Haydar Sahin | National University of Singapore (original) (raw)

Papers by Haydar Sahin

Communications physics, Jun 27, 2023

Much of the qualitative nature of physical systems can be predicted from the way it scales with s... more Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional LC circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper's equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present.

Journal of Magnetism and Magnetic Materials, Apr 1, 2023

arXiv (Cornell University), Aug 5, 2021

Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena that are ab... more Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena that are absent in the Hermitian systems. One of these key features is the extreme eigenstate localization of eigenstates, also known as non-Hermitian skin effect (NHSE), which occurs in open chains. However, many new and peculiar non-Hermitian characteristics of the eigenstates and eigenvlaues that emerge when two such non-Hermitian chains are coupled together remain largely unexplored. Here, we report various new avenues of eigenstate localization in coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on and off by the inter-chain coupling amplitude. A very small inter-chain strength causes the NHSE to be present at both ends of an anti-symmetric coupled system because of the weak hybridization of the eigenstates of the individual chains. The eigenspectrum under open boundary conditions (OBC) exhibits a discontinuous jump known as the critical NHSE (CNHSE) as its size increases. However, when the hybridization between eigenstates becomes significant in a system with strong inter-chain coupling, the NHSE and CNHSE vanish. Moreover, a peculiar " half-half skin localization" occurs in composite chains with opposite signs of inverse decay lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide a new twist and insights for non-Hermitian phenomena in coupled non-Hermitian systems.

arXiv (Cornell University), Dec 5, 2022

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topo... more We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.

arXiv (Cornell University), Dec 12, 2022

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one-and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

arXiv (Cornell University), Aug 3, 2021

A non-Hermitian system is characterized by the violation of energy conservation. As a result of u... more A non-Hermitian system is characterized by the violation of energy conservation. As a result of unbalanced gain or loss in the forward and backward directions due to non-reciprocal couplings, the eigenmodes of such systems exhibit extreme localization, also known as non-Hermitian skin effect (NHSE). This work explores unconventional scenarios where the interplay of multiple asymmetric couplings can cause the NHSE to vanish, with the admittance spectra taking identical dispersion under open boundary conditions (OBC) and periodic boundary conditions (PBC). This is unlike known non-Hermitian models where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE, with the overall eigenmode localization determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asymmetric hoppings alone. Furthermore, our generalized model can be transformed into a square-root lattice simply by tuning the coupling capacitors, where the topological edge states occur at a non-zero admittance, in contrast to the zero-admittance states of conventional topological insulators. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, optics and quantum circuits.

arXiv (Cornell University), Mar 20, 2023

We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topo... more We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topological gapless and chiral phases. We first study a higher-order Dirac semimetal phase that exhibits a hinge-like Fermi arc linking the Dirac points. This circuit can be extended to host highly tunable first-and second-order Weyl semimetal phases by introducing a non-reciprocal resistive coupling in the x − y plane that breaks time reversal symmetry. The first-and second-order Weyl points are connected by zero-admittance surface and hinge states, respectively. We also study the emergence of first-and second-order chiral modes induced by resistive couplings between similar nodes in the z-direction. These modes respectively occur in the midgap of the surface and hinge admittance bands in our circuit model without the need for any external magnetic field.

Frontiers in Physics, Nov 25, 2022

We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) lay... more We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) layer. The spin orbit interaction in silicene couples the valley, pseudospin, and real spin degrees of freedom resulting in a topological Berry curvature in the system. The finite Berry curvature in turn induces a transverse Hall conductance. In particular, if the Fermi level E f is within the bulk energy gap, the Hall conductance is quantized to integer multiples of π. We study the quantum spin and valley Hall conductivities (QSH and QVH) as functions of the applied out-of-plane electric field for different values of E f and temperature. Both conductivities vary linearly as 1/|E f | when E f is within the conduction or valence bands but reach a quantized plateau value when E f is within the bulk gap. Further, by coupling silicene to a FE layer, the QSH and QVH signals can be modulated by means of the coupling strength. This can potentially provide a robust topological memory read-out with distinct binary outputs over a wide temperature range.

Physical review, Aug 31, 2022

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in... more In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.

arXiv (Cornell University), Mar 20, 2023

Journal of Magnetism and Magnetic Materials

arXiv (Cornell University), Dec 5, 2022

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topo... more We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit’s parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su–Schrieffer–Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions...

Physical Review B

We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic e... more We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., "type-I") corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.

Frontiers in Physics

We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) lay... more We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) layer. The spin orbit interaction in silicene couples the valley, pseudospin, and real spin degrees of freedom resulting in a topological Berry curvature in the system. The finite Berry curvature in turn induces a transverse Hall conductance. In particular, if the Fermi level Ef is within the bulk energy gap, the Hall conductance is quantized to integer multiples of π. We study the quantum spin and valley Hall conductivities (QSH and QVH) as functions of the applied out-of-plane electric field for different values of Ef and temperature. Both conductivities vary linearly as 1/|Ef| when Ef is within the conduction or valence bands but reach a quantized plateau value when Ef is within the bulk gap. Further, by coupling silicene to a FE layer, the QSH and QVH signals can be modulated by means of the coupling strength. This can potentially provide a robust topological memory read-out with distin...

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su-Schrieffer-Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

Physical review, Jun 10, 2022

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in... more In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.

Communications physics, Jun 27, 2023

Much of the qualitative nature of physical systems can be predicted from the way it scales with s... more Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional LC circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper's equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present.

Journal of Magnetism and Magnetic Materials, Apr 1, 2023

arXiv (Cornell University), Aug 5, 2021

Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena that are ab... more Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena that are absent in the Hermitian systems. One of these key features is the extreme eigenstate localization of eigenstates, also known as non-Hermitian skin effect (NHSE), which occurs in open chains. However, many new and peculiar non-Hermitian characteristics of the eigenstates and eigenvlaues that emerge when two such non-Hermitian chains are coupled together remain largely unexplored. Here, we report various new avenues of eigenstate localization in coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on and off by the inter-chain coupling amplitude. A very small inter-chain strength causes the NHSE to be present at both ends of an anti-symmetric coupled system because of the weak hybridization of the eigenstates of the individual chains. The eigenspectrum under open boundary conditions (OBC) exhibits a discontinuous jump known as the critical NHSE (CNHSE) as its size increases. However, when the hybridization between eigenstates becomes significant in a system with strong inter-chain coupling, the NHSE and CNHSE vanish. Moreover, a peculiar " half-half skin localization" occurs in composite chains with opposite signs of inverse decay lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide a new twist and insights for non-Hermitian phenomena in coupled non-Hermitian systems.

arXiv (Cornell University), Dec 5, 2022

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topo... more We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.

arXiv (Cornell University), Dec 12, 2022

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one-and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

arXiv (Cornell University), Aug 3, 2021

A non-Hermitian system is characterized by the violation of energy conservation. As a result of u... more A non-Hermitian system is characterized by the violation of energy conservation. As a result of unbalanced gain or loss in the forward and backward directions due to non-reciprocal couplings, the eigenmodes of such systems exhibit extreme localization, also known as non-Hermitian skin effect (NHSE). This work explores unconventional scenarios where the interplay of multiple asymmetric couplings can cause the NHSE to vanish, with the admittance spectra taking identical dispersion under open boundary conditions (OBC) and periodic boundary conditions (PBC). This is unlike known non-Hermitian models where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE, with the overall eigenmode localization determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asymmetric hoppings alone. Furthermore, our generalized model can be transformed into a square-root lattice simply by tuning the coupling capacitors, where the topological edge states occur at a non-zero admittance, in contrast to the zero-admittance states of conventional topological insulators. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, optics and quantum circuits.

arXiv (Cornell University), Mar 20, 2023

We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topo... more We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topological gapless and chiral phases. We first study a higher-order Dirac semimetal phase that exhibits a hinge-like Fermi arc linking the Dirac points. This circuit can be extended to host highly tunable first-and second-order Weyl semimetal phases by introducing a non-reciprocal resistive coupling in the x − y plane that breaks time reversal symmetry. The first-and second-order Weyl points are connected by zero-admittance surface and hinge states, respectively. We also study the emergence of first-and second-order chiral modes induced by resistive couplings between similar nodes in the z-direction. These modes respectively occur in the midgap of the surface and hinge admittance bands in our circuit model without the need for any external magnetic field.

Frontiers in Physics, Nov 25, 2022

We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) lay... more We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) layer. The spin orbit interaction in silicene couples the valley, pseudospin, and real spin degrees of freedom resulting in a topological Berry curvature in the system. The finite Berry curvature in turn induces a transverse Hall conductance. In particular, if the Fermi level E f is within the bulk energy gap, the Hall conductance is quantized to integer multiples of π. We study the quantum spin and valley Hall conductivities (QSH and QVH) as functions of the applied out-of-plane electric field for different values of E f and temperature. Both conductivities vary linearly as 1/|E f | when E f is within the conduction or valence bands but reach a quantized plateau value when E f is within the bulk gap. Further, by coupling silicene to a FE layer, the QSH and QVH signals can be modulated by means of the coupling strength. This can potentially provide a robust topological memory read-out with distinct binary outputs over a wide temperature range.

Physical review, Aug 31, 2022

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in... more In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.

arXiv (Cornell University), Mar 20, 2023

Journal of Magnetism and Magnetic Materials

arXiv (Cornell University), Dec 5, 2022

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topo... more We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit’s parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su–Schrieffer–Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions...

Physical Review B

We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic e... more We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., "type-I") corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.

Frontiers in Physics

We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) lay... more We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) layer. The spin orbit interaction in silicene couples the valley, pseudospin, and real spin degrees of freedom resulting in a topological Berry curvature in the system. The finite Berry curvature in turn induces a transverse Hall conductance. In particular, if the Fermi level Ef is within the bulk energy gap, the Hall conductance is quantized to integer multiples of π. We study the quantum spin and valley Hall conductivities (QSH and QVH) as functions of the applied out-of-plane electric field for different values of Ef and temperature. Both conductivities vary linearly as 1/|Ef| when Ef is within the conduction or valence bands but reach a quantized plateau value when Ef is within the bulk gap. Further, by coupling silicene to a FE layer, the QSH and QVH signals can be modulated by means of the coupling strength. This can potentially provide a robust topological memory read-out with distin...

Resonances in an electric circuit occur when capacitive and inductive components are present toge... more Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su-Schrieffer-Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

Physical review, Jun 10, 2022

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in... more In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.