Magnetoresistance measurements of graphene at the charge neutrality point

Direct Evidence of Klein and Anti-Klein Tunneling of Graphitic Electrons in a Corbino Geometry

Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hall bar magnetic focusing setups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular "edgeless" Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or monolayer graphene which show instead a sharpened collimation of transmission paths. The local maxima on the bilayer magnetoconductance plots migrate to higher fields with increasing doping density. These experimental results are in good agreement with detailed numerical simulations and analytical predictions.

An epitaxial graphene platform for zero-energy edge state nanoelectronics

Graphene's original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in conventionally patterned graphene epitaxially grown on a silicon carbide substrate (epigraphene) are stabilized by the substrate and support a protected edge state. The edge state has a mean free path that is greater than 50 microns, 5000 times greater than the bulk states and involves a theoretically unexpected Majorana-like zero-energy non-degenerate quasiparticle that does not produce a Hall voltage. In seamless integrated structures, the edge state forms a zero-energy one-dimensional ballistic network with essentially dissipationless nodes at ribbon-ribbon junctions. Seamless device structures offer a variety of switching possibilities including quantum coherent devices at low temperatures. This makes epigraphene a technologically viable graphene nanoelectronics platform that has the potential to succeed silicon nanoelectronics.

Experimental Determination of the Energy per Particle in Partially Filled Landau Levels

We describe an experimental technique to measure the chemical potential μ in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of μ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating μ over filling factor ν, we obtain the ground state energy per particle, which can be directly compared to numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, a comparison between experimental and numerical data suggests the importance of valley anisotropic interactions and reveals a possible presence of valley-textured electron solids near odd filling.

Analysing quantized resistance behaviour in graphene Corbino p-n junction devices

Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 μA to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at the ν = 2 plateau (R H ≈ 12906 Ω) and agree with numerical simulations performed with the LTspice circuit simulator. The formulae describing experimental and simulated data are empirically derived for generalized placement of up to three current terminals and accurately reflects observed partial edge channel cancellation. These results support the use of ultraviolet lithography as a way to scale up graphene-based devices with suitably narrow junctions that could be applied in a variety of subfields.

Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy

Circular-polarization-resolved magneto-infrared studies of multilayer epitaxial graphene (MEG) are performed using tunable quantum cascade lasers in high magnetic fields up to 17.5 T. Landau level (LL) transitions in the monolayer and bilayer graphene inclusions of MEG are resolved, and considerable electron-hole asymmetry is observed in the extracted electronic band structure. For monolayer graphene, a four-fold splitting of the n = 0 to n = 1 LL transition is evidenced and attributed to the lifting of the valley and spin degeneracy of the zeroth LL and the broken electron-hole symmetry. The magnetic field dependence of the splitting further reveals its possible mechanisms. The best fit to experimental data yields effective g-factors, g_VS^* = 6.7 and g_ZS^* = 4.8, for the valley and Zeeman splittings, respectively.

High-Quality Magnetotransport in Graphene Using the Edge-Free Corbino Geometry

We report fabrication of graphene devices in a Corbino geometry consisting of concentric circular electrodes with no physical edge connecting the inner and outer electrodes. High device mobility is realized using boron nitride encapsulation together with a dual-graphite gate structure. Bulk conductance measurement in the quantum Hall effect (QHE) regime outperforms previously reported Hall bar measurements, with improved resolution observed for both the integer and fractional QHE states. We identify apparent phase transitions in the fractional sequence in both the lowest and first excited Landau levels (LLs) and observe features consistent with electron solid phases in higher LLs.

Quantitative Transport Measurements of Fractional Quantum Hall Energy Gaps in Edgeless Graphene Devices

Owing to their wide tunability, multiple internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Here, we report FQH thermal activation gap measurements in dual graphite-gated monolayer graphene devices fabricated in an edgeless Corbino geometry. In devices with substrate-induced sublattice splitting, we find a tunable crossover between single- and multicomponent FQH states in the zero energy Landau level. Activation gaps in the single-component regime show excellent agreement with numerical calculations using a single broadening parameter Γ≈7.2  K. In the first excited Landau level, in contrast, FQH gaps are strongly influenced by Landau level mixing, and we observe an unexpected valley-ordered state at integer filling ν=-4.

Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene

Competition between liquid and solid states in two-dimensional electron systems is an intriguing problem in condensed matter physics. We have investigated competing Wigner crystal and fractional quantum Hall (FQH) liquid phases in atomically thin suspended graphene devices in Corbino geometry. Low-temperature magnetoconductance and transconductance measurements along with IV characteristics all indicate strong charge density dependent modulation of electron transport. Our results show unconventional FQH phases which do not fit the standard Jain's series for conventional FQH states, instead they appear to originate from residual interactions of composite fermions in partially filled Landau levels. Also at very low charge density with filling factors [Formula: see text], electrons crystallize into an ordered Wigner solid which eventually transforms into an incompressible Hall liquid at filling factors around ν ≤ 1/7. Building on the unique Corbino sample structure, our experiments pave the way for enhanced understanding of the ordered phases of interacting electrons.

Thermal Transport Signatures of Broken-Symmetry Phases in Graphene

In the half filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end, we calculate the spectrum of spin and valley waves in the ν=0 quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields, it is possible to determine the nature of the symmetry breaking. Temperature-dependent measurements may yield additional information about gapped modes.

Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

Magnetoresistance in two-component systems

Two-component systems with equal concentrations of electrons and holes exhibit nonsaturating, linear magnetoresistance in classically strong magnetic fields. The effect is predicted to occur in finite-size samples at charge neutrality due to recombination. The phenomenon originates in the excess quasiparticle density developing near the edges of the sample due to the compensated Hall effect. The size of the boundary region is of the order of the electron-hole recombination length that is inversely proportional to the magnetic field. In narrow samples and at strong enough magnetic fields, the boundary region dominates over the bulk leading to linear magnetoresistance. Our results are relevant for two-and three-dimensional semimetals and narrow band semiconductors including most of the topological insulators.

Charge and spin transport in edge channels of a ν=0 quantum Hall system on the surface of topological insulators

Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor ν=0 under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate energy spectra of surface Weyl fermions in the ν=0 QHE and find that gapped edge states with helical spin structure are formed from Weyl fermions on the side surfaces under certain conditions. These edge channels account for the nonlocal charge transport in the ν=0 QHE which is observed in a recent experiment on (Bi_{1-x}Sb_{x})_{2}Te_{3} films. The edge channels also support spin transport due to the spin-momentum locking. We propose an experimental setup to observe various spintronics functions such as spin transport and spin conversion.

Magnetoconductance of the Corbino disk in graphene: chiral tunneling and quantum interference in the bilayer case

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, using the mode-matching method to give an effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Rycerz 2010 Phys. Rev. B 81 121404; Katsnelson 2010 Europhys. Lett. 89 17001), conductance at the Dirac point shows oscillations with the flux piercing the disk area ΦD characterized by the period Φ(0) = 2 (h/e) ln(R(o)/R(i)), where R(o)(R(i)) is the outer (inner) disk radius. The oscillation magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations being R(o)/R(i) ≃ [ Rit⊥/(2ℏvF) ](4/p) (for R(o)/R(i) ≫ 1), where t⊥ is the interlayer hopping integral, vF is the Fermi velocity in graphene, and p is an even integer. Odd-integer values of p correspond to vanishing oscillations for the normal Corbino setup, or to oscillation frequency doubling for the Andreev-Corbino setup. At higher Landau levels, magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in a two-dimensional electron gas is also provided in order to illustrate the role of chiral tunneling in graphene.

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

Splitting of the zero-energy Landau level and universal dissipative conductivity at critical points in disordered graphene

We report on robust features of the longitudinal conductivity (σ(xx)) of the graphene zero-energy Landau level in the presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both σ(xx) and Hall σ(xy)). As long as valley degeneracy is maintained, the obtained critical conductivity σ(xx) =/~ 1.4e(2)/h is robust upon an increase in disorder (by almost 1 order of magnitude) and magnetic fields ranging from about 2 to 200 T. When the sublattice symmetry is broken, σ(xx) eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a σ(xy) = 0 plateau) change to σ(xx) =/~ e(2)/h, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the nondissipative nature of the quantum Hall effect in disordered graphene in the presence of Landau level splitting.

Quantized Casimir force

We investigate the Casimir effect between two-dimensional electron systems driven to the quantum Hall regime by a strong perpendicular magnetic field. In the large-separation (d) limit where retardation effects are essential, we find (i) that the Casimir force is quantized in units of 3ħcα(2)/8π(2)d(4) and (ii) that the force is repulsive for mirrors with the same type of carrier and attractive for mirrors with opposite types of carrier. The sign of the Casimir force is therefore electrically tunable in ambipolar materials such as graphene. The Casimir force is suppressed when one mirror is a charge-neutral graphene system in a filling factor ν=0 quantum Hall state.

Dipole-interaction-mediated laser cooling of polar molecules to ultracold temperatures

We present a method to design a finite decay rate for excited rotational states in polar molecules. The setup is based on a hybrid system of polar molecules with atoms driven into a Rydberg state. The atoms and molecules are coupled via the strong dipolar exchange interaction between two rotation levels of the polar molecule and two Rydberg states. Such a controllable decay rate opens the way to optically pump the hyperfine levels of polar molecules and it enables the application of conventional laser cooling techniques for cooling polar molecules into quantum degeneracy.