Transport Studies of the Topological States in Bernal-stacked Bilayer Graphene
Restricted (Penn State Only)
- Author:
- Huang, Ke
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 30, 2024
- Committee Members:
- Venkatraman Gopalan, Outside Unit & Field Member
Jainendra Jain, Major Field Member
Nitin Samarth, Major Field Member
Jun Zhu, Chair & Dissertation Advisor
Mauricio Terrones, Program Head/Chair - Keywords:
- Bernal-stacked bilayer graphene
Quantum Hall effect
Fractional quantum Hall effect
Quantum valley Hall kink state - Abstract:
- In condensed matter systems, the interplay of topology, strong correlation, and internal electronic degrees of freedom often gives rise to exciting emergent quantum phenomena. Bernal-stacked bilayer graphene (BLG) is an excellent platform to study such physics owing to its high sample quality and wide device tunability. In this dissertation, we made advances in the electrical transport study of the quantum Hall effect (QHE) and quantum valley Hall effect (QVHE) in BLG. These findings are enabled by the fabrication of state-of-the-art BLG devices with low disorder, high-quality ohmic contacts, and complex device structures achieved using precision lithography. This dissertation contains two main topics, namely the QHE and QVHE in BLG, and is divided into six chapters. Chapter 1 is an introduction to BLG and the QHE. Chapters 2 and 3 present our work in fractional and integer QHE in Bernal BLG and Chapter 4 presents the fractal QHE in a BLG/hBN moiré superlattice. Chapter 5 introduces the QVHE in BLG. Our experimental results are presented in Chapter 6. Owing to the spin, valley, and orbital degeneracy, the E = 0 Landau level (LL) of bilayer graphene is a rich playground to explore many-body physics and construct novel multicomponent states. Furthermore, the valley degree of freedom in BLG can be tuned electrically by a perpendicular displacement field (D-field), offering a powerful knob to control the characters of the LLs and enable unprecedented tuning of the valley Zeeman splitting in ways impossible to achieve for the real electron spin. In Chapter 1, we introduce the electronic structure of BLG and the integer and fractional QHE. In Chapter 2, we study the fractional quantum Hall effect (FQHE) in the E = 0 LL. Devices with high-quality ohmic contacts and low disorder are fabricated, allowing us to probe regimes obscured by disorder in previous studies. Four main findings are described. (1) We constructed an experimental phase diagram of the valley isospin polarization transitions for the Jain sequence FQH states near filling factor ν = 3/2. The results are well explained by the free composite fermion theory with a two-component spin/isospin, thus establishing the SU(2) nature of the valley isospin in BLG. (2) We observed a new even-denominator FQH state in BLG at ν = 5/2. The ground state of the even-denominator FQH states is proposed to be the Moore-Read (MR) state, the excitations of which are non-Abelian anyons fundamental to topological quantum computing. Two important properties are predicted for the MR state: spontaneous spin/isospin polarization and broken particle-hole symmetry. Here, we examined them in the even-denominator FQH states in BLG. First, we show that the ν = 5/2 is spontaneously valley isospin polarized in the limit of vanishing valley Zeeman splitting, in accord with the theoretical predictions. Second, flanking the even-denominator states at ν = 3/2, 7/2, and -1/2 appear the Levin-Halperin daughter states of the MR Pfaffian, whereas the daughter states of the MR anti-Pfaffian appear near ν = -5/2. These results explicitly demonstrate the broken particle-hole symmetry of the even-denominator states in BLG. These findings contribute fresh insights to an ongoing discussion of this fundamental topic. (3) The N = 1 LL in bilayer graphene is an admixture of the n = 0 and n = 1 wave functions in GaAs and the weight of the n = 0 component grows with increasing magnetic field. BLG exhibits odd-denominator FQH states on the N = 1 LL, the nature of which remains unclear. The ν = 2/5 and 3/7 states are predicted to undergo a phase transition from a non-Abelian state at low magnetic fields to an Abelian state at high fields. We experimentally investigated the magnetic field evolution of the 2/5 state. Our measurements suggest that substantial interaction change occurs near 28 T but evidence of a field-driven phase transition remains unclear. (4) We observed the appearance of hetero-orbital two-component FQH states at the crossing of the N = 0 and 1 LLs. Two-component states of dissimilar orbital wave functions have not been observed in previous experiments. Our measurements of the hetero-orbital two-component states reveal a number of characteristics different from previous homo-orbital two-component states. Exact diagonalization calculations performed by collaborators (Ajit C. Balram and Jainendra K. Jain) highlight the importance of the underpinning anisotropic interactions. Results included in this chapter are reported in Huang et al, PRX 12, 031019 (2022) and Huang et al, manuscript in preparation (2024). In Chapter 3, we studied the profound impact of the Coulomb interaction on the broken-symmetry IQH states in BLG in ultra-clean samples. We first constructed a phase diagram for filling factor ν = 2 as a function of the D- and B-fields. Our results show that it is spontaneously valley polarized at B-fields less than 12 T and exhibits orbital/valley polarized phases at low/high D-field respectively for B > 12 T. We then measured the D- and B- dependence of the energy gaps at ν = 1, 2, and 3. The gap of the orbital polarized ν = 2 state at low D is about 2 - 3 times larger than that of the valley polarized state at high D. The ν = 1 state exhibits the largest gap (Δ1) compared to both phases of the ν = 2. The ν = 3 gap, Δ3, linearly depends on D in the small D-region, whereas both Δ1 and Δ2 are D-independent. These measurements are very different from the predictions of a single-particle-like LL diagram and previous results obtained in lower-quality devices. They highlight the strong impact of Coulomb interactions. Possible explanations for their gap size and B- and D-dependence are discussed. Results included in this chapter are reported in Khana et al, PRB (Letter), 108, L041107 (2023) (in collaboration with Shimshon group) and Guo et al, manuscript in preparation (2024). In Chapter 4, we present our preliminary study in a BLG/hBN (hexagonal boron nitride) moiré superlattice, where the physics of the Hofstadter’s butterfly and fractional Chern insulator takes place. We observed the integer and fractional QHE, Chern insulator and symmetry-breaking Chern insulator states, and fractional Chern insulator states in our device. We studied the D-field dependence of these states and explore potential topological phase transitions among different states. In Chapter 5, we introduce the QVH kink state in BLG, a helical topological edge state system induced by the bulk gap inversion at an internal domain boundary. The kink state includes four pairs of valley-momentum-locked edge modes. A dual-split-gate device structure is adapted to realize the kink state. Fabrication details of the device are given in detail. Two generations of devices have been made by former members of our group. The existence of the kink state and its valleytronics applications such as waveguide, valve, and beam splitter have been demonstrated. In this dissertation, we fabricated the third-generation devices, where higher quality is achieved. Chapter 6 describes four major results obtained in such devices. (1) We achieved robust resistance quantization of the kink states at zero magnetic field. The quantization remains nearly temperature-independent up to tens of Kelven. We realized a topological switch, the underlying mechanism of which is an electric-field-induced topological phase transition. (2) We demonstrated the complete lifting of the four-fold degeneracy of the kink state by applying a magnetic field and tuning the D-field. We are able to obtain a single pair of spin/valley-momentum locked counter-propagating edge modes inside the junction. This is a promising platform to pursue topological superconductivity. (3) We studied the impact of the device geometry on the properties of the kink state. Measurements on wide junctions with misaligned split gates are described. Resistance variation of hundreds of ohms, away from the expected h/4e2 plateau are observed. These variations may originate from the backscattering induced by the band structure in wide and misaligned split gates. Insights gained from the results are discussed. (4) We present our effort to couple the kink state to a NbSe2 thin flake, which is an s-wave superconductor. Preliminary results are presented. Results of this chapter are published in Huang et al, Science (accepted) (2024) and Huang et al, manuscript in preparation (2024).