Our research is driven by the idea that nanoscale synthesis and characterization of materials can give rise to novel phenomena. Our main interests include:

Atomicscale design of interacting quantum materials, such as topological and correlated electron systems, including oxides, using molecular beam epitaxy (MBE)

Characterization of the emergent phenomena using lowtemperature spectroscopic imaging scanning tunneling microscopy (SISTM) and spinpolarized scanning tunneling microscopy (SPSTM)
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I. Correlated electron systems
Spinorbit coupled Iridiumbased oxides
Out of the array of transitionmetal oxides (TMOs), iridiumbased oxides (iridates) have attracted significant attention due to an intriguing combination of strong spinorbit coupling (SOC) λ, onsite Coulomb repulsion U and crystalline fields. In particular, the SOC strength in 5d iridates is much higher than that in 3d/4d TMOs (λ ~400 meV in iridates vs. ~20 meV in 3d TMOs), which is one of the critical factors leading to the emergence of novel electronic phenomena in iridates. With a handful of exceptions (i.e. SrIrO_{3}), the ground state of most iridates is both insulating and magnetically ordered. This is in contrast to the naïve expectation that they should be metallic due to the large bandwidth of 5d electron orbitals.
The type and the onset temperature T_{N} of magnetic ordering varies from material to material within the iridates family. For example, it is inplane canted AF with T_{N} ~ 240 K in Sr_{2}IrO_{4} (Sr214), outofplane AF with T_{N} ~ 285 K in Sr_{3}Ir_{2}O_{7} (Sr327) and the “zigzag” AF with T_{N} ~ 18 K in the honeycomb iridate Na_{2}IrO_{3} (Na213) (Figure 1). To capture the surprising insulating behavior observed in most iridates, it has been shown that a SOCdriven J_{eff} = 1/2 model works reasonably well (albeit it may break down in some iridates where crystal fields and SOC are comparable). Within this model, SOC λ separates the J_{eff} = 1/2 and J_{eff} = 3/2 band; out of the five 5d electrons of Ir4+, four completely fill the J_{eff} =3/2 band, while the fifth electron and one hole occupy the two states in the J_{eff} =1/2 band. In the presence of strong Coulomb U, J_{eff} =1/2 band can split, opening a Motttype gap. A hallmark example of this interplay of SOC λ and Coulomb U in iridates is the J_{eff} = 1/2 Mott state in Sr214.
We use a combination of SISTM and SPSTM to: (1) visualize the evolution and collapse of the AF order as a function of charge carrier doping, temperature and energy in various iridates, (2) elucidate the relationship between the inhomogeneous electronic structure and the AF order at the nanoscale, and (3) search for spin and pseudospinordered phases beyond Ir spin ordering.
We imaged the atomicscale evolution of magnetic ordering in an antiferromagnetic Mott insulator (Sr_{1x}La_{x})_{2}IrO_{4} , which is the first SPSTM measurement of any complex oxide todate (Zhao et al, Nature Physics AOP (2019)). We found that near insulatortometal transition (IMT), the longrange antiferromagnetic order melts into a fragmented shortrange state before its ultimate collapse (Figure 2). Surprisingly, we discovered that this shortrange order is locally uncorrelated with the nanoscale electronic inhomogeneity, thus revealing that static shortrange antiferromagnetic order is not the culprit behind the emergence of pseudogap regions near IMT.
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HighT_{c} superconductors
under construction
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II. Topological Materials
Topological Insulators (TIs)
Topological insulators (TIs) are a new state of matter characterized by an odd Z_{2} topological invariant calculated from the electronic band structure, and they are experimentally found in strong spinorbit coupled systems with an inverted bulk band structure. Even though TIs are bulk insulators, topology of the band structure dictates the existence of gapless electronic states at the boundary occupied by massless Dirac fermions. In a 2D TI, these metallic states occur at the edge of the system; in a 3D TI such as Bi_{1x}Sb_{x} or Bi_{2}(Se,Te)_{3}, these states occur at the surface (Fig. 1). All Dirac fermions across different TIs share several fundamental properties:
 energymomentum band dispersion is linear
 spin is locked to the momentum resulting in the chiral spin texture
 the twofold degenerate Dirac node is protected by time reversal symmetry (TRS)
Using MBE, we can create heterstructures of various TIs to generate new phenomena. For example, Fig. 1(c,d) shows a longscale Moire pattern formed in a thin film of Bi2Te3 grown on top of its TI cousin Bi2Se3.
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Topological Crystalline Insulators (TCIs)
In contrast to TRSprotected Z_{2} TIs, TCIs are a state of matter in which the topological phase is protected by a discrete group of crystalline symmetries (TRS is still present but not crucial). Although TCIs are classified as trivial under the Z_{2} classification due to even number of points within the first Brillouin zone (BZ) where the bulk band inversion occurs, topological protection by crystalline symmetries commands the presence of topological Dirac states. Numerous types of symmetries can in principle lead to a TCI phase (rotation, reflection, etc.), but only one class of 3D TCIs based on mirror symmetries in IVVI rocksalt cubic semiconductor Pb_{1x}Sn_{x}Te (and related Pb_{1x}Sn_{x}Se) has been experimentally realized so far in a wide range of alloying compositions (Fig. 2). Fundamental properties of Dirac fermions observed in Z_{2} TIs still hold in TCIs, such as linear dispersion, chiral spin texture and symmetry protection of the Dirac surface states. However, Dirac fermions in TCIs are tunable across a much wider parameter space, providing a rich playground for the exploration of novel phenomena. For example, mirrorsymmetry protection of the Dirac points allows controllable opening of the Dirac gap via ferroelectric distortion without breaking TRS. Strain is expected to cause pseudomagnetic fields similar to those observed in graphene and unconventional superconductivity, while both strain and alloying composition change can induce topologicaltotrivial crossover by lifting the band inversion, and shifting the Dirac cones in momentum space, as these are not pinned to TRSinvariant points.
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Topological Superconductors (TSCs)
The interest in TSCs has been ignited by the prediction that these systems host Majorana fermions (MFs), exotic particles that are also their own antiparticles governed by nonAbelian statistics. The quest for achieving TSCs is motivated not only by physical implications of MFs in particle physics, but also by the prospects of their utilization in applications. Theoretically, TSCs can be classified into multiple different categories based on the presence or absence of timereversal and spinrotation symmetries. Timereversalinvariant TSCs have garnered much of the attention of experimentalists due to the multitude of theoretically proposed systems with different geometries which could be experimentally realized both in 2D and 3D. In 2D, timereversalinvariant TSC is a superconducting cousin of Quantum Spin Hall state with a new flavor of helical Majorana modes at its boundary. The most prominent theoretical proposal for realizing such a phase involves creating a heterostructure of an swave SC and a Z_{2} TI which should give rise to proximityinduced superconductivity at the surface of TI (Fig. 3), with MF bound states inside magnetic vortex cores at zero energy. In 3D, timereversalinvariant TSC can be viewed as a superconducting counterpart of a TI, with superconducting gap in the bulk but topologically protected electronic states at its surface. MF in this geometry would be delocalized at the surface, gapless, with the dispersion spanning the SC gap. Promising candidates to host topological materials include several systems, including Cuintercalated Bi_{2}Se_{3} and Indoped Pb_{1x}Sn_{x}Te.