We report drastically different onset temperatures of the reentrant integer quantum Hall states in the second and third Landau level. This finding is in quantitative disagreement with the HartreeFock theory of the bubble phases which is thought to describe these reentrant states. Our results indicate that the number of electrons per bubble in either the second or the third Landau level is likely different than predicted.In systems of charged particles strong Coulomb interactions stabilize a periodic ground state called the Wigner solid (WS) [1,2]. The WS has been observed in two-dimensional electron gases (2DEG) floating atop superfluids [3], in 2DEGs confined to GaAs/AlGaAs heterostructures [4], and electron bilayers [5]. There is a resurgence of interest in the WS stimulated by recent work on electrons confined to less than two dimensions [6], 2DEG in complex oxide heterostructures [7], and in graphene [8]. The WS was also realized in ion clouds [9] and, most recently, in cold atomic gases with dipolar interactions [10] and it plays a role in charged colloidal suspensions [11] and neutron stars [12].Long range interactions may also stabilize periodic ground states which are more intricate than the WS [23,24]. One such many-body ground state is the electronic bubble phase which was predicted to form in the 2DEG subjected to a perpendicular magnetic field B [23][24][25][26][27][28][29][30]. Electrons in this system move on circular Landau orbitals, their energy is quantized to equidistant Landau levels (LL), and their ground states are labeled by the LL filling factor ν at which they form. According to theory, the guiding centers of the Landau orbitals cluster into so called electron bubbles and, furthermore, the bubbles order into an isotropic lattice. Such a bubble phase can therefore be thought of as a WS with an internal degree of freedom, i.e. with several electrons per unit cell [23].The experimentally measured reentrant integer quantum Hall states (RIQHS) have been identified with the bubble phases [13][14][15][16][17][18][19][20][21][22]. Indeed, dc [13][14][15][16][17][18][19] and microwave transport features [20][21][22] of the RIQHSs are, generally speaking, consistent with the bubble interpretation. However, for the RIQHSs the number of electrons per bubble remains unknown to date. In lack of any direct measurements on the structure of the bubbles one has to turn to the theory. In the second Landau level (SLL) both two and one electron bubble phases are predicted to form [29] while in the third Landau level (TLL) only two electron bubble phases are expected [25,[27][28][29][30]. These theories, however, have their limitations. The HartreeFock approach, the only one used for bubble phases both the TLL [25,29,30] and the SLL [29], is exact only in the limit of large LL occupation [24,26], and may therefore not capture all aspects of bubbles at the lowest LL occupation, i.e. those in the second and third LLs. In addition, the presence of competing nearby fractional quantum Hall states in the SLL [17,18]...

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.The second Landau level (SLL) of the two-dimensional electron gas (2DEG) is astonishingly rich in novel ground states [1][2][3]. Recent experiments [3][4][5][6][7][8][9] suggest that there are both conventional [10,11] as well as exotic fractional quantum Hall states (FQHSs) [12,13] in this region. The study of the latter has enriched quantum many-body physics with numerous novel concepts such as paired composite fermion states with Pfaffian correlations, non-Abelian quasiparticles [12][13][14][15][16][17][18][19], topologically protected quantum computing [20], and established connections between the 2DEG and p-wave superconductivity in Sr 2 RuO 4 and fermionic atomic condensates.The eight reentrant integer quantum Hall states (RIQHSs) form another set of prominent ground states in the SLL [1]. The transport signatures of the RIQHSs are consistent with electron localization in the topmost energy level [1]. However, the nature of the localization is not yet well understood. Depending on the relative importance of the electron-electron interactions, the ground state can be either an Anderson insulator or a collectively pinned electron solid.FQHSs owe their existence to the presence of the interelectronic Coulomb interactions [10,11]. Since FQHSs and RIQHSs alternate in the SLL, it was argued that Coulomb interactions must be important and, therefore, the RIQHSs in the SLL must be electron solids [1]. Subsequent density matrix renormalization group [21] and Hartree-Fock calculations [22] also favored the electron solid picture and predicted the solid phase similar to the Wigner crystal, but having one or more electrons in the nodes of the crystal [22]. Recently reported weak microwave resonances in one such RIQHS are suggestive of but are far from being conclusive on the formation of a collective insulator [23]. Our understanding of the RIQHSs in the SLL, therefore, is still in its infancy and the collective nature of these states has not yet been firmly established.We report a feature in the temperature dependent magnetoresistance unique to the the RIQHSs in the SLL, a feature which is used to define the onset temperature of these states. The scaling of onset temperatures with the Coulomb energy reveals that Coulomb interactions play a central role in the formation of RIQHSs and, therefore, these reentrant states are exotic electronic solids rather than Anderson insulators. We also report an unexpected trend of the onset temperatures within each spin branch. This trend is inconsistent with current theories and can be unde...

We study Escherichia coli chemotaxis behaviors in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillate in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies.

We report quantitative measurements of the impact of alloy disorder on the ν = 5/2 fractional quantum Hall state. Alloy disorder is controlled by the aluminum content x in the Al(x)Ga(1-x)As channel of a quantum well. We find that the ν = 5/2 state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the ν = 5/2 state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.

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