Session Y20: Graphene Quantum Hall

Tunneling Spectroscopy of Quantum Hall States via a Dual-gated Graphene Quantum Point Contact

We study low-temperature magneto-transport across a dual-gated graphene point contact. We demonstrate selective control over the evolution, hybridization, and transmission of quantum Hall states in the channel. By tuning the coupling between quantum Hall edge states, we characterize their energy gap via tunneling spectroscopy.   

Noninvasive charge sensing of graphene in quantum Hall regime with scanning tunneling microscopy

Under strong magnetic field, electrons in mono-layer graphene form highly degenerate Landau levels, hence the strongly enhancement of electron-electron interaction. As a result, fractional charge excitation appears and uniform electron liquid becomes unstable which gives rise to exotic charge order phases such as Wigner crystal, bubble, and stripe phase. Although evidence of fractional excitation has been found by various experimental techniques and strong indications of exotic charge orders have been revealed by transport anomalies, a noninvasive probe with spatial resolution of sub-magnetic length that is capable of imaging fractional charges or exotic charge orders is still lacking. Here, we map the intrinsic compressibility and electrostatic potential of graphene in quantum Hall regime using scanning tunneling microscopy. We fabricate double-layer graphene devices which consist of two mono-layer graphene separated by a thin hBN flake. By controlling the total charge density and inter-layer bias potential, we are able to use the top graphene layer as a sensor layer and probe the intrinsic properties of the second graphene layer. This method can potentially become a universal noninvasive charge sensing technique.

    

Effects of coupling strength and edge disorder on coherent transport through a quantum Hall antidot system

In an quantum Hall (QH) antidot, quasi particles of QH fluid can be localized and organized in quantized energy levels. In this work, we used hBN encapsulated graphene samples to study the coherent transport properties through QH antidot systems. In those samples the utilization of side gates and co-axial gate leads to great tunability in coupling between antidot and charge reservoir as well as individual intra antidots coupling, which allows the characterization of effects from coupling strength and edge disorders on the quantum coherence. This pave ways for achieving more complex QH antidots systems as hosts of anyons with exotic exchange statistics.   

Programmable quantum Hall array resistance standards in epitaxial graphene devices

The quantum Hall effect (QHE) provides an invariant reference for resistance related to the elementary charge e and Planck constant h, and the International System of Units (SI) unit of resistance has been redefined, thereby fixing the von Klitzing constant , to a constant value[1-3]. Graphene, due to its inherently two-dimensional structure and superior electrical properties, has a robust quantum Hall plateau at , where  is the filling factor, and has become an ideal material for developing quantum Hall resistance standards.

Based on a single Hall bar device with quantized resistance value (R_K/2~12.9 kΩ), many possible resistance values (m*R_K/2) can be obtained by connecting quantum Hall devices in parallel or in series connection [4]. So far, the nearly 1 kΩ and 1.29 MΩ quantum Hall resistance array standards have been tested [5,6] using Multi-terminal superconducting contacts are used for interceonnection and magnetotransport measurements [7].

In this work, epitaxial graphene is grown on a SiC substrate [8], and is functionalized with Cr(CO)₃ [9].  The quality of graphene is assessed by confocal laser scanning microscopy. To obtain various quantized resistances, we fabricated graphene Hall bar network devices using graphene as interconnections. We use top gate to manipulate graphene interconnections, and program the graphene array. Precision measurements are obtained with a DC current comparator and cryogenic current comparator.   

Edge effects in microwave measurements of correlated electronic phases in graphene

Strongly correlated electronic phases such as the fractional quantum Hall effect (fQHE) and Wigner crystal (WC) have been studied in 2D electron gases (2DEGs) using DC and AC resistivity measurements. However, the study of WCs using AC measurements have been mostly limited to 2DEGs at the interface of GaAs/AlGaAs heterojunctions. To study WC and fQHE in graphene in the AC regime, we construct devices which incorporate a co-planar waveguide (CPW) coupled to a monolayer graphene (MLG) for microwave transmission spectroscopy studies. There are several design challenges for building devices that have high sensitivity and incorporate pristine MLGs that support these quantum phases. Device designs where MLGs are capacitively coupled to CPWs have low sensitivity. Alternatively, devices where the MLG is resistively coupled to the CPW alleviate the sensitivity issue but introduce frequency-dependent contributions from edges. A third option is creating a gate-defined MLG region that is resistively coupled to the CPW without direct edge contacts. In this talk we will discuss the observation of Landau levels and strongly correlated electronic phases at high magnetic fields and low temperatures using microwave transmission spectroscopy for the various device architecture outlined above.

    

Author not Attending

The most recognizable feature of graphene’s electronic spectrum is its Dirac point around which interesting phenomena tend to cluster. At low temperatures, the intrinsic behavior in this regime is often obscured by charge inhomogeneity but thermal excitations can overcome the disorder at elevated temperatures and create an electron-hole (e-h) plasma of Dirac fermions. The Dirac plasma has recently been found to exhibit unusual properties including quantum critical conductivity and hydrodynamic flow. However, little is known about its behavior in magnetic fields. Here we report magnetotransport in this quantum-critical regime. In low fields, the plasma exhibits giant parabolic magnetoresistivity reaching >100% in 0.1 T even at room temperature. This is orders of magnitude higher than magnetoresistivity found in any other system at such temperatures. We show that this behavior is unique to monolayer graphene, being underpinned by its massless spectrum and ultrahigh mobility, despite frequent (Planckian-limit) scattering. With the onset of Landau quantization in a few T, where the e-h plasma resides entirely on the zeroth Landau level, giant linear magnetoresistivity emerges. It is practically independent of temperature and can be suppressed by proximity screening, indicating a many-body origin. The linear behavior is qualitatively explained by diffusion of cyclotron orbits on the zeroth Landau level through a network of shallow e-h puddles. Clear parallels with magnetotransport in strange metals and so-called quantum linear magnetoresistance predicted for Weyl metals offer an interesting playground to further explore relevant physics using this well-defined quantum-critical 2D system. 

    

High-Temperature Thermal Magneto-Conductivity in Graphene Corbino

Measurement of thermal transport in strongly interacting and correlated electronic systems can reveal exotic new physics that may be elusive to electrical transport, such as neutral modes or emergent collective behavior. Graphene can host a strongly interacting quantum-critical Dirac fluid, where the thermal conductivity can deviate from the Wiedemann Franz law. Application of a magnetic field in the Dirac fluid can further enrich the thermal transport in the system as thermally drifting electron and hole motions differ from each other. In this talk, we present thermal magneto-conductivity measurements of graphene performed using Johnson noise thermometry and channel self-heating. In a Hall bar geometry, this measurement would not work due to hot spot formation near the contacts; however, the rotational symmetry of a Corbino geometry allows measurement of the radial component of electrical and thermal conductivity under a magnetic field. Under low applied magnetic field, we find the thermal magneto-conductivity changes sign as a function of density and magnetic field, while the electrical magneto-conductivity always remains negative. We discuss the thermal magneto-conductivity in the context of zero-field Wiedemann Franz deviations and hydrodynamics.

    

Novel interlayer quantum Hall states in double bilayer graphene

Bilayer graphene hosts exotic even-denominator fractional quantum Hall states due to the special form of Coulomb interaction in its N=1 Landau level. On the other hand, when we bring two two-dimensional electron systems close to each other, the introduction of interlayer Coulomb interaction gives rise to a set of new interlayer correlated states. Previous experiments [1,2] on the double-layer structure of bilayer graphene revealed exciton condensation phases, or equivalently interlayer quantum Hall states with integer total filling factors, when both bilayer graphene layers are in the N=0 Landau level. Now with improved quality in devices of such a system, here we report our observation of interlayer quantum Hall states with fractional total fillings when both layers are in the N=0 Landau level. More interestingly, we also observe integer interlayer states when both layers are in the N=1 Landau level, which show different signatures compared to their N=0 counterparts.

[1] Liu, X. et al. Nature Phys 13, 746–750 (2017)

[2] Li, J. et al. Nature Phys 13, 751–755 (2017)   

Gate-Tunable Helical Currents in Commensurate Topological Insulator/Graphene Heterostructures

Interfaces between graphene and the topological insulator Bi₂Te₂Se feature a lattice-matched, commensurate stacking, where proximity effects have been predicted to impart an anisotropic and electronically tunable spin texture [1]. Here, we demonstrate the growth of such expitaxial and commensurate interfaces, we characterize their interfacial symmetries by optical spectroscopies, and we adress the gate-tunable spin-orbit poximity by polarization resolved photocurrent spectroscopy. As a main finding, we demonstrate a circular photogalvanic effect which is drastically enhanced at the Dirac point of the proximitized graphene. We attribute the gate-tunability to the proximity-induced interfacial spin structure, which could be exploited, for example, in spin filters [2].

[1] Song et al. Nano Lett. 18, 2033 (2018)

[2] Kiemle et al. ACS Nano 16, 12338 (2022).   

Fabrication and Measurement of Electron Interferometers in vdW Hetrostructures

   Fabry-Perot interferometry has been proposed as an experimental tool to detect the effective charge of quasiparticles and the anyonic statistics in the FQH regime. The electronic interferometers are defined by two quantum point contacts (QPCs) which induce controllable backscattering and partitioning, by bringing the forward propagating edge channel in proximity with the backward propagating edge channel. Recently, clean Van der Waals heterostructures has emerged as a new platform for interferometry experiments due to their gate tunability and control over confinement potentials. In this talk I will discuss different approaches to fabricate electron interferometers by utilizing vdW technique and AFM based nanolithography. I will also present transport measurements of these confined geometries in QH regime where coherent phenomena can be observed.

    

Emerging Interlayer Coherence in Twist-Controlled Graphene Double Layers

In closely spaced double layer systems in the quantum Hall regime, enhanced interlayer interactions can lead to interlayer exciton condensates when each layer is at half-integer filling of the lowest Landau level. We study interlayer tunneling in double layers of graphene separated by a thin hBN tunnel barrier, where accurate rotational alignment of the graphene monolayers leads to energy and momentum conserving resonant tunneling. At half-integer layer fillings of the lowest orbital Landau level, we observe Josephson-like zero-bias tunneling conductance peaks that are insensitive to variations of layer filling factors. The zero-bias tunneling conductance peaks have a significantly narrower linewidth compared to 2D-2D tunneling resonances observed at zero magnetic field when the energy bands of the two layers are aligned, indicating that electrons occupy an interlayer coherent superposition of states in both layers. Additionally, the tunneling spectrum provides insight into the types of paired states. Our results establish twist control as key to probing interlayer exciton condensates through tunneling anomalies in double layers of two-dimensional materials.

    

Scanning tunneling spectroscopy of exciton condensate in graphene double-layers

Fermions can form a condensate by pairing up into composite bosons, such as in superconductors and superfluid He₃. Interlayer exciton condensate is one of the few demonstrated fermionic condensates, where electrons and holes reside in spatially separated parallel layers couple to form excitons that condense at low temperatures. Previous transport measurements have established exciton condensation in graphene double-layer devices. However, there has not been spectroscopic measurements of this exotic state. Here we use scanning tunneling spectroscopy to probe the graphene double-layer devices under strong magnetic fields. In addition to incompressible states at the integer and fractional fillings of each layer, we observed gapped states when the total filling factor of the two layers is an integer as interlayer charge imbalance is continuously varied. These gaps, which are smaller than the those of integer quantum Hall states in individual layers, correspond to exciton condensates. Our spectroscopic measurements reveal information on the strength of the condensate states at different charge imbalance, the evolution of fractional quantum Hall states with changing dielectric environments, and competition between exciton condensation and fractional quantum Hall states of each layer. Future spectroscopic imaging experiments may uncover signatures of other remarkable electron behaviors in the double-layer system, such as exciton solids and topological excitations.

    

Exciton-mediated unconventional superconductivity in graphene multilayers

We uncover a purely repulsive mechanism for superconductivity in graphene multilayers relying on interband processes and occurring upon doping a band insulator, mediated by excitons forming between the two bands. The symmetry of the pairing order parameter depends on the quantum geometry of the valence band, is generically non s-wave, and undergoes transitions as a function of applied electric field. The attraction can be attributed, in real space, to fluctuations of the electron lattice representing the filled valence band. We apply our theory to results in Bernal bilayer and rhombohedral trilayer graphene, suggesting the importance of exciton-mediated pairing in these systems.   

Tunable electrical control of magnetism in chiral stacked graphene-transition metal dichalcogenide heterostructures

Electrical control of magnetism has been a longstanding goal of the spintronics community. In this talk, I will explain how such control can be potentially realized in a two-dimensional heterostructure of chiral stacked multilayer graphene sandwiched in between transition metal dichalcogenides (TMDs). We show that, the proximity induced spin-orbit coupling (SOC) in chiral multilayer graphene will favor two isospin (spin/valley) flavors over the other two, and then the Coulomb interaction will spontaneously pick one of the two via the Stoner mechanism. By choosing a proper alignment between the graphene multilayer and TMDs, the sign of the proximity induced SOC in graphene, and therefore the favored isospin flavor, can be reversed by flipping the direction of the perpendicular electric field. Combining these ingredients, we show how to use the perpendicular electric field to flip either spin or valley depending on their g factors. We also show how to control the valley g factor by the number of graphene layers and the magnitude of the perpendicular electric field, which allows one to flip spin or valley on demand.   

Electronic band properties of graphene on SrTiO3

Graphene on SrTiO₃ (STO) substrate is a promising platform for emerging exotic quantum phenomena (e. g. quantum Hall ferromagnetism [1] and charge-density-wave order [2]) owing to the large dielectric permittivity of STO that significantly screens the electron-electron interaction in graphene. Additionally, the use of STO as a back-gate material allows doping of a substantial number of carriers and, therefore, investigation of the electronic band structure of graphene at high energies (> 1 eV). To study the electronic band properties of graphene in a weakly interacting electron environment, we measured electrical transport on graphene/STO in high magnetic fields up to 60 T and a wide temperature range of 1.5 – 300 K. In this talk, we will present findings inferred from the quantum Hall effect and quantum oscillations results on graphene/STO devices. Our detailed investigation on back-gate and temperature dependence of quantum Hall effect and quantum oscillations suggests a strong impact of STO substrate on the Fermi level of graphene.

References:

[1] L. Veyrat et al., Science 367, 781 (2020).

[2] A. Coissard et al., Nature 605, 51 (2022).