# Research

### Overview

How do material properties change as a result of interactions among electrons, and what is the nature of the new phases that result? What novel physical phenomena and functionality (e.g., symmetry breaking or topological excitations) can be realized by combining materials and device elements to produce emergent behavior? How can we leverage nontraditional measurement techniques to gain new insight into quantum materials? These are some of the overarching questions we seek to address in our research.

We are interested in a variety of quantum systems, especially those composed of two-dimensional flakes and heterostructures. This class of materials has been shown to exhibit an incredible variability in their properties, with the further benefit that they are highly tunable through gating and applied fields. The lab itself has lots of fun toys to play with, including: a glove box for preparing air-sensitive samples, a quasi-custom scanning single-electron transistor microscope (see below), a 3He system with a vector magnet, and a dry dilution refrigerator with a vector magnet and optical access.

Please contact me if you would like to learn more!

*Scanning single-electron transistor*

A single-electron transistor (SET) is a quantum device consisting of a small metallic island separated by tunnel junctions from source and drain leads. When temperature is low compared to the charging energy of the island, the conductance through the SET depends very sensitively on the local electrostatic environment. The relative energies of states on the island compared to the Fermi levels of the leads determines whether electrons are forbidden (a) or allowed (b) to hop onto and off of the island, a phenomenon known as Coulomb blockade (c). As a result, the current through the SET oscillates as a function of external gate voltage, with each period corresponding to adding a single electron to the island (d).

When implemented on a scanning probe tip, the SET can be used to measure local electrostatic potential, charge distribution, and electronic compressibility (i.e. many-body density of states) in 2D materials by scanning the tip over the sample of interest (see schematic below). It therefore serves as a versatile local probe of electronic properties, and the ability to directly measure thermodynamic properties complements other experimental techniques.

To fabricate SET tips, we use a special scheme to evaporate aluminum onto a quartz rod with an intermediate *in situ* oxidation step between lead and island evaporations to form the tunnel junctions. Through this procedure, we obtain SET tips with ~100 nm spatial resolution and achieve a voltage sensitivity better than 10^{-5} uV/sqrt(Hz), corresponding to less than 1 part in 10^{4} of an electron on the island.

*Magic-angle twisted bilayer graphene*

When two materials with similar lattice constants are twisted by a small angle, a spatial moiré superlattice develops which can dramatically alter the low-energy electronic states. In magic-angle twisted bilayer graphene (MATBG), where the two layers are twisted by about 1.1 degrees, this generates extremely flat electronic bands, forming a synthetic strongly correlated electron system that exhibits, superconductivity, magnetism, and nontrivial topology. We are studying MATBG and other twisted graphene systems using both thermodynamic and transport techniques. By measuring the local electronic compressibility using our scanning SET, we resolved novel correlated Chern insulators in MATBG as well as sharp phase transitions between them. The thermodynamic measurements allow us to extract the strongly correlated Hofstadter spectrum in a magnetic field and map out the phase diagram of spin/valley flavor occupation.

At low magnetic fields, we also observe thermodynamically gapped states at even integer filling factors (number of electrons per moiré unit cell). Surprisingly, the corresponding gaps are flat or increasing at low magnetic fields but decrease linearly at moderate fields, evidence of a field-tuned crossover from spin skyrmions to bare particle-hole excitations. This suggests the underlying ground state belongs to a family of strong-coupling insulators with a particular topological structure. Our local imaging demonstrates that the correlated insulators are destabilized as strain and/or twist angle variations broaden the flat bands and suppress the effects of interactions.

Finally, we are developing new multilayer twisted graphene device architectures to address the detailed spin and valley ordering of the interaction-induced states described above. This may also provide opportunities to tune screening and even realize Kondo lattice physics.

*Twisted transition metal dichalcogenides*

We're also exploring other twisted moiré systems, including those composed from transition metal dichalcogenides. These provide a highly tunable platform to engineer a variety of correlated and topological phases because they do not require a specific magic angle and the moiré bands are sensitive to applied electric and magnetic fields. They are therefore of interest for simulating Hubbard model physics. For example, we find that twisted double bilayer WSe_{2} hosts a triangular moiré lattice and supports correlated insulating states at integer and fractional filling factors. These are spin-polarized, and their gap evolution with magnetic field indicates novel composite quasiparticles known as spin polarons in which a missing particle is bound to a spin-flip excitation. We can tune between moiré bands at different valleys (momenta) with a displacement field, providing a potential route to explore honeycomb and possibly kagome geometries.

Our scanning SET is capable of overcoming twist angle disorder to probe very long moiré wavelengths in lattice-matched compounds. We realize a moiré atomic limit in twisted WSe_{2}/MoSe_{2} heterobilayers, whose deep triangular moiré superlattice potential favors multiple electrons occupying the same sites. The lowest s-like orbitals are two-fold degenerate and produce extremely flat bands that favor charge-ordered states. In contrast, the larger overlap of higher p-like orbitals forms more dispersive bands that favor Hofstadter states. We can tune the relative energies of these states and therefore their occupancies by adjusting magnetic field and carrier density, leading to a rich phase diagram of competing topological fluids and electron solids, including reentrant charge order involving cooperative crystallization of light and heavy fermions.

We are continuing to investigate other materials combinations and heterostructures to explore the possibility of engineering nontrivial topology and demonstrating control over the ground and excited states of moiré quantum matter.

### Past Projects:

*Nematic and ferroelectric phases on the surface of bismuth*

The surface states of bismuth offer a unique platform to study electronic correlations in a two-dimensional electron system. In particular, the Bi(111) surface combines extremely low disorder and accessibility to local probes with a Fermi surface containing six degenerate teardrop-shaped hole pockets. We perform spectroscopy with a scanning tunneling microscope (STM), which shows that this valley degeneracy is completely lifted at high magnetic field by a combination of strain and electron-electron interactions. Using the STM to directly image individual electronic wave functions allows us to identify two classes of novel broken-symmetry quantum Hall phases. At even filling factors, exchange interactions favor occupation of pairs of valleys with a particular anisotropy; this preferred directionality manifests as anisotropic Landau level wave functions that break the rotational symmetry of the crystal lattice to produce a nematic quantum Hall phase. Moreover, exchange interactions further lift the remaining two-fold valley degeneracy. By imaging fine spatial interference patterns of the resulting singly degenerate Landau levels around atomic-scale defects, we identify a recently predicted ferroelectric quantum Hall phase characterized by wave functions with an intrinsic dipole moment.

This work was performed in the Yazdani Lab at Princeton University.

*Novel quantum Hall physics in graphene*

Graphene is another example of a highly tunable material with multiple internal degrees of freedom: electrons can occupy two inequivalent valleys in addition to the usual spin degeneracy. In the quantum Hall regime, this approximate SU(4) degeneracy is lifted by electron-electron interactions, and in bilayer graphene the lowest two orbital indices are also degenerate, yielding an even richer system. Through transport and electronic compressibility measurements, we demonstrate the existence of broken-symmetry states at all integer filling factors and also show that the underlying symmetries lead to unconventional sequences of fractional quantum Hall states in monolayer and bilayer graphene. By tuning external parameters such as electric and magnetic field, we are able to induce phase transitions between different types of ordering at a fixed filling factors in both the integer and fractional regimes.

This work was performed in the Yacoby Lab at Harvard University.

*Atomic chain platform for Majorana Fermions*

Majorana fermions, exotic quasiparticles that are their own antiparticle, have generated tremendous excitement due to scientific interest and their potential for use in topological quantum computation. A number of solid state realizations have been proposed and experimentally pursued, including one-dimensional spinless systems coupled to a superconductor. These ingredients combine to form a topological superconductor with Majorana fermion zero-energy modes localized at its ends. We realize such a system by combining ferromagnetic atomic chains (Fe) on the surface of a superconductor with strong spin-orbit coupling (Pb). High-resolution STM measurements at dilution refrigerator temperatures show the existence of a zero-bias peak localized to the ends of such chains. Moreover, conductance mapping at zero bias reveals a distinctive 'double eye' spatial pattern. This observation, combined with measurements of chains capped by Pb overlayers, indicate that the Majorana mode has substantial weight in the superconductor. Taken together, our experimental results as well as their correspondence with detailed theoretical modeling, provide evidence for the predicted topological superconductivity in this system and the interpretation of the zero-bias features as Majorana fermion modes.

This work was performed in the Yazdani Lab at Princeton University.