Microwaving and stirring the quantum Hall spaghetti

Two-dimensional (2D) electron materials such as semiconductor quantum wells and graphene form exotic phases when placed in a strong magnetic field and cooled down to low temperatures. The energy spectrum of such systems consists of macroscopically degenerate energy levels (Landau levels) that lead to the rich physics of integral and fractional quantum Hall effects (IQHE and FQHE). Different states of 2D electron matter appear when the degeneracy of the topmost partially filled Landau level is lifted by interactions among electrons. In an article in Physical Review Letters, Igor Kukushkin at the Institute for Solid State Physics in Chernogolovka, Russia, and coauthors in Stuttgart and Israel present the results of an experiment [1] that probes a particularly intriguing quantum Hall state—the stripe phase—that is believed to form when the topmost Landau level is nearly half filled. The stripe phase can be thought of as a periodic one-dimensional array of linear domains in which the topmost Landau level is either completely empty or completely full. The electron density is periodically modulated as well; hence the stripe phase is a type of charge-density wave. The stripe phase was predicted 15 years ago [2], and its existence was soon confirmed by transport measurements [3, 4]. It has attracted much interest [5] because it is different from other quantum Hall phases and also because similar structures have been discovered more or less simultaneously in other strongly correlated systems such as high-Tc superconducting cuprates and manganites. The stripe phase and its close relative the bubble phase—a triangular crystal of circular domains—are also ubiquitous in other fields of physics, chemistry, and biology. Examples include magnetic films, pattern-formation systems, “conventional” charge-density waves, nuclear matter, and liquid crystals. However, this author’s favorite analogy to the stripe phase is the quantum Hall spaghetti. The image of spaghetti emerges if one realizes that the stripes are quite flexible and so are not expected to be perfectly straight. Disorder and thermal and quantum fluctuations should introduce distortions in the ideal stripe pattern, making them somewhat twisted and randomized, like spaghetti on a plate. In their experiment, Kukushkin et al. investigated the stripe phase in a state-of-the-art GaAs quantum well structure with a technique combining surface acoustic waves (SAW), microwaves, and photoluminescence. The goal of the experiment was to probe the energy-momentum dispersion of the collective modes—magnetophonons—of the system. One can think of the magnetophonons as undulations of the stripes under the influence of a weak in-plane electric field and a strong transverse magnetic field (Fig. 1). According to the interpretation given in the article, the SAW impart momentum to the system (“stir” it), while the electromagnetic radiation imparts energy (“microwaves” it). When this combination of energies and momenta match its dispersion relation, the system starts to resonantly absorb the energy. This causes heating of 2D electron gas, which is detected from the enhancement of photoluminescence signal. Although both SAW and microwaves have been used to study quantum Hall systems, the combination of the two has been applied only once: Two years ago this very team used it to reveal the spectrum of collective modes of FQHE states at very high magnetic fields where all electrons reside in the lowest Landau level [6]. This task calls for considerable experimental skills to maintain the temperature in the tens of millikelvin range—with a dilution refrigerator—in the presence of radiation and strong magnetic fields. Though we do not yet understand how this sophisticated technique works, the ingenious method of exciting a system by simultaneous action of light and sound has proven to be powerful and uniquely suited to investigation of 2D electrons in quantum wells. At this point, a brief survey of previous experimental results pertaining to the stripe phase is in order. The