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

**atomic-scale design**of interacting quantum materials, such as topological and correlated electron systems, including oxides, using molecular beam epitaxy (MBE)**manipulation of properties**using strain, electrostatic gating and magnetic field**characterization**of the emergent phenomena using low-temperature spectroscopic imaging scanning tunneling microscopy (SI-STM)

**Z**_{2} topological Insulators (TIs)

_{2}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 spin-orbit 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_{1-x}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:

- energy-momentum band dispersion is linear
- spin is locked to the momentum resulting in the chiral spin texture
- the two-fold 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 long-scale Moire pattern formed in a thin film of Bi2Te3 grown on top of its TI cousin Bi2Se3.

**Topological Crystalline Insulators (TCIs)**

In contrast to TRS-protected 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 IV-VI rock-salt cubic semiconductor Pb_{1-x}Sn_{x}Te (and related Pb_{1-x}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, mirror-symmetry 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 topological-to-trivial crossover by lifting the band inversion, and shifting the Dirac cones in momentum space, as these are not pinned to TRS-invariant points.

**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 non-Abelian 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 time-reversal and spin-rotation symmetries. Time-reversal-invariant 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, time-reversal-invariant 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 *s*-wave SC and a Z_{2} TI which should give rise to proximity-induced superconductivity at the surface of TI (Fig. 3), with MF bound states inside magnetic vortex cores at zero energy. In 3D, time-reversal-invariant 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 Cu-intercalated Bi_{2}Se_{3} and In-doped Pb_{1-x}Sn_{x}Te.