Direct observation of a magnetic field-induced Wigner crystal

Like solids which composed of ions, the electrons can also spontaneously form a crystalline phase, driven by their strong interactions. This amazing electron solid is predicted first by Eugene Wigner in 1934, now termed Wigner crystal (WC), and has been under intensive investigation over the past few decades, primarily in 2D electron gas systems with macroscopic probes (transport and spectroscopy etc).

Using scanning tunneling microscopy (STM), I directly image a magnetic field-induced electron WC in Bernal-stacked bilayer graphene (BLG). This is the first time such a quantum crystal is imaged and its microscopic details captured. The WC lattice symmetry, lattice constant are all checked to follow the prediction. A lot of interesting aspects of the WC are also discussed: competition with FQH states; the strongly interacting liquid phase; high temperature melting; observation of an unexpected stripe phase; and its quantum crystak nature etc. 

This study demonstrates that STM can be readily employed to inspect many other electron solids, such as skyrme crystal and bubble phases. 

Check out details here

Local tunneling spectroscopy of Fractional Quantum Hall states

and their energy gaps

At partial fillings of a flat Landau level, the electron interactions drives new incompressible states, Fractional quantum Hall (FQH) states, with their Hall conductivity quantized at simple fractions of a quantum conductance. FQH states host new low energy excitation, which is neither Fermion nor Boson, but a unique type that only lives in two dimension - anyon, with fractionalized charge and exchange statistics. Among them, even-denominator FQH states are of particular interests as they potentially host non-abelian anyons, promising for fault-tolerant quantum computing.

Using scanning tunneling spectroscopy (STS), I study the FQH states in the lowest Landau levels of Bernal stacked bilayer graphene (BLG) and identify incompressible gap features related to both odd- and even-denominator FQH states. The sharpe tunneling resonances at the FQH states are signature of probing the bound states of anyons. This also provides the most faithful measure of the large energy gaps of FQH states, in particular the non-abelian candidates which is about 5 times larger then its counterpart in GaAs. 

Preprint

Strongly interacting Hofstadter states in MATBG

Moiré quantum materials, composed of rotated 2d atomic layers, are emerging flat band platforms to study the physics of correlation and topology. Unlike the flat Landau level, the moiré lattice potential, modulating on an length scale comparable to the magnetic length (13 nm at 4 T) , plays an significant role and leads to the famous fractal energy spectrum, known as the Hofstadter butterfly. The non-interacting Hofstadter spectrum and its associated topological states are widely explored, yet little is known of the emergent charge density waves (CDW) and fractionalized states in its strong interacting limit. Magic-angle twisted bilayer graphene (MATBG) is a benchmark system with flat electronic bands at zero magnetic field, thus allows access to the strongly interacting Hofstadter states at a comparatively small magnetic fields. 

Using quantum transport measurements, I explore the interacting Hofstadter states in the state-of-art MATBG sample. I uncover a remarkable cascade sequence of symmetry-broken Chern insulator (SBCI) states (the CDWs), which is also captured by our self-consistent Hartree-Fock calculations. I also observe a series of Jain-sequence FQH states, however with a unconventional phase transition towards a dissipative Fermi liquid at a higher magnetic field. We propose that the FQH states in MATBG can be better understood as in-field fractional Chern insulators (in-field FCI), due to its nontrivial quantum geometry properties.

Preprint

Electron correlation and topology in twisted graphene multilayers

The flat bands are ubiquitous feature of moiré quantum materials beyond MATBG. I also study a variety of correlated insulating states, orbital magnetic states, and interacting Hofstadter states in the twisted graphene multilayers using quantum transport measurements, including those in:

Twisted monolayer-bilayer graphene (tMBG, 1+2) ;

Twisted double bilayer graphene (tDBG, 2+2). 

The phase diagrams of these systems are notably different from that of MATBG, primarily due to the broken C2T symmetry thus the existence of isolated flat Chern bands, sometimes with high Chern number. The flavor symmetry breaking at integer fillings are different and they can be more tunably using displacement field. These are promising platforms to design and engineer correlated and topological states at zero magnetic field.

See details here:  tDBG (1, 2); tMBG (1, 2).

My general exam's talk at UW