Session D56: Graphene: Quantum Hall effect and Correlated States

Spectroscopic imaging of Landau orbits in graphene using a scanning tunneling microscope

In strong magnetic fields, the kinetic energy is quenched and Dirac fermions in graphene form highly interacting quantized Landau levels. Spectroscopic mapping with the scanning tunneling microscope (STM) can be used to determine the orbital angular momentum for the non-degenerate Landau levels[1]. Following a similar approach, we examine lifting of the orbital degeneracy of the zeroth Landau level (ZLL) in the vicinity of charged impurities when the system is in an incompressible state. We observe that the orbital splitting in the single particle gaps follows a simple electrostatic model discussed in previous works[2], thereby allowing us to quantify the Coulomb potential induced by charged defects as well as the screening effect of the STM tip. Furthermore, we observe additional features in the symmetry breaking gaps of the ZLL that are not captured in the single-particle description and require further theoretical investigation. Our ability to image Landau orbits in a pristine graphene device paves the way for resolving the orbital splitting of the fractional quantum hall states and probing anyons in graphene in the quantum hall limit with the STM[3].

[1]B. Feldman et al. Science 354, 316–321(2016).

[2]A. Mayer et al. PRL 112, 036804(2014).

[3]Z. Papić et al. PRX 8, 011037(2018).   

Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekule phase, we visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley ordered phases and their topological excitations in a wide range of materials.   

Scanning tunneling spectroscopic features of partially filled Landau levels under different tip conditions

Under strong magnetic fields, 2D electron gases form flat Landau levels (LL) that are highly degenerate. Such degeneracy can be lifted by electron-electron interaction and the presence of impurities which creates localized states that leads to quantization of Hall conductance. Here we perform density tuned scanning tunneling spectroscopy study of LL in graphene using tips that have different tip-sample workfunction mismatch. When the mismatch is near zero, spectral measurements reveal sashes cutting through the partially filled LL. These features, called Haldane sashes, reported in pulse tunneling experiment in GaAs, separate states with different isospins and are a result of Haldane pseudo-potential between the incoming electrons and existing electrons in LL. When the spectroscopy is taken with positive (negative) workfunction mismatch, the sashes are replaced by uptick (downtick) features emanating from integer gaps. We further study the origin of tick features by bringing the tip closer to a charged defect and observing the energy evolution of such features as the tip-induced potential interacting with the impurity potential. Similar features also manifest around fractional gaps, the origin of which require further investigation and may reveal information on the anyon.   

Electronic Thermal Transport Measurement in Low-Dimensional Materials with Graphene Nonlocal Noise Thermometry

In low-dimensional systems, the combination of reduced dimensionality, strong interactions, and

topology has led to a growing number of many-body quantum phenomena. Thermal transport, which

is sensitive to all energy-carrying degrees of freedom, provides a discriminating probe of emergent

excitations in quantum materials and devices. However, thermal transport measurements in low

dimensions are dominated by the phonon contribution of the lattice, requiring an experimental

approach to isolate the electronic thermal conductance. Here, we show how the measurement of

nonlocal voltage fluctuations in a multiterminal device can reveal the electronic heat transported

across a mesoscopic, low-dimensional bridge. By using two-dimensional graphene as

a noise thermometer, we demonstrate quantitative electronic thermal conductance measurements of

graphene and carbon nanotubes up to 70 K, achieving a precision of ~1% of the thermal conductance

quantum at 5 K. Employing linear and nonlinear thermal transport, we observe signatures of long range

interaction-mediated energy transport in one-dimensional electron systems, in agreement with a

theoretical model. Our versatile nonlocal noise thermometry allows new experiments probing energy

transport in emergent states of matter and devices in low dimensions.   

Thermal Transport Study of Broken Symmetry Quantum Hall States Using Noise Thermometry

A number of phases with spontaneously broken symmetry, including canted-antiferromagnetism and valley-polarized states, are predicted to be present in the half-filled zero-energy Landau level of graphene. While results from charge-based transport measurements concur with the theory, a more direct probe is needed to demonstrate that neutral modes, such as spin and valley waves, exist in the insulating phases. Using a non-local noise measurement technique, where graphene serves as nanoscale heater and thermometer, we extract the thermal conductance of graphene at $\nu=0$ and observe thermal transport signatures of a phase transition between two different broken symmetry states, consistent with theory. Thermal transport measurement offers a new route towards understanding the intriguing spontaneous symmetry breaking in quantum Hall regimes in graphene and other van der Waals materials.   

Electrical and thermoelectric transport in random-edged graphene quantum dots in the lowest Landau level

Etch-defined graphene quantum dots have inherent randomness on their edges which can generate disorder. Under quantizing magnetic fields, such disorder broadens Landau levels in the system, except the lowest Landau level (LLL) at the charge neutrality point, which remains sharply degenerate due to the chiral symmetry of graphene. The combination of quantum confinement and disorder effects in the partially filled LLL may generate novel non-Fermi liquid behavior with distinct electrical and thermal signatures. We report measurements of electrical conductance and thermopower through an etch-defined graphene island coupled to high-quality graphene reservoirs in a perpendicular magnetic field at low temperatures. The carrier densities in the island and reservoirs are independently tunable, enabling complete or partial transmission or reflection of quantum Hall edge states from the reservoir through the island at certain gate configurations, despite strong spatial confinement. We will discuss the implications of electrical and thermoelectric transport through the graphene quantum dot under strong magnetic fields, where random edge disorder enables strong interactions between localized states in the dot in the lowest Landau level.   

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The fragile nature of quantum phases makes them difficult to realize and probe experimentally. One of the prerequisites for studying quantum phases in materials is to work with pristine materials and devices that have minimal defect concentrations in order to prevent quantum decoherence from scattering and disorder. In this work we construct layered heterostructure devices consisting of a graphene monolayer encapsulated between two atomically smooth layers of hexagonal boron nitride with a bottom graphite gate for tuning the charge carrier density in the monolayer. We then fabricate a coplanar waveguide on top of the device in order to measure the monolayer's high frequency response in the radio to microwave range (10 MHz – 25 GHz). These devices are optimally designed to investigate strongly correlated electronic states at large magnetic fields and millikelvin temperatures. We investigate the competition of Wigner crystal and bubble phases with the fractional quantum Hall states in low Landau levels. Pinning of these states to remnant disorder produces resonances that provide insight into the nature of these states and electron-electron interactions.   

Distribution of Current in Closely Spaced Fine Metal Contacts Used in Graphene Hall Bar Devices

The future of resistance metrology will involve the development of quantum Hall array resistance standards (QHARS). At NIST, we have fabricated QHARS devices using monolayer graphene epitaxially grown on SiC. In order to develop next generation QHARS devices designed to specific resistance values, the arrays will need to be miniaturized to increase the density of devices on chip, and consequently will involve a high density of closely spaced split contacts. To better understand how current is distributed among closely spaced split contacts, we present our measurements of contacts spaced <10 um apart on graphene Hall bar devices, fabricated using a mixture of resist-residue-free photolithography and E-beam lithography, and measured using a Cryogenic Current Comparator with a DC SQUID as a current detector to enable ultra-high measurement sensitivity. We also present a comparison of our experimental data for closely packed contacts to published works on split contacts of larger scale Hall bar devices.   

Observation of quantum hall effect in graphene using surface acoustic waves

Surface acoustic waves (SAWs) have been used to great effect in GaAs/AlGaAs heterostructures in the contactless measurement of length-scale dependent conductivity in high magnetic fields and low temperatures, where the system enters the QH and FQH regimes. SAWs would appear to be an ideal technique for two-dimensional (2D) heterostructures, where it can be difficult or impossible to make reliable electrical contact, and where there are emergent and engineered lengthscales such as charge density wavelengths and Moire periodicities. However, the quantum transport regime has been inaccessibe due to two main challenges. First, a piezoelectric substrate compatible with high-mobility 2D device fabrication and electrostatic gating needs to be identified. Second, the change in the SAW signal is directly proportional to the sample size, and high-quality exfoliated two-dimensional material devices are two to four orders of magnitude smaller than those used in semiconductor-based 2DESs studies. Here, we report the incorporation of a high-mobility, hexagonal boronitride (hBN)-encapsulated, graphene heterostructure into a SAW resonant cavity patterned on a piezoelectric LiNbO3 substrate. We show that the resonant cavity geometry increases signal-to-noise by two orders of magnitude over the traditional delay-line geometry. We observe strong quantum oscillations in both the cavity frequency and in the linewidth in the quantum Hall regime of graphene as a function of magnetic field and gate voltage. This establishes SAW resonant cavities as a viable technique for performing contactless, wavelength-dependent conductivity measurements in the quantum transport regime of 2D heterostructures.   

Abrupt Interfaces and Andreev Conversion in Graphene-Superconductor Junctions

We theoretically study chiral transport between quantum Hall graphene and an s-wave superconductor in junctions with varied interface transparency and structure. We focus on the lowest Landau level with the minimum of two chiral edge or interface modes. We find that Andreev conversion is more robust to poor interfaces at strong magnetic field than in the zero field multimode regime. Since intervalley scattering is necessary in graphene for chiral transport around a crystallographic corner, a localized corner mode is essential in zigzag structures when the coupling to the superconductor is weak. At strong coupling, on the other hand, Andreev conversion is enabled by means of the valley content of the chiral Andreev edge state. By studying the regime between these two limits, we develop an understanding of the Andreev reflection probability in presence of imperfections. Moreover, we show how to influence the amount of Andreev versus normal scattering and, consequently, the current and the noise in these graphene devices.    

Experimental observation of spin-split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures

We report the experimental determination of the band structure of single-layer graphene in the presence of strong proximity induced spin-orbit coupling. We achieve this in high-mobility hBN-encapsulated single-layer graphene and WSe₂ heterostructures by measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover confirmation of a bandgap opening and band inversion in the single-layer graphene. Further, we establish that the deviation of the low-energy band structure from pristine single-layer graphene is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane-Mele SOC being inconsequential. Despite the robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in single-layer graphene was lacking. Our combined experimental and theoretical study fills this lacuna.   

Imaging tunable quantum Hall broken-symmetry orders in charge-neutral graphene

Charge-neutral graphene under perpendicular magnetic field was predicted to harbor a rich variety of many-body ground states with distinct topological and symmetry breaking orders. In this talk, I present atomic-scale imaging of the electronic wavefunction of three distinct broken-symmetry phases in graphene using scanning tunneling spectroscopy. We explored the phase diagram by controllably tuning the magnetic field and the screening of the Coulomb interaction by close proximity to a low or high dielectric constant substrate. In the unscreened case, we unveiled a Kekul´e bond order. Under dielectric screening, a sublattice-unpolarized ground state emerged at low magnetic fields, and transited to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.   

Emergence of novel magneto-oscillations near the charge neutrality point in dc current biased graphene

Understanding of many-particle interaction effects on the zeroth Landau level (zLL) in graphene is of great interest and importance in modern condensed matter physics. Typical magnetotransport experiments in this regime are performed at small ac currents, with perpendicular magnetic fields.  In this work, we explore magnetotransport in the non-equilibrium regime by introducing high dc currents in addition to small ac excitations in a large area, high mobility graphene-hBN heterostructure.  The high dc current density (1 A/m) introduces a Hall field, resulting in the tilting of LLs. Shubnikov-de Haas oscillations corresponding to higher LL indices (ν = 18, 14, 10, 6) were found to be shifted with dc current. Intriguingly, we observe novel magnetoresistance oscillations near the zLL that develop as a function of dc current.  These oscillations show a non-linear dispersive behavior as a function of carrier density and magnetic field.  Overall, our experimental findings show signatures of inter-LL transitions in the higher LLs and Hall field-induced insulating states near the charge neutrality point.    

Systematic experimental delineation of splitting, crossings, and electron-hole asymmetry in the Landau octet and higher levels of bilayer graphene

The highly tunable band structure and eightfold degeneracy of the zero-energy Landau level of bilayer graphene (BLG) make it an ideal platform for engineering new quantum Hall states. However, determining the orbital, valley and spin order of quantum Hall states at different filling factors and electric fields is still an unresolved question. In this talk, we will present systematic measurements of unprecedented precision of Landau level spectra of a BLG device at millikelvin temperatures and magnetic fields up to 14 T. The high-quality device and widely accessible electric field allow us to observe previously undetected zero-energy Landau level crossings at filling factors -2, 1 and 3 in high electric fields. In addition, we find that both zero- and high-energy Landau level crossings exhibit strong electron-hole asymmetry. Our observations enable us to constrain the parameters for constructing a realistic theoretical model, which can be used to comprehensively determine the quantum Hall states. The model also confirms states at filling factor -2 in high electric fields which had been previously unresolved. These states are both valley and orbital polarized.   

Temperature-induced phase transitions in the correlated quantum Hall state of bilayer graphene

The quantum Hall systems can be used to study many-body physics owing to its multiple internal electronic degrees of freedom and tunability. While quantum phase transitions have been studied intensively, research on the temperature-induced phase transitions of this system is limited. We focused on the easy-plane antiferromagnetic quantum Hall state with U(1) symmetry, which is established at the zero-energy of bilayer graphene. Using Corbino samples, we measured the pure bulk conductivity of a quantum Hall antiferromagnetic state in bilayer graphene over a wide range of temperatures and observed nonmonotonic temperature dependence which is characterized by two different energy scales. Based on previous studies and theoretical considerations, we found that they are associated with the breaking of the long-range order, i.e., the Kosterlitz–Thouless transition, and short-range antiferromagnetic order. This is the first study for the temperature-induced phase transition in quantum Hall antiferromagnet and indicates a similarity between quantum Hall magnetic systems and other strongly correlated systems such as Mott insulators.