Nanomechanical topological insulators with an auxiliary orbital degree of freedom

Abstract

Discrete degrees of freedom, such as spin and orbital, can provide intriguing strategies to manipulate electrons, photons, and phonons. With a spin degree of freedom, topological insulators supporting backscattering-immune edge states have stimulated intense interests in condensed-matter physics 1 , optics 2,3 , acoustics 4 , and mechanics 5-7 . However, orbital as another fundamental attribute in crystals has seldom been investigated in topological insulators. Here, we invent a new type of topological insulators with both spin and auxiliary orbital degrees of freedom on a nanomechanical platform. Specifically, we experimentally demonstrated spin-polarized topological edge states in a nanomechanical crystal whose orbitals can arbitrarily be manipulated by the crystal configuration. Harnessing this unique feature, we further experimentally realized adiabatic transition between distinct topological phases without closing the energy bandgap. The auxiliary orbital degree of freedom has unveiled unprecedented strategies to manipulate topological phase transitions and to study topological phases of matter, which enable new generations of integrated devices and circuits that may lead to future quantum computers.

Topological phonon transport in an optomechanical system

“…2 d), both of which show a bulk bandgap that covers an interval from 316 to 338 MHz. We note that compared to recent nanomechanical implementations 25 , 26 , combining piezoelectric actuation and optical interferometric read-out, the displacement sensitivity in our cavity-based measurements is boosted by the cavity finesse. This has allowed us to detect tiny thermal vibrations with amplitudes on the order of 10 fm (Supplementary Note 7 and Supplementary Fig.…”

“…Using sensitive, spatially resolved optical read-out 33 , 34 we detect thermal phonons traveling along a topological edge channel. We observe a substantial reduction of backscattering in a 0.325–0.34 GHz band demonstrating unprecedented carrier frequency and bandwidth compared to the only existing nanoscale on-chip topological mechanics implementations 25 , 26 . A key innovation of our work is to introduce a design paradigm for optomechanical devices based on multiscale optomechanical crystals (OMCs).…”

“…Building on these developments, theoretical proposals have shown that larger-scale optomechanical arrays can be used to modify the propagation of phonons, realizing a form of topologically protected phonon transport 12 – 16 . This optomechanical approach is part of a broader endeavor to realize topological mechanical devices 17 in a variety of platforms ranging from pendula 18 , 19 , to sound waves in fluids 20 , 21 , and vibrations in solids 22 – 26 , exploiting the general concepts of topologically robust wave propagation 27 . It is motivated by the quest to reduce the footprint of mechanical topological devices towards systems at the nanoscale, where hypersonic frequency (≳GHz) acoustic wave circuits consisting of robust delay lines 28 and non-reciprocal elements 29 – 32 may be implemented.…”

Observing polarization patterns in the collective motion of nanomechanical arrays

“…

In recent years, nanomechanics has evolved into a mature field, with wide-ranging impact from sensing applications [1-3] to fundamental physics [4][5][6], and it has now reached a stage which enables the fabrication and study of ever more elaborate devices. This has led to the emergence of arrays of coupled nanomechanical resonators as a promising field of research [7][8][9][10][11], serving as model systems to study collective dynamical phenomena such as synchronization [12,13] or topological transport [10,11,14,15]. From a general point of view, the arrays investigated so far represent scalar fields on a lattice.

…”

“…Going from one or a few such resonators with polarization degrees of freedom to an entire coupled array would enable accessing the wealth of phenomena in polarization fields that have so far only been studied for electromagnetic waves. In recent years, coupled nanomechanical arrays have emerged as a promising platform for observing collective phenomena and transport [10][11][12][13][14][15]. However, what has been missing so far is a successful integration of polarization degrees of freedom into an array of coupled resonators.…”