionally, a group of the circuit nodes further includes a capacitor C3, and the first circuit node and the third circuit node are both grounded through the capacitor C3; and an inductor L3, and the second circuit node and the fourth circuit node are both grounded through the inductor L3.

[0014] Optionally, multiple groups of circuit nodes are included, and the circuit nodes between two adjacent groups are

[0015] An inductor L2 is connected between the first circuit node and the third circuit node;

[0016] A capacitor C2 is connected between the second circuit node and the fourth circuit node;

[0017] The negative impedance converter is connected between the first circuit node and the third circuit node and between the second circuit node and the fourth circuit node;

[0018] The capacitor c1 is connected between the first circuit node and the second circuit node and between the third circuit node and the fourth circuit node.

[0019] In summary, the present invention includes at least one of the following beneficial effects:

[0020] 1. High robustness and anti-interference ability. Due to the non-Hermitian topological protection characteristics of the present invention, the present invention can still maintain the stability of signal transmission even under environmental disturbances or device defects. This high robustness makes it particularly suitable for complex communication environments and high-precision sensor applications.

[0021] 2. Low-loss unidirectional signal transmission. The present invention utilizes the non-Hermitian skin effect to naturally gather and enhance electrical signals in a specific direction, thereby significantly reducing scattering and loss during signal transmission. This feature helps to achieve lossless or low-loss efficient energy transmission.

[0022] 3. Strong non-reciprocity and topological protection. The non-Hermitian-Mobius insulator structure realizes non-reciprocal coupling in the system of the present invention, ensuring that the signal can only propagate in one direction and avoiding reflection interference. This non-reciprocity improves the stability and performance of the system of the present invention in a multi-band range.

[0023] 4. Dynamic adjustability and flexible configuration: By adjusting the value of capacitor Cg, the present invention can achieve dynamic adjustment of system parameters and support multi-channel and multi-band signal transmission requirements. This feature allows the system to be flexibly configured according to different application scenarios.

[0024] 5. The non-reciprocal signal transmission characteristics and topological protection state of the system of the present invention support the construction of highly sensitive sensors and high-performance communication equipment. Its structure is suitable for miniaturization and high-integration design, meeting the requirements of modern communication and sensor systems for equipment compactness and reliability.

[0025] 6. The system of the present invention provides an experimental platform for simulating and verifying topological quantum states, supporting the research and development of future quantum computing and quantum communication. This makes the invention have broad potential value in academic research and industrial applications.

[0026] 7. The signal loss is reduced through unidirectional transmission and skin effect, which improves the energy utilization rate of the system of the present invention. This feature helps to reduce the operating cost and power consumption of equipment in the field of efficient energy transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0028] Figure 1 The schematic diagram of the highly sensitive non-Hermitian sensing circuit based on the Mobius insulator of the present invention;

[0029] Figure 2It is a schematic diagram of a negative impedance converter circuit of the present invention;

[0030] Figure 3 A schematic diagram of a lattice model corresponding to the high-sensitivity non-Hermitian sensing circuit based on a Mobius insulator according to the present invention;

[0031] Figure 4 For the present invention C g =1nF circuit frequency (obtained from the real part of the admittance matrix) and wave vector k y Relationship diagram;

[0032] Figure 5 For the present invention C g =1nF when the imaginary part of the admittance matrix and the wave vector k y Relationship diagram;

[0033] Figure 6 For the present invention C g =10nF circuit frequency (obtained from the real part of the admittance matrix) and wave vector k y Relationship diagram;

[0034] Figure 7 For the present invention C g =10nF when the imaginary part of the admittance matrix and the wave vector k y Relationship diagram;

[0035] Figure 8 The frequency of the present invention varies with the parameter C g / C1 change relationship diagram;

[0036] Fig. 9 For the present invention C g =1nF, the boundary characteristic state distribution diagram in the high-sensitivity non-Hermitian sensing circuit system based on the Möbius insulator;

[0037] Fig.10 For the present invention C g =10nF, the boundary characteristic state distribution diagram in the high-sensitivity non-Hermitian sensing circuit system based on the Möbius insulator;

[0038] Fig.11 For the present invention C g =1nF, the distribution diagram of the in vivo characteristic state in the high-sensitivity non-Hermitian sensing circuit system based on the Möbius insulator;

[0039] Fig.12 For the present invention C g =10nF, the distribution diagram of the in vivo characteristic state in the high-sensitivity non-Hermitian sensing circuit system based on the Möbius insulator;

[0040] Fig.13 For the present invention C g=1nF, voltage distribution diagram of high-sensitivity non-Hermitian sensing circuit based on Mobius insulator at frequency 486Khz;

[0041] Fig.14 For the present invention C g =1nF, voltage distribution diagram of high-sensitivity non-Hermitian sensing circuit based on Mobius insulator at frequency 486Khz;

[0042] Fig.15 For the present invention C g =1nF, voltage distribution diagram of high-sensitivity non-Hermitian sensing circuit based on Mobius insulator at frequency 330Khz;

[0043] Fig.16 For the present invention C g =10nF, voltage distribution diagram of high-sensitivity non-Hermitian sensing circuit based on Möbius insulator at frequency 330Khz. DETAILED DESCRIPTION

[0044] In order to facilitate understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are shown in the drawings, but the present invention can be implemented in many different forms and is not limited to the embodiments described in the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0045] Unless otherwise defined, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art. The terms used in this specification are intended to describe specific embodiments and are not intended to limit the present invention.

[0046] It should be understood that no matter the terms "element", "module", "component", "region" or "layer" are used in the description of the present invention, these terms are only used to refer to the various parts and structures of the present invention, and they can be replaced or used in combination without departing from the teachings of the present invention. Therefore, "element" can mean "module", "component" or "region" without departing from the present invention.

[0047] It should be understood that when a module is considered to be "connected" to another module, it can be directly connected to another module, or connected to another module through an intermediate module. In addition, in an embodiment of the present invention, "connection" can also be regarded as a connection method with signal or current transmission, for example, understood as "electrical connection" or "signal connection", etc. It should be understood that the singular form of "one", "one" or "said" can include plural forms, unless the context clearly indicates otherwise. It should also be understood that the words "including / comprising" and "or" when used only indicate the presence of the stated features, steps, operations, modules or components, but do not exclude the possibility of a combination of one or more other features, steps, operations, modules or components. At the same time, when used herein, the term "and / or" should be understood to indicate any and all combinations of and / or.

[0048] In the description of the present invention, the term "non-Hermitian circuit" is used to refer to circuit structures with non-reciprocal terms, which are different from conventional Hermitian circuits and can achieve unidirectional transmission of signals and skin effect. "Mobius insulator" refers to a topological geometric structure used in the circuit, which is characterized by having a single side and a single edge, which is used to enhance the non-reciprocal transmission characteristics of the signal.

[0049] In the present invention, "non-reciprocal coupling" means that the signal in the system can only propagate in a specific direction and not in the reverse direction, thereby avoiding signal reflection interference; "skin effect" refers to the phenomenon that the signal tends to gather at the edge of the circuit at certain frequencies.

[0050] It should be understood that the non-reciprocal coupling element is the negative impedance converter. The negative impedance converter is similar to the function of a diode, which allows the current to flow in one direction. This function is similar to the fact that atoms in physics can only transition in one direction on the lattice points of a crystal lattice, so it is called non-reciprocal coupling. In other words, the negative impedance converter is an actual circuit element, and the non-reciprocal coupling element is the name of the negative impedance converter in the physical model. The two are equivalent.

[0051] The "negative impedance converter" in the present invention refers to a special amplifier module, whose internal specific structure is described in detail below. It includes an operational amplifier, a resistor and a capacitor, and is used to realize a specific non-reciprocal coupling effect in a circuit system so that the signal in the circuit has a directional transmission characteristic.

[0052] Embodiment 1

[0053] Reference Figure 1The present invention discloses a highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator, comprising: at least one group of circuit nodes, wherein the group of circuit nodes comprises a first circuit node 1, a second circuit node 2, a third circuit node 3, a fourth circuit node 4 connected in sequence and at least one group of non-reciprocal coupling components, for realizing unidirectional transmission of signals within the system; a group of non-reciprocal coupling components comprises two negative impedance converters to provide non-reciprocal coupling and enhance the transmission characteristics of a topological protection state; wherein one of the negative impedance converters is arranged between the first circuit node 1 and the third circuit node 3, and the other negative impedance converter is arranged between the second circuit node 2 and the fourth circuit node 4.

[0054] The group of circuit nodes further includes an inductor L1 arranged between the first circuit node 1 and the third circuit node 3 ; and a capacitor C1 arranged between the second circuit node 2 and the fourth circuit node 4 .

[0055] The group of circuit nodes further includes a capacitor c1 , and the capacitor c1 is connected between the first circuit node 1 and the second circuit node 2 , and between the third circuit node 3 and the fourth circuit node 4 .

[0056] A group of circuit nodes further includes a capacitor C3, through which the first circuit node 1 and the third circuit node 3 are both grounded; and an inductor L3, through which the second circuit node 2 and the fourth circuit node 4 are both grounded.

[0057] Reference Figure 2 In detail, in this embodiment, the negative impedance converter includes:

[0058] Operational amplifier A; resistor R a , resistor R a One end of the resistor is connected to the positive input port of the operational amplifier A and the input voltage V1, and the other end is connected to the output port of the operational amplifier; b , resistor R b One end is connected to the output port of the operational amplifier and the resistor R a The other end of the capacitor C g , capacitor C g One end of the resistor R is connected to the negative input port of the operational amplifier A and the b The other end of the capacitor C g The other end is connected to the input voltage V2.

[0059] In detail, in this embodiment, the capacitor C g The value of the negative impedance converter is adjustable by adjusting the coupling capacitor C g The negative impedance converter dynamically adjusts the system parameters by adjusting the value of capacitor C to meet the transmission requirements of multi-channel and multi-band signals. g The value of capacitor C gThe ratio of capacitance C1 is used to adjust the frequency band structure of the sensing circuit system to adapt to the topological protection state transmission requirements in different frequency bands.

[0060] Embodiment 2

[0061] Reference Figure 1 The present invention discloses a highly sensitive non-Hermitian sensing circuit system based on a Mobius insulator, comprising a plurality of groups of circuit nodes, between two adjacent groups of circuit nodes

[0062] An inductor L2 is connected between the first circuit node 1 and the third circuit node 3;

[0063] A capacitor C2 is connected between the second circuit node 2 and the fourth circuit node 4;

[0064] Negative impedance converters are connected between the first circuit node 1 and the third circuit node 3 and between the second circuit node 2 and the fourth circuit node 4;

[0065] A capacitor c1 is connected between the first circuit node 1 and the second circuit node 2 , and between the third circuit node 3 and the fourth circuit node 4 .

[0066] It should be noted that the values ​​of capacitors C1, C2 and c1 are all the same, and are just a reference value.

[0067] Reference Figure 3 , is a schematic diagram of the lattice model corresponding to the highly sensitive non-Hermitian sensing circuit based on the Möbius insulator, combined with Figure 1 ,in, Figure 1 The circuit connection c1 simulates Figure 3 In the lattice model, t, that is, c1 corresponds to the coupling coefficient t. Similarly, L1 L2 corresponds to negative coupling coefficients -J1 and -J2, and C1 and C2 also correspond to positive coupling coefficients J1 and J2. ±C g Corresponding to ±δ y This coupling structure that alternately uses capacitors and inductors can form a frequency-selective transmission channel.

[0068] Figure 1 The characteristic equation of the constructed topological circuit and Figure 2 The characteristic equation of the lattice model has the same mathematical form. According to Kirchhoff's current law, for each node column circuit equation, we can get:

[0069]

[0070] in:

[0071]

[0072] j c=iωC1

[0073] j d1 =iωC3

[0074]

[0075] j e1 =iωC1+iωC g

[0076] j e2 =iωC1-iωC g

[0077] j f1 =iωC2-iωC g

[0078] j f2 =iωC2+iωC g

[0079] Among them, I n (n=1,2,3,4) represents the current flowing into node n, i is the imaginary unit, w is the angular frequency, is the response voltage of node n, and the superscripts x and y indicate the location of the unit cell. For periodic structures, according to Bloch's theorem, we can get

[0080]

[0081] Where m and l are integers representing the translation of the lattice. For a two-dimensional lattice, m usually represents the translation along the x direction, while l represents the translation along the y direction, and k x and k y are the wave vectors in the x and y directions respectively. According to Bloch's theorem, the present invention can simplify Kirchhoff's current formula to:

[0082]

[0083] J is the Laplacian matrix of the circuit:

[0084]

[0085] in:

[0086]

[0087] When solving the eigenfrequency of the circuit system, the present invention sets I n =0, JV = 0. The present invention can obtain the characteristic frequency / energy band of the non-Hermitian circuit system by solving det[J] = 0, but this method has certain limitations. When the admittance matrix is ​​complex, it is difficult to find the characteristic frequency, so the present invention can construct a Hamiltonian to obtain the energy band of the non-Hermitian circuit.

[0088] The relationship between the Hamiltonian matrix and the admittance matrix is ​​as follows:

[0089]

[0090] H is the Hamiltonian of the non-Hermitian circuit system, L and C are the inductance and capacitance matrices respectively, E is the unit matrix, and O represents the zero matrix. The eigenvalues ​​solved by det(H) are divided into two parts (ω, -ω * ) The real part of ω is positive, which can be used as the characteristic frequency of the circuit. The change of the characteristic frequency with respect to the wave vector k is the energy band of the periodic structure.

[0091] When the present invention takes the x direction as an open boundary condition and the y direction as a PBC periodic boundary condition, the Bloch theorem is only used in the y direction. At this time, the admittance matrix of the primitive cell is:

[0092]

[0093] For example, the present invention can set the values ​​of the circuit components as follows: C1 = 10nf, C2 = 33nf, L1 = 10μH, L2 = 3.3μF.

[0094] Theoretically, L2 should be equal to 3.03μF, but for the convenience of circuit component selection, the present invention selects L2 equal to 3.3μF. Due to the robustness of the topology, slight deviations from the ideal value will not affect its characteristics. Here is a brief description of the first circuit node 1 and the third circuit node 3 connected in parallel with a 43nF capacitor C3, and the second circuit node 2 and the fourth circuit node 4 connected in parallel with a 2.5μH inductor L3. The values ​​of these grounded circuit components can be calculated from the grounded Laplace matrix. C g is introduced by the complex impedance transformer, C g The positive and negative of is determined by the coupling direction. The negative impedance converter components are selected as follows: The op amp used is the high-performance precision operational amplifier OPA1611AID, which has the advantages of ultra-low noise and extremely low distortion. The resistance value of the resistor in the circuit is 20Ω, and the adjustment capacitor C g The skin effect of the circuit can be adjusted. After numerical analysis, C g The skin effect is stronger when 10nF is used. After determining the coefficient, the dispersion diagram can be obtained by solving the Hamiltonian matrix corresponding to the circuit. Figure 4-Figure 7 From the dispersion diagram, we can see that the red cross bands indicate that there are still topologically protected states in the system, which is an important feature of Möbius dispersion. This shows that even under complex non-Hermitian conditions, the energy levels of the system still cross symmetrically along the periodic direction, maintaining the characteristics of its topological phase. g Finally, the non-reciprocal coupling of the system comes into play, making the imaginary part of the energy spectrum (i.e. the imaginary part of the complex frequency) appear.

[0095] Subsequently, the present invention studies the coupling capacitor C introduced with the negative impedance converter. g How the system energy level evolves with the change in the relative change in coupling capacitance with the reference capacitor C1. g / C1 increases, the frequency band gradually reconstructs, see Figure 8 .

[0096] See also Figure 9-12 The present invention obtains a characteristic matrix composed of characteristic vectors from the Hamiltonian matrix. The elements of each column correspond to the information of all nodes at a certain frequency. The columns corresponding to the edge dispersion frequency and the body band dispersion frequency are taken, and the conjugate product is made to obtain the energy field distribution. Fig. 9 and Fig.10 They are Cg=1nF and C g =10nF when the edge dispersion frequency (columns 12 and 13) corresponds to the energy field distribution. It can be seen that as C g As the value increases, the energy is more concentrated in the boundary area, showing a stronger skin effect. Fig.11 and Fig.12 C g =1nF and C g When =10nF, the energy distribution corresponding to the body band dispersion frequency has the same rule as the edge state.

[0097] In some regions, the aggregation of multiple energy levels may indicate the existence of exceptional points (EPs) in the system. These exceptional points are singular points in non-Hermitian systems, reflecting changes in the system's energy spectrum structure. Through numerical analysis, the present invention observes the distribution of the eigenvectors of the circuit H matrix at different positions in the circuit, revealing the localized characteristics in the system. The main components of the eigenvectors corresponding to the boundary states are concentrated at the boundary nodes of the circuit. This is a typical topologically protected boundary state characteristic, and as C g In addition, by adjusting C g Capacitance value, the present invention can also achieve the characteristic state of the body to be concentrated towards the boundary.

[0098] pass Figure 9-12 This shows that as the Cg value increases, skin effect will occur in both the bulk state and the boundary state, and the skin effect becomes more obvious as Cg increases.

[0099] Figure 13-Figure 16 The voltage distribution is used in the simulation to illustrate the non-Hermitian skin effect. Figure 9-12 The law is similar. In order to better demonstrate the skin effect, the present invention constructs a 6*8 primitive cell circuit matrix and analyzes its electric field distribution. In order to further study the characteristics of the topological edge state, the present invention places the excitation source precisely in the middle of the right boundary (such as Fig.13The configuration is designed to enhance the response of edge states and ensure that the excitation source can effectively excite topological modes propagating along the edges. By measuring the voltage response of each node of the circuit, the present invention obtains a voltage distribution diagram. The results show that the electric energy is significantly concentrated in the edge area of ​​the circuit and decays rapidly along the x direction, further proving the existence of topological edge states. This phenomenon shows that the topological effect dominates the propagation of current at the edge, while in the internal area of ​​the circuit, the energy decay is more obvious, showing a typical topological non-trivial state. The frequency 486Khz is the frequency corresponding to the edge state, and 330Khz is the frequency corresponding to the body band. It can be observed that whether it is the edge state or the body band, when Cg is enhanced, the high voltage is more concentrated on the right boundary. This phenomenon is due to the influence of the skin effect.

[0100] The present invention can provide researchers with an experimental platform for simulating topological phase transitions and skin effects under non-reciprocal terms by designing a highly sensitive non-Hermitian sensing circuit system based on a Mobius insulator. It can help understand the dynamic mechanism behind physical phenomena and provide theoretical support for other fields (such as photonics and quantum information). The non-Hermitian skin effect circuit can make the signals in the system naturally gather to one side, thereby achieving lossless or low-loss transmission. This feature is extremely advantageous in anti-interference design and can be used to build highly robust communication components and topological amplifiers. In addition, using the skin effect, sensors that are highly sensitive to input changes can be designed. These sensors can detect small signal changes and avoid signal reflection problems in traditional sensors, providing new ideas for the development of high-precision sensors.

[0101] By introducing non-Hermitian elements into the circuit and precisely adjusting their parameters, the unidirectional aggregation and enhancement of current or signal in a specific direction is achieved, namely the non-Hermitian skin effect. This effect enables the signal to be transmitted along a specific path, effectively reducing the scattering loss of the system and improving the transmission efficiency and directional selectivity.

[0102] The above are all preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Therefore, any equivalent changes made based on the structure, shape, and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator, characterized in that: include: At least one group of circuit nodes, the group of circuit nodes comprising A first circuit node (1), a second circuit node (2), a third circuit node (3), a fourth circuit node (4) and at least one group of non-reciprocally coupled components connected in sequence, The set of non-reciprocal coupling components includes two negative impedance converters, one of which is arranged between the first circuit node (1) and the third circuit node (3), and the other of which is arranged between the second circuit node (2) and the fourth circuit node (4).

2. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 1, characterized in that: A set of said circuit nodes also includes An inductor L1 is arranged between the first circuit node (1) and the third circuit node (3); The capacitor C1 is arranged between the second circuit node (2) and the fourth circuit node (4).

3. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 2, characterized in that: The negative impedance converter comprises: Operational amplifier A; Resistor R a , the resistor R a One end of the circuit is connected to the positive input port of the operational amplifier A and the input voltage V1 at the same time, and the other end is connected to the output port of the operational amplifier; Resistor R b , the resistor R b One end of the operational amplifier is connected to the output port and the resistor R a The other end of Capacitor C g , the capacitor C g One end of the operational amplifier A is connected to the negative input port and the resistor R b The other end of the capacitor C g The other end is connected to the input voltage V2.

4. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 3, characterized in that: The capacitor C g The negative impedance converter is adjustable by adjusting the capacitance C g The value of capacitor C g The ratio of capacitance C1 is used to adjust the frequency band structure of the sensing circuit system.

5. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 4, characterized in that: A set of said circuit nodes also includes Capacitor c1 is connected between the first circuit node (1) and the second circuit node (2) and between the third circuit node (3) and the fourth circuit node (4).

6. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 5, characterized in that: A set of said circuit nodes also includes Capacitor C3, the first circuit node (1) and the third circuit node (3) are both grounded via the capacitor C3; Inductor L3, the second circuit node (2) and the fourth circuit node (4) are both grounded via the inductor L3.

7. The highly sensitive non-Hermitian sensing circuit system based on a Möbius insulator according to claim 6, characterized in that: It includes multiple groups of circuit nodes, and the circuit nodes between two adjacent groups are An inductor L2 is connected between the first circuit node (1) and the third circuit node (3); A capacitor C2 is connected between the second circuit node (2) and the fourth circuit node (4); The negative impedance converter is connected between the first circuit node (1) and the third circuit node (3) and between the second circuit node (2) and the fourth circuit node (4); The capacitor c1 is connected between the first circuit node (1) and the second circuit node (2) and between the third circuit node (3) and the fourth circuit node (4).

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