The fractional quantum Hall effect (FQHE) in two-dimensional electron system (2DES) is an exotic, superfluid-like matter with an emergent topological order. From the consideration of Aharonov-Bohm interaction of electrons and magnetic field, the ground state of a half-filled lowest Landau level is mathematically transformed to a Fermi sea of composite objects of electrons bound to two flux quanta, termed composite fermions (CFs). A strong support for the CF theories comes from experimental confirmation of the predicted Fermi surface at $ν$ = 1/2 (where $ν$ is the Landau level filling factor) from the detection of the Fermi wave vector in the semi-classical geometrical resonance experiments. Recent developments in the theory of CFs have led to a prediction of a $π$ Berry phase for the CF circling around the Fermi surface at half-filling. In this paper we provide the first experimental evidence for the detection of the Berry phase of CFs in the fractional quantum Hall effect. Our measurements of the Shubnikov-de Haas oscillations of CFs as a function carrier density at a fixed magnetic field provide a strong support for an existence of a $π$ Berry phase at $ν$ = 1/2. We also discover that the conductivity of composite fermions at $ν$ = 1/2 displays an anomalous linear density dependence, whose origin remains mysterious yet tantalizing.
It is well established that the ground states of a two-dimensional electron gas with half-filled high ($N \ge 2$) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance $R_{xx}$ ($R_{yy}$) and a non-quantized Hall resistance $R_H$. Here, we report on emergent minima (maxima) in $R_{xx}$ ($R_{yy}$) and plateau-like features in $R_H$ in half-filled $N \ge 3$ Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temper…
We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $π$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple mo…
Using the $α$-T$_3$ model, we carried out analytical and numerical calculations for the static and dynamic polarization functions in the presence of a perpendicular magnetic field. These results were employed to determine the longitudinal dielectric function and the magnetoplasmon dispersion relation. The magnetic field splits the continuous valence, conduction and flat energy subband into discrete Landau levels which present significant effects on the polarization function and magnetoplasmon dispersion. We present results for a doped layer in the integer quantum Hall regime for fixed hopping …
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。
The fractional quantum Hall state at Landau level (LL) filling factor 5/2 is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering. We discuss the advantage of this bulk probe over the existing edge probes.
An effective field theory of composite Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)] as a theory of the half-filled Landau level with explicit particle-hole symmetry. We compute the electromagnetic response of this Son-Dirac theory on the level of the random phase approximation (RPA), where we pay particular attention to the effect of an additional composite-fermion dipole term that is needed to restore Galilean invariance. We find that once this dipole correction is taken into account, spurious interband transitions and collective modes that are present in the response of…
Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
我们研究了在垂直磁场作用下的宽阱二维电子系统中，在最低和第一激发朗道能级的半填充时可能出现的数值上不同的相位。在仅考虑量子阱的两个最低电子子带的双组分模型中，我们推导出了与Shabani等人的实验相图相媲美的相图。[Phys. Rev. B 88，245413（2013）]。除了可压缩的复合费米子费米液体在狭窄的井与大量的子带隙和不可压缩的两个组件（331）Halperin状态，我们确定在最低的朗道水平的矩形维格纳晶体占据第二子带。这种晶体可能是实验观察到的绝缘相在宽阱和高电子密度的限制的起源。在第二个朗道能级中，不可压缩的Pfronan态，它发生在窄阱和大的子带隙，也被一个中间区域从一个大阱的限制，其中一个类似的矩形维格纳晶体在激发子带是基态，作为最低的朗道能级。然而，中间区域的特征在于不可压缩状态，其由每个组件中的两个四通量Pfrons组成。
We describe an experimental technique to measure the chemical potential, $μ$, in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of $μ$ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating $μ$ over filling factor, $ν$, we obtain the ground state energy per particle, which can be directly compared with numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Lan…
