Interaction Effects on Electric and Thermoelectric Transport in Graphene

Electron-electron (e-e) interactions in 2-dimensional electron gases (2DEGs) can lead to many-body correlated states such as the the fractional quantum Hall effect (FQHE), where the Hall conductance quantization appears at fractional filling factors. The experimental discovery of an anomalous integer quantum Hall effect in graphene has faciliated the study of the interacting electrons which behave like massless chiral fermions. However, the observation of correlated electron physics in graphene is mostly hindered by strong electron scattering caused by charge impurities. We fabricate devices, in which, electrically contacted and electrostatically gated graphene samples are either suspended over a SiO₂ substrate or deposited on a hexagonal boron nitride layer, so that a drastic suppression of disorder is achieved. The mobility of our graphene samples exceeds 100,000 cm²/Vs. This very high mobility allows us to observe previously inaccessible quantum limited transport phenomena. In this thesis, we first present the transport measurements of ultraclean, suspended two-terminal graphene (chapter 3), where we observe the Fractional quantum Hall effect (FQHE) corresponding to filling fraction ν=1/3 FQHE state, hereby supporting the existence of interaction induced correlated electron states. In addition, we show that at low carrier densities graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields. Since the quantitative characterization of the observed FQHE states such as the FQHE energy gap is not straight-forward in a two-terminal measurement, we have employed the four-probe measuremt in chapter 4. We report on the multi-terminal measurement of integer quantum Hall effect(IQHE) and fractional quantum Hall effect (FQHE) states in ultraclean suspended graphene samples in low density regime. Filling factors corresponding to fully developed IQHE states, including the ν±1 broken-symmetry states and the ν=1/3 FQHE state are observed. The energy gap of the 1/3 FQHE, measured by its temperature-dependent activation, is found to be much larger than the corresponding state found in the 2DEGs of high-quality GaAs heterostructures, indicating that stronger e-e interactions are present in graphene relative to 2DEGs. In chapter 5, we investigate the e-e correlations in graphene deposited on hexagonal boron nitride using the thermopower measurements. Our results show that at high temperatures the measured thermopower deviates from the generally accepted Mott's formula and that this deviation increases for samples with higher mobility. We quantify this deviation using the Boltzmann transport theory. We consider different scattering mechanisms in the system, including the electron-electron scattering. In the last chapter, we present the magnetothermopower measurements of high quality graphene on hexagonal boron nitride, where we observe the quantized thermopower at intermediate fields. We also see deviations from the Mott's formula for samples with low disorder, where the interaction effects come into play . In addition, the symmetry broken quantum Hall states due to strong electron-electron interactions appear at higher fields, whose effect are clearly observed in the measured in mangeto-thermopower. We discuss the predicted peak values of the thermopower corresponding to these states by thermodynamic arguments and compare it with our experimental results. We also present the sample fabrication methods in chapter 2. Here, we first explain the fabrication of the two-terminal and multi-terminal suspended graphene and the current annealing technique used to clean these samples. Then, we illustrate the fabrication of graphene on hexagonal boron nitride as well as encapsulated graphene samples with edge contacts. In addition, the thermopower measurement technique is presented in Appendix A, in which, we explain the temperature calibration, DC and AC measurement techniques

Enhanced Thermoelectric Power in Graphene: Violation of the Mott Relation By Inelastic Scattering

We report the enhancement of the thermoelectric power (TEP) in graphene with extremely low disorder. At high temperature we observe that the TEP is substantially larger than the prediction of the Mott relation, approaching to the hydrodynamic limit due to strong inelastic scattering among the charge carriers. However, closer to room temperature the inelastic carrier-optical-phonon scattering becomes more significant and limits the TEP below the hydrodynamic prediction. We support our observation by employing a Boltzmann theory incorporating disorder, electron interactions, and optical phonons.Comment: 5 pages, 4 figure

Magnetoresistance measurements of Graphene at the Charge Neutrality Point

We report on transport measurements of the insulating state that forms at the charge neutrality point of graphene in a magnetic field. Using both conventional two-terminal measurements, sensitive to bulk and edge conductance, and Corbino measurements, sensitive only to the bulk conductance, we observed a vanishing conductance with increasing magnetic fields. By examining the resistance changes of this insulating state with varying perpendicular and in-plane fields, we probe the spin-active components of the excitations in total fields of up to 45 Tesla. Our results indicate that \nu=0 quantum Hall state in single layer graphene is not spin polarized

Interaction Driven Quantum Hall Wedding cake-like Structures in Graphene Quantum Dots

Quantum-relativistic matter is ubiquitous in nature; however it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a table-top prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we provide a spatial visualization of the interplay between spatial and magnetic confinement in a circular graphene resonator. We directly observe the development of a multi-tiered "wedding cake"-like structure of concentric regions of compressible/incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can therefore yield insights into the behaviour of quantum-relativistic matter under extreme conditions

Frank–van der Merwe Growth versus Volmer–Weber Growth in Successive Stacking of a Few-Layer Bi2Te3/Sb2Te3 by van der Waals Heteroepitaxy: The Critical Roles of Finite Lattice-Mismatch with Seed Substrates

1133Ysciescopu

Interaction-driven quantum Hall wedding cake–like structures in graphene quantum dots

Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels. We directly observe the development of a “wedding cake”–like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.United States. National Science Foundation. STC Center for Integrated Quantum Materials (Award 1231319)United States. Army Research Office. Institute for Soldier Nanotechnologies (Contract W911NF-13-D-0001

An On/Off Berry Phase Switch in Circular Graphene Resonators

The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wavefunction may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry-phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a small critical magnetic field is reached. This behavior results from turning on a $\pi$-Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 mT, potentially enabling a variety of optoelectronic graphene device applications

Observation of the Fractional Quantum Hall Effect in Graphene

When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields