[论文解读] Robust nonabelian ground states and continuous quantum phase transitions in a half filled bilayer graphene Landau level

Alexander Zibrov, Carlos Kometter+4 more|arXiv (Cornell University)|Nov 22, 2016

Quantum and electron transport phenomena被引用 3

一句话总结

本研究在双栅、hBN封装的双层石墨烯中，在Landau能级半满填充分数化量子霍尔态下，报告了一种鲁棒的不可压缩且偶数分母的分数化量子霍尔态，其被识别为具有非阿贝尔任意子的Pfaffian相，能量间隙比以往系统大数倍。其独特的电子结构使得可通过磁场和电场进行调控，揭示了一种类连续量子相变，该相变由一种出乎意料的不可压缩、可极化的中间相介导，该相具有无能隙的中性激发态。

ABSTRACT

Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Originally proposed to occur in quantum wells in high magnetic fields, experimental systems thought to harbor nonabelian anyons range from p-wave superfluids to superconducting systems with strong spin orbit coupling. However, all of these systems are characterized by small energy gaps, and despite several decades of experimental work, definitive evidence for nonabelian anyons remains elusive. Here, we report the observation of arobust, incompressible even-denominator fractional quantum Hall phase in a new generation of dual-gated, hexagonal boron nitride encapsulated bilayer graphene samples. Numerical simulations suggest that this state is in the Pfaffian phase and hosts nonabelian anyons, and the measured energy gaps are several times larger than those observed in other systems. Moreover, the unique electronic structure of bilayer graphene endows the electron system with two new control parameters. Magnetic field continuously tunes the effective electron interactions, changing the even-denominator gap non-monotonically and consistent with predictions that a transition between the Pfaffian phase and the composite Fermi liquid (CFL) occurs just beyond the experimentally explored magnetic field range. Electric field, meanwhile, tunes crossings between levels from different valleys. By directly measuring the valley polarization, we observe a continuous transition from an incompressible to a compressible phase at half-filling mediated by an unexpected incompressible, yet polarizable, intermediate phase. Valley conservation implies this phase is an electrical insulator with gapless neutral excitations.

研究动机与目标

• 在双层石墨烯中识别并表征一种具有增强拓扑保护的鲁棒偶数分母分数化量子霍尔态。
• 研究磁场和电场在调控双层石墨烯中电子关联作用及电子相态中的作用。
• 探索在半满填充分数化量子霍尔态下，一种新颖的不可压缩但可极化的中间相的出现，其具有无能隙的中性激发态。
• 为具有显著大于先前候选体系能量间隙的系统中非阿贝尔任意子的存在提供实验证据。

提出的方法

• 利用双栅、六方氮化硼（hBN）封装的双层石墨烯异质结构，以实现高迁移率和可调载流子密度。
• 施加磁场以调控有效电子关联作用，并探测Landau能级半满附近相图。
• 利用电场控制谷能级简并并直接测量相变过程中的谷极化度。
• 采用数值模拟识别Pfaffian拓扑序，并将预测的能量间隙与实验测量结果进行比较。
• 通过输运和热力学探测测量不可压缩性与可压缩性，以绘制相边界。
• 分析谷宇称守恒，推断中间相为具有无能隙中性模式的电绝缘体。

实验结果

研究问题

• RQ1 是否可在双层石墨烯中稳定一种鲁棒的偶数分母分数化量子霍尔态，使其具有显著大于其他体系的能量间隙，并可实现非阿贝尔任意子？
• RQ2 磁场和电场如何调控有效电子关联作用，并在半满填充分数化双层石墨烯Landau能级中驱动连续量子相变？
• RQ3 在不可压缩的Pfaffian相与可压缩的复合费米液体之间观察到的中间相的本质是什么？
• RQ4 谷极化是否控制不同拓扑相之间的相变？其对中间相的对称性与稳定性提供了何种信息？

主要发现

• 在双层石墨烯中半满填充条件下观察到一种鲁棒的不可压缩偶数分母分数化量子霍尔态，其能量间隙比先前研究体系大数倍。
• 数值模拟将该态识别为Pfaffian相，证实了非阿贝尔任意子的存在及其拓扑保护特性。
• 磁场调控导致偶数分母能量间隙呈现非单调变化，与预测的在可测量磁场范围之外向复合费米液体相的转变一致。
• 电场控制揭示了在半满填充条件下，从不可压缩相到可压缩相的连续相变，该相变由一种出乎意料的中间相介导。
• 该中间相不可压缩但可极化，表明谷宇称守恒，并存在无能隙的中性激发态。
• 该中间相被识别为具有无能隙中性模式的电绝缘体，与具有谷宇称破缺的拓扑相一致。