Graphene, a single atomic layer of carbon atoms, has been extensively studied in recent years. Its unique electronic property has attracted the attention of physicists in both theoretical and experimental areas. To experimentally study the electronic transport property of graphene devices, we acquire high mobility in suspended graphene devices fabricated by sophisticated techniques. My research focused on studying electronic transport property of few layer graphene, including bilayer, trilayer and tetralayer graphene devices, as well as heterojunctions that consist of regions with different number of layers.

In the first part of the dissertation, two types of techniques in fabrication are described -- the lithography free shadow mask method and the multi-level lithography technique developed from the fabrication protocols of suspended top gates. These free-standing devices eliminates substrates that are often the mobility bottleneck, and allow current annealing to remove contaminants, thus providing a platform for experimental realization of many fascinating phenomena in high mobility devices, such as fractional quantum Hall effect.

The second part of the dissertation focuses on experimental study of few layer graphene devices. Evidence for fractional quantum Hall effect is observed in bilayer and trilayer graphene. For heterojunction devices, both magnetic field and electrical field are applied to study the electrical transport properties in quantum Hall regime. Heterojunction trends to behave like the thinner layer graphene in quantum Hall regime. In one bilayer-trilayer heterojunction, we find an apparent transition from the nematic state to a gapped state that resembles the layer antiferromagnetic state induced by current annealing. This shed light on the debate of the ground state at the charge neutrality point in bilayer graphene. In tetralayer graphene, we observed an unusual re-entrant insulating state at the charge neutrality point, which is not predicted by the tight binding model calculations. This phenomenon could arise from Landau level crossing or Moire pattern due to a small relative twist between the layers.

Future work in this area include (1) using in-plane magnetic field effect to probe few layer graphene to determine their dependence on total spin, (2) top-gated heterojunction devices to locally control the carrier density and band structure of the two regions, (3) other layered materials, such as topological insulators and transition metal dichalcogenides. These studies could contribute to both our fundamental understanding of low-dimensional physics and technology applications.

This thesis summarizes our work in the past few years in the field of transport studies of carbon nanotubes and graphene. The first half of the thesis focuses on carbon nanotube (CNT) Josephson junctions (JJ) formed by coupling CNTs to superconducting electrodes. They exhibited Fabry Perot resonance patterns, enhanced differential conductance peaks, multiple Andreev reflection peaks, gate-tunable supercurrent transistor behaviors, hysteretic current-voltage line shape and "superconductor-insulator" transition. The junction behavior can be understood based on the dissipation dynamics and phase diffusion on the model of resistively and capacitively shunted junctions (RCSJ). In addition, we investigated Fano resonance on a particular device. The transport spectroscopy exhibited "inverse" Coulomb blockade structures superimposed on Fabry-Perot resonance patterns, indicating quantum interference between a channel that is well-coupled to the electrodes and another channel that is poorly-coupled channel. Our transport data was reproduced reasonably by the simulation.

The second half of the thesis discusses our results on graphene. Firstly, by developing a technique to fabricate suspended top gates, we were able to fabricate exceedingly clean, high quality graphene pnp junctions. In the high magnetic fields, we observed quantum hall plateaus at fractional values, which arise from edge state propagation and equilibration in regions with different filling factors, in agreement with the theoretical predictions. In zero magnetic fields, we observed Fabry-Perot conductance oscillations in the bipolar regime, demonstrating the high quality of our devices. Secondly, we explored specular Andreev reflection and have observed conductance peaks at the superconducting energy gap in normal metal - graphene - superconductor (NS) junctions. However, the intended goal of the project, observation of specular Andreev reflection, was not achieved. As significant progress has been made towards fabrication of high quality suspended devices, we expect that specular Andreev reflection could be observed in the near future.

Two-dimensional (2D) materials are ones that are only single to a few atomic layers in thickness, and exhibit novel material properties not found in their three-dimensional counterparts. The research of 2D materials starts to take off after the isolation and transport measurements of graphene in 2004. Graphene has a unique dispersion relation and unprecedented material properties such as extreme mechanical strength, high thermal conductivity, and exceedingly high charge carrier mobility. The first part of this thesis describes the fabrication and transport measurements of suspended twisted bilayer graphene devices.

The second part of this dissertation focuses on 2D molybdenum disulfide (MoS2), which, unlike graphene, has a band gap. However, its low mobility severely restricted the applications of MoS2 and the mechanism for mobility bottleneck is unclear. To investigate the role played by substrates, we fabricate suspended MoS2 field effect transistor devices and develop an effective gas annealing technique that significantly improves device quality and increases conductance by 3-4 orders of magnitude. Mobility of the suspended devices ranges from 0.01 to 46 cm2/Vs before annealing, and from 0.5 to 105 cm2/Vs after annealing. Temperature dependence measurements reveal two transport mechanisms: electron-phonon scattering at high temperatures and thermal activation over a gate-tunable barrier height at low temperatures. Our results suggest that transport in these devices is not limited by the substrates, but likely by defects, charge impurities and/or Schottky barriers at the metal-MoS2 interfaces.

Furthermore, we successfully apply ionic liquid for electrolyte gating on suspended MoS2 transistors and achieve very high coupling efficiency, up to 4.4×1013 cm-2V-1. Electrical characterization reveals contact-dominated electrical transport. From the Schottky emission model, the dielectric constant of ionic liquid DEME-TFSI is estimated to be ~11. Comparison between ionic liquid gating of substrate-supported and suspended devices also demonstrates far higher doping efficiency and better screening of charge impurities as well as Schottky barriers.

Recently, the realization of one-dimensional electrical contacts to hexagonal-boron nitride-encapsulated samples points a direction for transport studies of 2D materials. For instance, such MoS2 devices with graphene contacts have demonstrated unprecedented mobility. Furthermore, heterostructures consisting of various 2D atomic layers may be built to create artificial superlattices, thus enable the exploration of novel phenomena and devices with new functionalities.

Compared with traditional semiconductor materials, graphene has unparalleled advantages on mobility, thermal conductivity, mechanical strength and so on. Thus it was considered as a promising candidate material for the future semiconductor industry. However, since its band structure is gapless, band gap engineering has become a significant task for scientists. My dissertation focuses on chemical and physical modification methods that could pave the way to applications of graphene based devices and reveal a number of interesting phenomena.

The critical roadblock for graphene electronics is the absence of a band gap. We first focus on chemical functionalization of graphene as a route to band gap engineering. This is first achieved via grafting nitrophenyl groups onto single layer graphene sheets. The functionalized graphene samples behave like semiconductors. Substrate supported and suspended samples demonstrate transport gaps as large as ~0.1eV and ~1eV, respectively. Secondly, we developed a different chemical functionalization approach based on organometallic chemistry. Apart from behaving like semiconductors, functionalized samples also retains the high mobility of the pristine state.

The second part of the thesis focuses on physical modifications of graphene a. Suspended graphene-based switch was developed using a special pulsing breakdown technique. Voltage pulses of 2.5V~4V and 8V can turn a switch device to ON (high conductance) state and OFF (low conductance) state, respectively. We provide experimental evidence that these behaviors arise from motions of atomic-scale carbon chains and reformation of chemical bonds.

Finally, strain engineering is another approach for modifying transport properties of graphene. We proposed and developed novel nano-electromechanical system (NEMS)-like devices that allows in situ modulation of strain on suspended graphene flakes, which in turn induces interesting changes in both transport and morphological properties of graphene.

In summary, this dissertation presents our studies on chemical and physical modification approaches of graphene samples, and related novel phenomena that emerge amid these devices, with implications on next generation electronic devices.

Graphene, a two-dimensional honeycomb lattice of carbon atoms, has become the hottest platform for condensed matter physics and a promising next generation electronic material. The band structures of single-, bi- and tri-layer graphene differ dramatically, yet all host chiral charge carriers with competing symmetries (such as spin, valley and orbital) that may be broken spontaneously or by an external field. In this thesis we present comprehensive transport studies on double-gated single-, bi- and tri-layer graphene, which lead to further insight into single particle and many-body physics in this fascinating 2D system.

A prevailing motif in these studies was the use of suspended structures with the aim to eliminate extrinsic factors such as disorder, which obscure intrinsic physical phenomena. Our efforts were most successful with dual gated suspended bilayer graphene where an unprecedented sample quality was achieved.

These studies are discussed in chapters six through nine. First, we focus on the observation of a spontaneous zero conductance gap at the charge neutrality point with zero out of plane electric and magnetic fields. By applying fields this gap can be closed with an electric field of either polarity, and grows monotonically with increasing magnetic field. These findings provide insight into the underlying symmetries of this correlated electron phenomena.

Secondly, we performed a systematic study using several devices of the minimum conductivity at charge neutrality. These devices fall into one group with finite, and another with zero minimum conductivity. Because the second group consists of only high quality samples we surmise this insulating state is intrinsic. By tuning temperature we found this gapped insulating state has a critical temperature suggesting a phase transition between insulating and conducting states. Additionally, the transition is tuned by disorder, out-of-plane electric field, or carrier density, suggesting a quantum phase transition.

Lastly, we study broken symmetry QH states at finite carrier density in the presence of zero and finite out of plane electric field. We find minute electric fields, which are commonly induced in single gated samples, significantly affect the broken symmetry states. Hence this study with zero electric field is the first genuine measurement of these states.

The study of two-dimensional (2D) materials began with the seminal work of experimental isolation and fabrication of monolayer graphene field-effect transistors by the Manchester group in 2004, and has remained one of the frontiers of condensed matter physics ever since. Mono- and few-layer graphene, which host chiral charge carriers with competing symmetries (valley, spin and orbital), have proved to be fascinating platforms for investigating the quantum Hall (QH) physics. Research efforts were soon extended to other 2D materials such as transition metal dicalcogenides (TMD). One such material is phosphorene (mono- or few-layer black phosphorous), which has attracted much attention due to its large direct band gap and high mobility. This thesis describes our comprehensive transport studies of bi- and tetra-layer graphene, as well as few-layer phosphorene (FLP).

By fabricating devices that are either suspended or encapsulated within hexagonal boron nitride (hBN) layers, we are able to reduce disorders and achieve high quality devices. In suspended bilayer graphene (BLG) devices, we observe both integer and fractional QH states. The interplay between symmetries and electric and magnetic fields gives rise to two distinct phases of the QH state at filling factor $\nu$ = 1, with different pseudospin and real spin polarizations, and different energy gaps. Moreover, the $\nu$ = 2/3 fractional QH state and a feature at $\nu$ = 1/2 are only resolved at finite electric field and large magnetic field. These findings provide insight into the competing symmetries in BLG.

We also present our transport studies of hBN-encapsulated tetralayer graphene devices, of which the band structure can be decomposed into two BLG-like bands. Unlike mono-, bi- and tri-layer graphene, which display sharp resistance peaks at the charge neutrality point (CNP), we observe a local resistance minimum at the CNP, flanked by three resistance peaks at higher charge densities. Such non-monotonic dependence on density is attributed to the trigonal warping that induces Lifshitz transitions as a function of charge density and electric field. In the QH regime, we observe rich Landau level (LL) crossing patterns between the two BLG-like bands. A perpendicular electric field breaks the inversion symmetry of tetralayer graphene, lifting the valley degeneracy of the LLs. By fitting the calculated LL spectra to the crossing features in our experimental data, we are able to obtain the values of hopping parameters and determine the symmetries of the LLs. These works provide us with the insight of the band structure of tetralayer graphene, the effects of remote hopping terms, as well as the importance of the interplay between competing symmetries and applied electric and magnetic fields.

Finally, in hBN-encapsulated FLP devices, we report the observations of weak localization (WL), from which the dephasing lengths could be extracted to be $\sim 30-100$ nm, and exhibit power-law dependences on temperature and charge density. We conclude that the dominant source of phase-relaxation is the electron-electron interactions, shedding light onto the understanding of the scattering mechanisms in FLP devices at low temperatures.

The studies of 2D materials constitute one of the most active frontiers of condensed matter research. Our results provide insight into the quantum transport properties of the 2D electron gas (2DEG) systems in Bernal-stacked bi- and tetra-layer graphene and FLP devices. The techniques of fabricating high quality devices enable us to explore other 2D materials as well. Novel physical phenomena such as the QH effect in few-layer graphene with other stacking orders, $e.g.$ rhombohedral-stacking order, need further experimental studies. The integer and fractional QH effect in FLP devices await further explorations as well.

Novel two-dimensional materials with weak interlayer Van der Waals interaction are fantastic platforms to study novel physical phenomena. This thesis describes our investigation on two different Van der Waals materials: graphene and bismuth selenide with calcium doping (CaxBi2-xSe3, x as the doping level) in the topological insulator family. Firstly, we characterize the electrical transport behaviors of high-quality substrate-supported bilayer graphene devices with suspended metal gates. The device exhibits a transport gap induced by external electric field with an on/off ratio of 20,000, which could be explained by variable range hoping between localized states or disordered charge puddles. At large magnetic field, the device presents quantum Hall plateau at fractional values of conductance quantum, which arises from the equilibration of edge states between differentially doped regions. Secondly, we present our study on the electronic transport of CaxBi2-xSe3 thin films, which are three-dimensional topological insulators and coupled with superconducting leads. In these novel Josephson transistors, we observe different characteristic features by energy dispersion spectrum (EDS) and Raman spectroscopy, and the weak suppression in the critical current Ic. Thirdly, we explore the thermal expansion of suspended graphene. By in-situ scanning electron microscope (SEM), we measure the thickness-dependence of graphene's negative thermal expansion coefficient (TEC). We propose that there is a competitive relation between the intrinsic TEC and the friction from the substrate and the graphene. Lastly, in collaboration with Dr. Nikolai Kalugin from New Mexico Tech., we explore the graphene's application as a quantum Hall effect infrared photodetector. This graphene-based detector can be operated at higher temperature (liquid nitrogen) and wider frequency than the previous implementations of quantum Hall detector.

Since the discovery of graphene, two-dimensional (2D) van der Waals materials research has flourished, with new crystals and novel phenomena discovered at a rapid pace. In 2014, black phosphorus (BP) was rediscovered as a member of 2D materials, displaying high quality electronic transport with in-plane anisotropy, though the first generation of layered devices suffered from poor stability and relatively low mobility. In this thesis, we overcome these challenges by employing van der Waals assembly techniques to create BP devices sandwiched between thin hexagonal boron nitride layers. These devices are air-stable, for more than two weeks, and boast mobility up to 500 cm2V-1s-1 at room temperature and 4,000 cm2V-1s-1 at low temperature. Using two-point and four-point geometries with global and local gates, we observe Shubnikov de Haas oscillations that yield effective mass of holes ~0.25 me to 0.31 me, where me is the mass of the electron. From weak localization measurements, we obtain phase relaxation length of ~30 nm to 100 nm. Moreover, we determine mobility bottleneck and transport mechanism from temperature dependence measurements: when the device is highly hole doped, the mobility µ exhibits power law dependence on temperature T, µ ~ T0.6, suggesting that it is limited by charged impurity scattering; close to the band edge, conduction is dominated by variable range hopping, with estimated localization length ~ 1.7 nm – 30 nm. The studies presented here contributed to our understanding of electronic properties of atomically thin BP, and will help to guide future efforts in fabrication, exploring, and engineering devices based on 2D semiconductors.

Graphene is a two-dimensional honeycomb lattice of carbon atoms. Since it is experimentally isolated in 2004, this 2D system becomes the prevailing platform for condensed matter physics. The band structures of single, bilayer and trilayer graphene differ dramatically. And it can be strongly dependent on stacking order in trilayer grahene. In this dissertation, we present comprehensive transport studies on double-gated trilayer graphene, exciting platform for study of such interplay, where the relative strengths of single particle physics and interaction effects are tunable via external parameters such as gate voltage and magnetic field. I will start with a brief introduction of graphene electron configuration including the density of state, Fermi energy and quantum Hall effect. Next I will discuss the energy band structure of single, bi-, trilayer graphene with the tight binding calculation. In chapter 3, I will describe how dual-gated suspended graphene devices are fabriacted. One of the strong advantages for the suspended structures is to remove the extrinsic factor with post current-annealing technique which can achieve the high quality samples on dual-gated ABA and ABC trilayer graphene. These studies are discussed in chapters five through seven. First, we focus on the observation of quantum Hall effect in ABA trilayer graphene. We demonstrate the symmetry broken states at the lowest Landau level. By applying out-of-plane electric field E⊥, we observe degeneracy breaking and transitions between QH plateaus. Secondly, we study a intrinsic gap of ABC trilayer graphene at the charge neutrality point with zero electric and magnetic fields. This gap can be partially suppressed by an electric field of either polarity and parallel magnetic field. By tuning temperature we found this gapped insulating state has a critical temperature suggesting a phase transition underlying symmetries of this correlated electron phenomena.

Lastly, we discuss broken symmetry quantum Hall states in dual-gated ABC trilayer graphene devices. We observe that the sequence of quantum Hall plateaus depends strongly on the interlayer potential bias and an intriguing "hexagon" pattern, which can be accounted for by a model based on crossings between symmetry-broken LLs reflecting the interplay between single particle remote hopping and interaction-induced symmetry breaking.

Graphene and carbon nanotubes are the two-dimensional and one-dimensional forms of carbon allotropes, respectively, and have been ideal materials for scientific and technological exploration due to their ultra small size and extraordinary physical properties such as high carrier mobility, large thermal conductivity and strong tensile strength. In this thesis, I focus on modifying the properties of graphene and carbon nanotubes, via chemical functionalization, strain, or encapsulation, so that they are better suited for applications.

To create a band gap in the otherwise gapless spectrum of graphene, one common route is chemical functionalization. However, most functionalization methods are invasive and result in degradation in graphene's quality. In contrast, our chemically functionalized graphene using organometallic chemistry behaves as semiconductors with improved on / off ratios, while retaining high mobility.

Application of strain in graphene is another route to tailor transport properties. We developed devices based on nano-electromechanical system (NEMS), which allows us to apply in situ strain in suspended graphene. Changes in contact resistance and mobility have been observed in single- and bi-layer graphene devices.

Apart from graphene, we also focus on carbon nanotube devices. We developed techniques to fabricate carbon nanotube devices encapsulated in hexagonal boron nitride (hBN) with zero-dimensional ohmic contacts. These devices can carry high current density, and Coulomb blockade diamonds with excited state have been observed.

Lastly, we explored a device geometry that combines both graphene and carbon nanotubes, with the goal of studying momentum-conserved tunneling between 1D and 2D systems. We developed techniques to fabricate suspended devices with dual gates, which allow us to observe interesting quantum transport features arising from both portions of graphene and carbon nanotubes. We also proposed hBN-based devices for future studies.