Transport Measurement of Landau Level Gaps in Bilayer Graphene with Layer Polarization Control

Velasco, Jairo; Lee, Y.; Zhao, Zhenyu; Jing, Lei; Kratz, Philip; Bockrath, Marc; Lau, Chun Ning

doi:10.1021/nl4043399

Cited by 17 publications

(24 citation statements)

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“…Phase I is only fully resolved at E > ¼ 0 and large B, and phase II is resolved at large E > and relatively small B. To further explore these two distinct n ¼ 2 QH states, we perform transport spectroscopy by using the source-drain bias V as a spectroscopic tool 35,40 . The details of this measurement technique and its application to QH states can be found in refs 36,40.…”

Section: Resultsmentioning

confidence: 99%

“…To further explore these two distinct n ¼ 2 QH states, we perform transport spectroscopy by using the source-drain bias V as a spectroscopic tool 35,40 . The details of this measurement technique and its application to QH states can be found in refs 36,40. Briefly, at each conductance plateau, BLG's Fermi level is pinned between the highest filled and the next unfilled LLs.…”

Section: Resultsmentioning

confidence: 99%

“…Our prior work 40 has shown that the LL gaps in dual-gated devices with controlled layer polarization are different from those in singly gated devices. Here we use transport spectroscopy 35,36,40 to study high-quality dual-gated suspended BLG devices at n ¼ ± 2 (refs 36,38,39,41-46) as a function of B and E > . Our results reveal two distinct states: (1) phase I is fully resolved only near E > ¼ 0 and large B, and has a relatively small gap that extrapolates to 0 at B ¼ 0.…”

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confidence: 95%

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Competing ordered states with filling factor two in bilayer graphene

et al. 2014

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The quantum Hall effect, in which a two-dimensional sample's Hall conductivities become quantized, is a remarkable transport anomaly commonly observed at strong magnetic fields. However, it may also appear at zero magnetic field if time-reversal symmetry is broken. Charge-neutral bilayer graphene is unstable to a variety of competing and closely related broken symmetry states, some of which have non-zero quantized Hall conductivities. Here we explore those states by stabilizing them with external fields. Transport spectroscopy measurements reveal two distinct states that have two quantum units of Hall conductivity, stabilized by large magnetic and electric fields, respectively. The majority spins of both phases form a quantum anomalous Hall state, and the minority spins constitute a Kekulé state with spontaneous valley coherence for phase I and a quantum valley Hall state for phase II. Our results shed light on the rich set of competing ordered states in bilayer graphene.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Competing ordered states with filling factor two in bilayer graphene

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“…1(a). In The knowledge of E10 (D, B) sheds considerable light on the widely varying reports of the LL gap energies in the literature [15,18,22,[35][36][37]. In Fig.…”

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Effective Landau Level Diagram of Bilayer Graphene

Tupikov

Watanabe

et al. 2018

Phys. Rev. Lett.

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The E = 0 octet of bilayer graphene in the filling factor range of -4 <  < 4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.2 Bilayer graphene provides a fascinating platform to explore potentially new phenomena in the quantum Hall regime of a two-dimensional electron gas (2DEG). The existence of two spins, two valley indices K and Kʹ, and two isospins corresponding to the n = 0 and 1 orbital wave functions results in an eight-fold degeneracy of the singleparticle E = 0 Landau level (LL) in a perpendicular magnetic field B [1,2]. This SU (8) phase space provides ample opportunities for the emergence of broken-symmetry manybody ground states [3][4][5][6][7][8][9][10][11][12][13][14][15]. The application of a transverse electric field E drives valley polarization through their respective occupancy of the two constituent layers [1,2]. Coulomb exchange interactions, on the other hand, enhance spin ordering and promote isospin doublets [11,15,16]. As a result of these intricate competitions, the E = 0 octet of bilayer graphene (integer filling factor range -4 <  < 4) exhibits a far richer phase diagram than their semiconductor counterparts. Experiments have uncovered 4, 3, 2, 1 coincidence points for filing factors = 0, ±1, ±2 and ±3 respectively, where the crossing of two LLs leads to the closing of the gap and signals the phase transition of the ground state from one order to another [13,[15][16][17][18]. Their appearance provides key information to the energetics of the LLs and the nature of the ground states involved. Indeed, coincidence studies on semiconducting 2DEGs are used to probe the magnetization of quantum Hall states [19] and measure the many-body enhanced spin susceptibility [20]. In bilayer graphene, the valley and isospin degrees of freedom increase the number of potential many-body coherent ground states. Furthermore, the impact of actively controlling these degrees of freedom became evident in the recent observations of fractional and even-denominator fractional quantum Hall effects [17,[21][22][23][24][25].A good starting point of exploring this rich landscape would be a single-particle, or single-particlelike LL diagram, upon which interaction effects can be elucidated perturbatively. Indeed, even in the inherently strongly interacting fractional quantum Hall effect, effective single-particle models, e.g. the composite fermion model [26], can capture the bulk of the interaction effects and provide conceptually simple and elegant ways to understand complex many-body phenomena. In bilayer graphene, a LL ...

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“…Here we fabricate dual-gated suspended [17][18][19] r-TLG devices 20 , where U > and n can be independently tuned. Device mobility ranges from 20,000 to 90,000 cm 2 V À 1 s À 1 .…”

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Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene

et al. 2014

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Many physical phenomena can be understood by single-particle physics; that is, treating particles as non-interacting entities. When this fails, many-body interactions lead to spontaneous symmetry breaking and phenomena such as fundamental particles' mass generation, superconductivity and magnetism. Competition between single-particle and many-body physics leads to rich phase diagrams. Here we show that rhombohedral-stacked trilayer graphene offers an exciting platform for studying such interplay, in which we observe a giant intrinsic gap B42 meV that can be partially suppressed by an interlayer potential, a parallel magnetic field or a critical temperature B36 K. Among the proposed correlated phases with spatial uniformity, our results are most consistent with a layer antiferromagnetic state with broken time reversal symmetry. These results reflect the interplay between externally induced and spontaneous symmetry breaking whose relative strengths are tunable by external fields, and provide insight into other low-dimensional systems.

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Transport Measurement of Landau Level Gaps in Bilayer Graphene with Layer Polarization Control

Cited by 17 publications

References 55 publications

Competing ordered states with filling factor two in bilayer graphene

Competing ordered states with filling factor two in bilayer graphene

Effective Landau Level Diagram of Bilayer Graphene

Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene

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