Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTopological circuits of inductors and capacitors
392
0
0.0
(
0
)
Authors
Erhai Zhao
Ask ChatGPT about the research
No Arabic abstract
Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea by analyzing a series of topological circuits consisting purely of inductors (L) and capacitors (C) connected to each other by wires to form periodic lattices. All the examples are treated using a unifying approach based on Lagrangians and the dynamical $H$-matrix. First, the building blocks and permutation wiring are introduced using simple circuits in one dimension, the SSH transmission line and a braided ladder analogous to the ice-tray model also known as the $pi$-flux ladder. Then, more general building blocks (loops and stars) and wiring schemes ($m$-shifts) are introduced. The key concepts of emergent pseudo-spin degrees of freedom and synthetic gauge fields are discussed, and the connection to quantum lattice Hamiltonians is clarified. A diagrammatic notation is introduced to simplify the design and presentation of more complicated circuits. These building blocks are then used to construct topological circuits in higher dimensions. The examples include the circuit analog of Haldanes Chern insulator in two dimensions and quantum Hall insulator in four dimensions featuring finite second Chern numbers. The topological invariants and symmetry protection of the edge modes are discussed based on the $H$-matrix.
rate research
Read More
Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness - topological protection, as well as the non-Hermitian skin effect. In this work, we report the first experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various novel states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for new applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.
The topological state that emerges at the surface of a topological insulator (TI) and at the TI-substrate interface are studied in metal-hBN-Bi2Se3 capacitors. By measuring the RF admittance of the capacitors versus gate voltage, we extract the compressibility of the Dirac state located at a gated TI surface. We show that even in the presence of an ungated surface that hosts a trivial electron accumulation layer, the other gated surface always exhibits an ambipolar effect in the quantum capacitance. We succeed in determining the velocity of surface Dirac fermions in two devices, one with a passivated surface and the other with a free surface that hosts trivial states. Our results demonstrate the potential of RF quantum capacitance techniques to probe surface states of systems in the presence of a parasitic density-of-states.
Using superconducting quantum circuits, we propose an approach to construct a Kitaev lattice, i.e., an anisotropic spin model on a honeycomb lattice with three types of nearest-neighbor interactions. We study two particular cases to demonstrate topological states (i.e., the vortex and bond states) and show how the braiding statistics can be revealed. Our approach provides an experimentally realizable many-body system for demonstrating exotic properties of topological phases.
Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian (nH) quantum systems. We propose here a circuit realization of nH Dirac and Weyl Hamiltonians subject to time-reversal invariant pseudo-magnetic field, enabling the exploration of novel nH physics. We identify the low-energy physics with a generic real energy spectrum from the nH Landau quantization of exceptional points and rings, which can avoid the nH skin effect and provides a physical example of a quasiparticle moving in the complex plane. Realistic detection schemes are designed to probe the flat energy bands, sublattice polarization, edge states protected by a nH energy-reflection symmetry, and a characteristic nodeless probability distribution.
Magnetic flux quantization in superconductors allows the implementation of fast and energy-efficient digital superconducting circuits. However, the information representation in magnetic flux severely limits their functional density presenting a long-standing problem. Here we introduce a concept of superconducting digital circuits that do not utilize magnetic flux and have no inductors. We argue that neither the use of geometrical nor kinetic inductance is promising for the deep scaling of superconducting circuits. The key idea of our approach is the utilization of bistable Josephson junctions allowing the representation of information in their Josephson energy. Since the proposed circuits are composed of Josephson junctions only, they can be called all-Josephson junction (all-JJ) circuits. We present a methodology for the design of the circuits consisting of conventional and bistable junctions. We analyze the principles of the circuit functioning, ranging from simple logic cells and ending with an 8-bit parallel adder. The utilization of bistable junctions in the all-JJ circuits is promising in the aspects of simplification of schematics and the decrease of the JJ count leading to space-efficiency.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
