Topological phase transition measured in a dissipative metamaterial

Abstract

We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipative topological transport can occur in a wider class of physical systems than considered before.

Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial

“…Previous studies have focused on nonlinearityinduced local self-interactions in the fundamental harmonic, which can give rise to solitons with anomalous * blzhang@ntu.edu.sg † yidong@ntu.edu.sg plateau-like decay profiles in nonlinear SSH chains [8,21], or chiral solitons in two-dimensional lattices [22][23][24][25][26][27]. It has also been suggested that topological edge states in nonlinear lattices could be used for robust traveling-wave parametric amplification [28], optical isolation [29], and other applications [30][31][32][33].…”

Nonlinear topological photonics

“…Electronic circuits have recently emerged as a convenient and accessible platform for studying the combination of non-linearity with band topology 13,85,[119][120][121][122][123][124][125][126][127] . Key advantages include the ease with which such circuits can be designed and fabricated using circuit simulators, printed circuit boards (PCBs), and other commodity technologies; the fact that they can be characterized using inexpensive laboratory equipment such as function generators and oscilloscopes; the availability of strongly nonlinear circuit elements; and the exciting prospect of using circuit wiring to implement complex geometries (like Möbius strips 119 ) that are practically impossible to realize on other platforms.…”

“…119 was designed to have multiple identical sublattices whose interconnections replicate the effects of the complex inter-site couplings associated with a magnetic vector potential 120 ; this ensured that the states of the target quantum Hall system, including the crucial topological edge states, are a multiply-degenerate subset of the states of the T-symmetric circuit. A variety of T-symmetric topological phases have also been realized with LC circuits without using this sublattice trick, including linear 1D and 2D Su-Schrieffer-Heeger models 122,125 , topological crystalline insulators 124 , higher-order topological insulators 123,126 , and intrinsically non-Hermitian topological lattices 121 .…”

“…In typical circuit experiments, the normal modes are studied using weakly-coupled probes such as pickup coils 119,124 , or direct connections to an oscilloscope or network analyzer 121,125 . Lee et al have also developed a rigorous frequency-domain formalism for analyzing circuits with explicit current sources and sinks 122 .…”

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

“…Non-Hermitian quantum mechanics has been attracting much attention in many fields of physics in the past decades. Many experimental studies have realized various physical systems with non-Hermitian effects [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Among these experimental studies, appearance of exceptional points and rings where some energy eigenvalues become degenerate and the corresponding eigenstates coalesce 20,21 , and intriguing phenomena have been observed [22][23][24][25][26][27][28][29][30][31][32][33] .…”