Multipolar orders describe the phenomena of long-range ordering of multipolar moments that develop from the complex electric or mag- netic dipole distributions within one primitive cell of solids. Although much less studied than dipolar orders (e.g., ferroelectricity (FE), ferromagnetism (FM)), multipolar orders are widely present in a broad class of quantum materials including f -electron systems, 5d TMOs, multiferroics, chiral magnets and so on, and play essential roles in determining such materials’ physical properties. The key challenge in investigating multipolar orders is the lack of proper experimental techniques to efficiently couple with their tensor order parameters, because they call for tensor fields of the right symmetries, which unfortunately are not readily available. Another focused effort in my group is to experimentally study multipolar orders in quantum materials.

• "Observation of a ferro-rotational order coupled with second-order nonlinear optical fields" Nature Physics 16, 42 (2020) with a "news and views" highlight at Nature Physics (Order!Order!!)

• "Ultrafast modulations and detection of a ferro-rotational charge density wave using time-resolved electric quadrupole second harmonic generation" Physical Review Letters 127, 126401 (2021)

• "Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides" Nature Physics doi: 10.1038/s41567-025-03008-2 (2025) with a "research briefing" by Nature Physics (The origin of the axial Higgs is a hidden ferroaxial electronic density wave)

• "Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses" Nature Physics in press (2025)

Of the various interactions among the four DoFs, strong electron correlations and strong SOC have led separately to the two major threads in quantum materials research, strongly correlated electron physics and topological electron physics, respectively. The combination of these two interactions holds prospects of realizing fundamentally new quantum phases of matter quite beyond a simple sum of those in the two individual research threads. Luckily, the experimental realization of coexisting strong electron correlations and strong SOC within a single material is achieved in high-quality single crystals of 4d and 5d transition metal oxides (TMOs) and topological magnets. One main research topic in my group is to experimentally investigate novel electronic and magnetic phases in these materials.

• "Symmetry-resolved two-magnon excitations in a strong spin-orbit-coupled bilayer antiferromagnet" Physical Review Letters 125, 087202 (2020)

• "Electric quadrupole second harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal" Nature Photonics 18, 26 (2023)

• "Incommensurate transverse peierls transition" Nature Communications in press (2025)

Spontaneous symmetry breaking orders are expected to exhibit distinct behaviors in reduced dimensionalities. On the one hand, the reduced dimensionality promotes electronic and magnetic instabilities, stimulating the development of new electronic and magnetic phases. On the other hand, the lower dimensionality enhances thermal and quantum fluctuations, prohibiting the formation of long-range orders. The outcome of this competition re- mains elusive, which has stimulated enormous interests in exploring phases and phase transitions in reduced dimensionalities. Thanks to the discovery of 2D atomic crystals, we now have the ideal platform to study electronic and magnetic ordering in 2D. One major research interest of my group is to experimentally explore 2D magnetic and electronic phases in atomic crystals.

• "Magnetic-field-induced quantum phase transitions in a van Der Waals magnet" Physical Review X 10, 011075 (2020) featured at APS Physics (Solving a Magnetic Puzzle)

• "Tunable layered-magnetism-assisted magneto-Raman effect in a two-dimensional magnet CrI3" Proceeding of National Academy of Sciences 117, 24664 (2020)

• "Observation of the polaronic character of excitons in a two-dimensional semiconducting magnet CrI3" Nature Communications 11, 4780 (2020)

• "Extraordinary phase transition revealed in a van der Waals antiferromagnet" Nature Communications 15, 6472 (2024)

A moiré superlattice results from the interference between two atomic lattices due to lattice mismatch or angular misalignment and emerges as one fruitful venue to design the physical properties of 2D materials. While a great number of discoveries have been made in moire electronics, the power of moire superlattice in designing the magnetic properties is less explored, partially because 2D magnetism itself is a much newer topic than 2D electronic materials. Thanks to the recent studies on natural 2D magnets, we now know that the interlayer stacking symmetry determines the interlayer magnetic exchange coupling (including both signs and magnitudes). Based on this knowledge, a moire superlattice contains a full parameter space of shift vector between adjacent layers, and therefore, a full range of periodic modulation of magnetic exchange coupling. One recent focus of my group is to investigate moire magnetism in twisted 2D magnets.

• "Twist engineering of the two-dimensional magnetism in double bilayer chromium triiodide homostructures" Nature Physics 18, 30 (2022)

• "Evidence of Noncollinear Spin Texture in Magnetic Moiré Superlattices" Nature Physics 19, 1150 (2023) with a "news and views" highlight at Nature Physics (Noncollinear spin textures with a twist)

When reducing from 3D bulk to 2D films, fluctuations become significantly more pronounced, hindering long-range orders. A common strategy to counteract fluctuations is to introduce interaction terms with discrete symmetries, which helps sustain long-range orders from 3D down to the 2D limit. For instance, in the research of 2D magnets, many efforts have focused on identifying vdW magnets with easy-axis anisotropy and expanding the pool of 2D magnets. However, it is equally important to explore what happens when fluctuations dominate – whether novel phenomena emerge when the long-range order present in 3D is destroyed by enhanced fluctuations in 2D. Another post-tenure research direction in my group at U-M is to explore the dimensional crossover of ordering phenomena from 3D to 2D, using vdW magnets as a platform. This branches out from our previous research of easy-axis vdW magnets. 

• "Dimensionality crossover to 2D vestigial nematicity from 3D zigzag antiferromagnetism in an XY-type honeycomb van der Waals magnet" Nature Physics 20, 1764 (2024) with a "news and views" highlight at Nature Physics (Intertwined vestigial orders in stacked magnetic flatlands)

In addition, we have four major collaborative projects that are actively ongoing in the Zhao group. Please see the COLLABORATIONS page for more details. 

• Endotaxial 2D polytype heterosturcture, through a NSF MRSEC center at Michigan.

• Nonlinear optics of AlN and Sc-doped AlN, through a NSF NQVL center at Michigan.

• Cavity-enabled Floquet effects in 2D materials, through a NSF-AFRL collaboration between Columbia and Michigan.

• Twisted 3D/3D bilayer crystals, through a MURI collaboration among Minnesota, Michigan, Harvard, and Temple.