A low-disorder, two-dimensional electron system (2DES) subjected to a large perpendicular magnetic field and cooled to very low temperatures provides a rich platform for studies of many-body quantum phases. The magnetic field quenches the electrons' kinetic energy and quantizes the energy into a set of Landau levels, allowing the Coulomb interaction to dominate. In excited Landau levels, the fine interplay between short- and long-range interactions stabilizes bubble phases, Wigner crystals with more than one electron per unit cell. Here we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram for the transition from bubble to liquid phases for Landau level filling factors $4\leqν\leq5$.
Melting of quantum Hall Wigner and bubble crystals
International Center for Quantum Materials, Peking University（北京大学量子材料科学中心）；Division of Physics and Applied Physics, Nanyang Technological University（南洋理工大学物理与应用物理系）；Leiden Institute of Physics, Leiden University（莱顿大学莱顿物理研究所）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Materials Research Laboratory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校材料研究实验室）；Hefei National Laboratory（合肥国家实验室）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究院暨轻元素先进材料研究中心）
While in the lowest Landau level the electron-electron interaction leads to the formation of the Wigner crystal, in higher Landau levels a solid phase with multiple electrons in a lattice site of crystal was predicted, which was called the bubble phase. Reentrant integer quantum Hall states are believed to be the insulating bubble phase pinned by disorder. We carry out nonlinear transport measurements on the reentrant states and study the de-pinning of the bubble phase, which is complementary to previous microwave measurements and provides unique information. In this study, conductivity is dir…
We discover a new topological excitation of two dimensional electrons in the quantum Hall regime. The strain dependence of resistivity is shown to change sign upon crossing filling-factor-specified boundaries of reentrant integer quantum Hall effect (RIQHE) states. This observation violates the known symmetry of electron bubbles thought to be responsible for the RIQHE. We demonstrate theoretically that electron bubbles become elongated in the vicinity of charge defects and form textures of finite size. Calculations confirm that texturing lowers the energy of excitations. These textures form he…
We study multielectron bubble phases in the $N=2$ and $N=3$ Landau levels in a high mobility GaAs/AlGaAs sample. We found that the longitudinal magnetoresistance versus temperature curves in the multielectron bubble region exhibit sharp peaks, irrespective of the Landau level index. We associate these peaks with an enhanced scattering caused by thermally fluctuating domains of a bubble phase and a uniform uncorrelated electron liquid at the onset of the bubble phases. Within the $N=3$ Landau level, onset temperatures of three-electron and two-electron bubbles exhibit linear trends with respect…
Strain-induced deformations in graphene are predicted to give rise to large pseudomagnetic fields. We examine theoretically the case of gas-inflated bubbles to determine whether signatures of such fields are present in the local density of states. Sharp-edged bubbles are found to induce Friedel-type oscillations which can envelope pseudo-Landau level features in certain regions of the bubble. However, bubbles which minimise interference effects are also unsuitable for pseudo-Landau level formation due to more spatially varying field profiles.
A longstanding puzzle for the lowest Landau level crystal phase has been an order of magnitude discrepancy between the theoretically calculated energy of the defects and the measured activation gap. We perform an extensive study of various kinds of defects in the correlated composite fermion crystal and find that the lowest energy defect is a six-fold symmetric "hyper-correlated bubble interstitial," in which an interstitial particle forms a strongly correlated bound state with a particle of the crystal. The energy of the bubble defect is a factor of $\sim$3 smaller than that of the lowest ene…
A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors ($ν\simeq1/5$). In dilute GaAs 2D \textit{hole} systems, on t…
We investigate non-equilibrium transport in the reentrant integer quantum Hall phases of the second Landau level. At high currents, we observe a transition from the reentrant integer quantum Hall phases to classical Hall-conduction. Surprisingly, this transition is markedly different for the hole- and electron sides of each spin-branch. While the hole bubble phases exhibit a sharp transition to an isotropic compressible phase, the transition for the electron side occurs via an intermediate phase. This might indicate a more complex structure of the bubble phases than currently anticipated, or a…
We report on transport signatures of eight distinct bubble phases in the $N=3$ Landau level of a Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As quantum well with $x = 0.0015$. These phases occur near partial filling factors $ν^\star \approx 0.2\,(0.8)$ and $ν^\star \approx 0.3\,(0.7)$ and have $M = 2$ and $M = 3$ electrons (holes) per bubble, respectively. We speculate that a small amount of alloy disorder in our sample helps to distinguish these broken symmetry states in low-temperature transport measurements.
In a $β$-Mn-type chiral magnet Co$_9$Zn$_9$Mn$_2$, we demonstrate that the magnetic field-driven collapse of a room temperature metastable topological skyrmion lattice passes through a regime described by a partial topological charge inversion. Using Lorentz transmission electron microscopy, the magnetization distribution was observed directly as the magnetic field was swept antiparallel to the original skyrmion core magnetization, i.e. negative magnetic fields. Due to the topological stability of skyrmions, a direct transition of the metastable skyrmion lattice to the equilibrium helical stat…
我们比较不同的电子固体，如气泡晶体与三角形和正方形对称性和条纹相，在部分填充的中间朗道水平的相关量子液体的能量。当改变最顶部部分填充的朗道能级的填充时，这些相之间的多个跃迁解释了所观察到的整数量子霍尔效应的再进入。的相变被确定为一阶。这导致了各种可测量的现象，例如在朗道能级填充因子范围$4.15 < nu < 4.26$内Wigner晶体和双电子泡相之间的相共存，这是最近在微波辐照下的输运测量中观察到的。
One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures ($T$) and small Landau level filling factors ($ν$), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder pot…
Reports of weak local minima in the magnetoresistance at $ν=2+3/5$, $2+3/7$, $2+4/9$, $2+5/9$, $2+5/7$, and $2+5/8$ in the second Landau level of the electron gas in GaAs/AlGaAs left open the possibility of fractional quantum Hall states at these filling factors. In a high quality sample we found that the magnetoresistance exhibits peculiar features near these filling factors of interest. These features, however, cannot be associated with fractional quantum Hall states; instead they originate from magnetoresistive fingerprints of the electronic bubble phases. We found only two exceptions: at $…
Microwave spectroscopy within the Landau filling ($ν$) range of the integer quantum Hall effect (IQHE) has revealed pinning mode resonances signifying Wigner solids (WSs) composed of quasi-particles or -holes. We study pinning modes of WSs in wide quantum wells (WQWs) for $ 0.8\leν\le1.2$, varying the density, $n$, and tilting the sample by angle $θ$ in the magnetic field. Three distinct WS phases are accessed. One phase, S1, is phenomenologically the same as the WS observed in the IQHEs of narrow QWs. The second phase, S2, exists at $ν$ further from $ν=1$ than S1, and requires a sufficiently …
We investigate the competition between electron-solid and quantum-liquid phases in graphene, which arise in partially filled Landau levels. The differences in the wave function describing the electrons in the presence of a perpendicular magnetic field in graphene with respect to the conventional semiconductors, such as GaAs, can be captured in a form factor which carries the Landau level index. This leads to a quantitative difference in the electron-solid and -liquid energies. For the lowest Landau level, there is no difference in the wave function of relativistic and non-relativistic systems.…
Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also under intense scrutiny in various strongly correlated electron systems. In contrast, the electronic bubble morphology is rare. Some of the most intriguing electron bubbles develop in the two-dimensional electron gas subjected to a perpendicular magnetic field. However, in contrast to bubbles forming in classical systems such as the Turing activator-inhibito…
The interplay between the surface and domain wall phenomena in multiferroic LaxBi1-xFeO3 in the vicinity of morphotropic phase transition is explored on the atomic level. Scanning Transmission Electron Microscopy (STEM) has enabled mapping of atomic structures of the material with picometer-level precision, providing direct insight into the spatial distribution of the order parameters in this material and their behavior at surfaces and interfaces. Here, we use the thermodynamic Landau-Ginzburg-Devonshire (LGD) approach to explain the emergence of spatially modulated phases (SMP) in La0.22Bi0.7…
The ground state of the two-dimensional electron systems in Bernal bilayer and ABC-stacked multilayer graphenes in the presence of a strong magnetic field is investigated with the Hartree-Fock approximation. Phase diagrams of the systems are obtained, focusing on charge density wave states including states with vortices of valley pseudospins (called a Skyrme crystal). The single-electron states in these stacked graphenes are given by two-component wave functions. That of the first excited Landau level has the same component as the lowest Landau level of the ordinary two-dimensional electrons. …
In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the $N=2$ Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that m…
