Session X51: Transport in Graphene Systems

Flat-Band Magnetism and Half-Metallicity in Twisted Bilayer Graphene

Evidence of flat-band magnetism and half-metallicity in compressed twisted bilayer graphene is provided with first-principles calculations. We show that dynamic band-structure engineering in twisted bilayer graphene is possible by controlling the chemical composition with extrinsic doping, the interlayer coupling strength with pressure, and the magnetic ordering with external electric field. By varying the rotational order and reducing the interlayer separation an unbalanced distribution of charge density results in the spontaneous apparition of localized magnetic moments without disrupting the structural integrity of the bilayer. Substitutional doping shifts the chemical potential of one spin distribution and leads to half-metallicity.   

Evidence for a three-layer-coherent quantum Hall state in graphene triple layers

Heterostructures consisting of two graphene monolayers separated by a thin BN spacer provides a rich platform in which to study correlated states driven by strong interlayer interactions. In the quantum Hall effect regime, tuning this system to total filling fraction \nu_tot = 1 (i.e. half filling of the lowest Landau level in each layer) results in a spontaneously formed interlayer coherent state believed to be a Bose-Einstein condensate of indirect excitons or a pseudo spin ferromagnet. Here we report the first realization of a triple layer system where three monolayer graphene layers are strongly coupled via coulomb interaction while maintaining negligible interlayer tunneling. We demonstrate independent control of the density in each layer, giving access to the entire phase space of this system. Tuning the relative filling fraction between all three layers allows us to effectively shift the exciton condensate between different layer pairs and then probe this phase with the third layer. When the total filling factor of all three layers equals 1, we observe simultaneous quantization of Hall resistance in the drive and drag layer and vanishing longitudinal resistance, suggesting a generalized exciton condensate phase with macroscopic phase coherence across all three layers.   

Nonlocal transport in twisted double bilayer graphene

In the spectrum of 2D materials, superlattices have emerged as a promising platform to modulate band structure. In graphene, it does the job of breaking the inversion symmetry between the K and K' points. In the case of bilayer graphene, spatial inversion symmetry can also be broken by applying a transverse electric field, which opens up a gap at CNP. Both these ways result in the generation of a valley current via the valley Hall effect. This shows up as non-local resistance, away from the path of charge current.
We integrate both these ways of valley current generation and implement it on dual gated twisted double bilayer graphene device, where the two copies of bilayer graphene have been rotated by 1.18^o. We observe large non-local resistance few microns away from local probes. We further demonstrate its tunability with electric field and with charge density.
One can thus explore this additional valley degree of freedom to transmit information coherently over distances of few microns in graphene. This may open up new avenues in the emerging field of valleytronics.   

Quantum Interferences in Monolayer Graphene PN Junctions

Ballistic Dirac-Fermion transport across gate-defined PN junctions exhibits strong dependence on incident angle due to the linear dispersion relationship. Multiple experiments have been performed utilizing the angle-dependence of Klein tunneling, in which novel electron-optics concepts including electron collimation [1] and Veselago lensing [2][3] have been demonstrated. Here we demonstrate preliminary experimental observations of quantum interferences based on these concepts. Preliminary transport data across carefully-engineered PN junctions will be presented and quantitative analysis based on Klein-tunneling probability will also be discussed.

[1] Ke Wang et al, Proc. Nat. Acad. Sci. 116, 6575-6579 (2019).
[2] Shaowen Chen et al, Science 353, 1522-1525 (2016).
[3] Gil-Ho Lee et al, Nature Physics 11, 925–929 (2015).   

Gate Controlled Suppression of Weak Localization in Bilayer Graphene due to Proximity Magnetic Effects

The transport properties of bilayer graphene are known to be affected by weak localization at low temperatures. In this study, we use differential conductance mapping to explore the transport properties in bilayer graphene at low temperatures, under conditions for which they are influenced by the proximal of the graphene to a ferromagnet (Co). The low-temperature differential conductance is measured around the Dirac point, with the floating Co “gate” both included in, and absent from, the current path. In the latter case the differential conductance shows the characteristic dip that is known to provide a signature of weak localization. With the Co gate in the current path, however, the differential conductance shows a zero-bias anomaly, implying the suppression of the weak localization at certain energies that are insufficient to cause dephasing of the carriers. The presence and the magnitude of the zero-bias anomaly is depending on the carrier concentration in graphene, making it gate controllable.   

Mini-Dirac cones in AB-stacked graphene in perpendicular electric fields

AB-stacked multilayer graphene with number of layers shows semi-metallic band structure arising from the overlap of bilayer-like bands. By conducting low temperature magnetotransport experiments using encapsulated graphene samples with a top and a bottom gate electrode, we observed that mini-Dirac cones are formed in a perpendicular electric field. In zero perpendicular electric fields, Landau level near the charge neutrality point showed structures which are characteristic of semi-metallic band structures. The structure showed significant variations in perpendicular electric fields. The variations of the Landau level structure were interpreted as a formation of levels arising from mini-Dirac cones from numerical calculations of dispersion relations and the Landau levels. The mini-Dirac cones originate from a trigonal warping in the band structure. The perpendicular electric field opens energy gaps between bilayer-like band, and the trigonal warping closes the gaps locally, thereby mini-Dirac cones form.

  

Anomalous Quantum Hall States in Bilayer Graphene

Bernal stacked bilayer graphene has a collection of competing broken symmetry states characterized by flavor-dependent spontaneous valley polarization.[1] The possible states include polarized and unpolarized orbital magnets and various quantum anomalous Hall states. By carefully evaluating the orbital magnetizations of the competing states, we find that the phase diagram is profoundly altered by a B field by favoring states of which its natural filling factor ν_N ≡ σ_H /(e²/h) is close to the actual filling factor ν, increasingly so as the B field strengthens. We have explored how coupling of orbital magnetization to external B fields is manifested in the dependence of ground state properties on weak gate V_g and magnetic fields B that favor particular states. We construct the ground-state phase diagram of this system, vs. V_g and B at fixed ν, and vs. V_g and ν at fixed B, and obtain excellent agreement with two-point conductivity measurements. This work explains why the ν_N = ±4 quantum Hall Effect in bilayer graphene is stable to anomalously weak B fields, and suggests that ν_N = ±2 anomalous quantum Hall effects could occur in the absence of a B field in samples of sufficiently high quality.

[1] PRL 106 (15), 156801   

Electronic Thermal Conductance Suppression in Lightly Doped Bilayer Graphene Measured via Johnson Noise Thermometry

Systems with strongly interacting and correlated electrons can exhibit exotic new physics, such as the hydrodynamics regime, where particles’ behavior is best collectively described as a viscous fluid rather than as individual particles. Several such systems have recently been both predicted and shown experimentally to have thermal conductivity enhanced or reduced relative to the near-universal Lorentz value expected from Wiedemann-Franz Law. Bilayer graphene presents a strong candidacy for quantum criticality and hydrodynamics at charge neutrality, where the carrier-carrier Coulomb energy dominates the kinetic energy of quasiparticles. We explore such behavior by measuring the electronic thermal conductivity of bilayer graphene encapsulated in boron nitride and gated by dual graphite gates, with residual density below 3×10¹⁰ cm^-2. We use our high-frequency Johnson noise thermometry technique to measure the electronic cooling of the electron system, extracting out the thermal conductivity. We observe a large reduction of the thermal conductivity below the Wiedemann Franz Law at electron doping slightly away from charge neutrality. We discuss these results in the context of hydrodynamics.   

Designing transport properties of graphene nanoribbon junctions

Graphene nanoribbons (GNRs) have recently emerged as promising candidates for next-generation electronic devices, including the realization of all-graphene nanocircuitry. Junctions connecting two or more GNRs are the elementary components of GNR circuits. We systematically address the electronic transport properties of 60°- and 120°-angled junctions connecting a pair of GNR leads of identical width and chirality utilizing tight-binding model calculations. An exhaustive exploration of GNR junctions carried out by screening over 50,000 configurations allows us to formulate general guidelines into engineering transport properties GNR circuits. For instance, we find that 120°-angled junctions with sublattice imbalance have a perfect transmission via a resonant state occurring at zero energy, and thus identified as ideal GNR interconnects.   

In-situ TEM observation of suspended graphene during Joule heating process

Dynamic surface modification of suspended graphene at high temperature was observed using in-situ transmission electron microscope (TEM) measurement. The suspended graphene were prepared on top of the SiN membrane with hole substrate so that TEM observation was conducted under Joule heating processes. Current-voltage characteristics of suspended graphene devices inside of TEM chamber were measured to monitor and control the high temperature condition of graphene surface by estimating electrical power on the devices. During the in-situ TEM observation, it was found that residual materials, previously remained on the graphene surface, were removed at high temperature. Dynamic movement of residue on the graphene surface and shrinkage of atomic distance of graphene were also observed while the Joule heating process.   

Excitonic Condensate Phase in Hybrid double-layer structures

In this talk I will present Coulomb transport measurement of exciton condensate phase in a hybrid double-layer structure, where twisted bilayer graphene (tBLG) and monolayer graphene (MLG) are separated by a thin insulating barrier. With a large twist angle, the lowest Landau level in twisted bilayer graphene features eight-fold degeneracy, where each broken symmetry state in the quantum Hall effect regime is described by Landau wavefunction with orbital index N=0 [1]. As such, excitonic pairing across the insulating barrier is expected to be robust over a large phase space, characterized by filling fractions n_MLG and n_tBLG, along with perpendicular electric field D. Using Coulomb drag measurement, we discovered multiple copies of fully developed exciton condensate phase in both the electron-electron and electron-hole quadrants of the phase space. Over a large filling fraction range, -5 < n_total < 5, the value of quantized Hall resistance plateaus varies with total filling fraction n_total. Most interestingly, the strength of exciton pairing is shown to be tunable with layer polarization in tBLG. This tunability adds an extra dimension to the phase space, which allows us to investigate the behavior of exciton condensate in a three-component system with three layers of graphene.   

High-order fractal quantum oscillations in highly doped graphene/BN superlattices

High temperature quantum oscillations have been reported in graphene/BN superlattices beyond secondary Dirac points both for electron and hole doping [1,2]. These so-called Brown-Zak (BZ) oscillations originate from periodic emergence of delocalized Bloch states in high magnetic field. However, the BZ oscillations is much less visible for hole doping than for electron doping due to strong electron-hole asymmetry. Here, we employed a newly developed electron beam doping technique to induce high electron and hole carrier densities in graphene/BN superlattices while maintaining high mobilities. Enhanced BZ oscillations are observed beyond the third-generation neutrality points at high temperatures. High-order magnetic Bloch states are also seen even for hole doping, demonstrating the effectiveness of our doping technique. Theoretical simulation of the magnetotransport provides qualitative agreement of the carrier density dependence of BZ oscillations with our experimental results.

References:
[1] R. K. Kumar, X. Chen, et al, Science 357, 181 (2017).
[2] R. K. Kumar, A. Mishchenko, et al, PNAS 115, 5135 (2018).   

Proximity-induced spin-orbit coupling in bilayer graphene/WSe2 heterostructures probed by quantum Hall measurements

The physical properties of 2D materials are highly sensitive to the interface in a van der Waals heterostructure [1], leading to intensive studies into the resulting proximity effects. In particular, significant effort has been made to increase the spin-orbit coupling (SOC) in graphene by coupling it to transition metal dichalcogenides [2]. However, it remains challenging to study high-quality quantum Hall signatures, which acts as a precise probe of SOC strength [3]. Here we report a direct observation of SOC in a bilayer graphene/WSe₂ heterostructure in quantum Hall measurements [4]. A distinct Landau level (LL) crossing pattern emerges when tuning the charge density and displacement field, originating from a layer-selective SOC proximity effect. By analyzing the LL structure, we simultaneously estimate both Ising (~-2.2 meV) and Rashba SOC (~15 meV) energy scales, which are consistent with the theoretical predictions of interlayer twist angle dependence. Our study provides a high mobility system with potential to realize novel topological electronic states and manipulate spin in nanostructures.
[1] A. K. Geim, et al. Nature 2013 499, 419
[2] A. Avsar, et al. Nat. Commun. 2014, 5, 4875
[3] J. O. Island, et al. Nature 2019 571, 85
[4] D. Wang, et al. Nano Lett. 2019 19 (10), 7028   

Atypical Quantized Hall Resistances in Millimeter-Scale Epitaxial Graphene p-n Junctions

Epitaxial graphene (EG) on silicon carbide (SiC), which grows on hexagonal SiC at high temperatures, can be nearly defect-free on the centimeter scale and exhibits properties that make it suitable for large-scale and high-current applications. We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene p-n junction devices using simple ultraviolet photolithography, thereby significantly reducing device processing time compared with electron beam lithography typically used for obtaining sharp junctions. This work presents the resulting experimental data obtained from these devices when introducing multiple current inputs in several different configurations. Furthermore, the LTspice circuit simulator is used to examine the various rearrangements of the electric potential in the device when injecting current at up to three independent sites. These measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at the v=2 plateau (R_H = 12.9 kΩ) that take the form: a/b *R_H. Here, a and b have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of R_H. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.   

Spin waves in canted antiferromagnet of bilayer graphene

Antiferromagnets are promising candidates for spintronics applications thanks to their high-frequency dynamics and insensitivity to external magnetic field perturbations. The \nu=0 quantum Hall state in bilayer graphene supports a canted antiferromagnetic (CAF) phase when a small electric field is applied perpendicular to the plane. This state is predicted to support dissipationless spin transport through a superfluidity mechanism [1]. Previous experiments showed that spin waves can be excited by a finite dc bias on one side of a quantum Hall region and detected on the other side using a non-local transport setup [2, 3]. Here we report on spin wave transport through the \nu=0 CAF state of bilayer graphene. In our devices, we observe spin wave excitations with non-zero dc bias thresholds similar to what’s reported [2]. We also observe, in certain measurement setups, strong non-local signals with a dc bias threshold close to zero, only when the \nu=0 state is in the CAF phase. We present the temperature, magnetic field, and electric field dependence of the zero-threshold signal and discuss potential origins.

[1] Takei et al., PRL 116, 216801 (2016)
[2] Wei et al., Science 362, 229–233 (2018)
[3] Stepanov et al., Nature Physics 14, 907–911 (2018)