Microwave spectroscopy of the low-filling-factor bilayer electron solid in a wide quantum well

Abstract

At the low Landau filling factor termination of the fractional quantum Hall effect series, two-dimensional electron systems exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well sample that can support single-layer or bilayer states depending on its overall carrier density. We find that the insulator exhibits a resonance which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are not accessible to dc transport measurements. As density is biased deeper into the bilayer solid regime, the resonance grows in specific intensity, and the transitions within the insulator disappear. These behaviours are suggestive of a picture of the insulating phase as an emulsion of liquid and solid components.

Microwave spectroscopic observation of a Wigner solid within the ν=1/2 fractional quantum Hall effect

“…Since η of the type-I WS resonance continues to decrease as ν goes from 0.485 toward 1/2, near-full participation of the carriers in the type-II WS resonance is consistent with the observed type-I WS resonance intensity. When ν goes below 0.48 the type-I WS resonance amplitude increases as the electrons solidify into the type-I WS; by ν = 0.4, η ∼ 100% for the type-I WS [26].…”

Topological kink plasmons on magnetic-domain boundaries

“…A Hall bar is fabricated on it, allowing in situ measurements and control of the 2DEG electron concentration . The fused silica spacer is topped by a 100 nm-thick e-beam evaporated Cr-coating, serving simultaneously as upper cavity wall and gate electrode 36,37 . A gate voltage of V can be applied across the Cr-coating–Hall bar junction to tune the electron concentration.…”

“…The sample–spacer–magnet assembly is glued by poly(methyl methacrylate) (PMMA) onto a customized Cu printed circuit board (PCB) with a 5 μm Ni and 200 nm Au surface finish. The PCB hosts a coplanar waveguide (CPW) connecting RF Ports 1 and 2 with mini-SMP connectors 36 . By design, the CPW has a 50 impedance with the sample–magnet assembly loaded.…”

“…We next seek experimental evidence for the theoretically predicted KMPs specific to our device. The device is inserted into a He-3 cryostat running at 0.5 K. An Agilent E5071C network analyzer (NA) is used to acquire power transmission (Port 1 to 2) and (Port 2 to 1) in the frequency range 300 kHz to 20 GHz 18,36,37 . Our focused frequency range is limited to 1–10 GHz, beyond which the cables and NA suffer high loss and noise, prohibiting acquisition of clear signals.…”

Observation of an Anisotropic Wigner Crystal

“…It is well established that in very clean 2D systems of charged carriers, at very small ν (ν < ∼ 1/5 for electrons and ν < ∼ 1/3 for holes) the FQHSs give way to IPs which are believed to be Wigner crystal (WC) phases that are pinned by the small but ubiquitous disorder [4][5][6][7][24][25][26][27]. For both 2D electron and hole systems in wide, symmetric GaAs QWs, the charge distribution becomes more bilayer-like with increasing density and the IP sets in at progressively larger ν [22,28,29]. These IPs are believed to be bilayer WC states which, thanks to the additional layer/subband degree of freedom, are stabilized at relatively large ν compared to the single-layer systems.…”