Contrasting energy scales of reentrant integer quantum Hall states

Abstract

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]...

Spin and Charge Ordering in the Quantum Hall Regime

“…However, also discrepancies to the bubble phases in higher Landau levels are evident. The onset temperatures normalized by the Coulomb energy strongly differ between the second and third Landau level [121]. This observation is in conflict with existing theories and emphasizes that the bubble phases in the second Landau level are of more complex nature.…”

Depinning transition of bubble phases in a high Landau level

“…In a square or Hall bar geometry, RIQHE is similar to IQHE with a vanishing longitudinal resistance, and more interestingly, with integer quantization of Hall resistance reentrant to the neighboring quantum Hall plateau. Being pinned by disorder, electrons in the partially filled LLs do not contribute to RIQHE's conductivities [16,17,[20][21][22][23][32][33][34][35]. The resistance measurements in Fig.…”

“…In order to systematically study the correlation physics in the N=1 LL, recent work has also been focused on the reentrant integer quantum Hall effect (RIQHE) around ν=5/2 [16][17][18][19][20][21]. In the N=2 LL, RIQHE between ν=4 and ν=5 integer quantum Hall effect (IQHE) has been observed in the square samples, with filling factors generally believed to be ~4.25 and ~4.75 [17,22,23]. For those two states, microwave experiments have confirmed the bubble phases by resonance in the real part of the diagonal conductivity [24].…”

High-temperature resistivity measured at ν=52 as a predictor of the two-dimensional electron gas quality in the N=1 Landau level

“…This design has been shown to yield the largest gap energy for the ν = 5/2 FQHS [4,7,9,10]. It is believed [2] that low conductivity electrons confined in the X-band of the AlAs barriers surrounding the narrow GaAs doping wells screen potential fluctuations caused by remote donor impurities, promoting expression of large gap FQHS in the N=1 LL.…”