Our Research

"A common mistake of beginners is the desire to understand everything completely right away. In real life understanding comes gradually, as one becomes accustomed to the new ideas. One of the difficulties of scientific research is that it is impossible to make progress without clear understanding, yet this understanding can come only from the work itself; every completed piece of research represents a victory over this contradiction."

Arkady Beynusovich Migdal, "Qualitative Methods in Quantum Theory"

Geometrically frustrated magnetism

Electrons in magnetic materials interact with each other predominantly through their spin degrees of freedom. In a ferromagnet (for instance, a lodestone), the interaction forces the electron spins to be parallel with each other. As a result, the spins align in the same direction, and their magnetic moments add up to produce a macroscopic magnetic field. By contrast, in an antiferromagnet, the interaction forces the electron spins to be anti-parallel. If the electrons line up to form a square lattice (for instance, in La2CuO4, the "parent compound" for high temperature superconductivity), the electron spins align in a regular, staggered pattern, which produces no macroscopic magnetic field at all. In such a pattern, each and every pair of neighboring spins point in opposite directions as the interaction requires.

Things are much trickier (therefore, more interesting) in geometrically frustrated magnets --- in these systems, the interactions between the electron spins are in conflict with each other due to the underlying lattice geometry. Consider the antiferromagnet again: instead of arranging the electron spins in a square lattice, now imagining they form a triangular lattice (such as the case with Hematite, Fe2O3). With the triangular lattice geometry, it is simply impossible to arrange the spins such that each and every pair of neighboring spins take exactly opposite directions. In this sense, the interactions are mutually conflicting, and the system is geometrically frustrated.

Left: Electron spins in a ferromagnet align in the same direction. Middle: In an antiferromagnet, neighboring spins prefer to align in opposite directions as the interaction requires. If the electrons form a square lattice, the spins settle into a regular, staggered pattern. Right: On the other hand, if the electrons in an antiferromagnet form a triangular lattice, the system is frustrated: it is impossible to make each and every two neighboring spins align in exactly opposite directions.

The geometrical frustration leads to numerous interesting consequences, some of which are potentially quite useful. As the interactions are mutually conflicting, the spins simply do not know where to go. If the conditions are right, the spins may enter a coordinated, quantum mechanical dance known as the quantum spin liquid state. The excitations in such a state may be neither fermions nor bosons but, in a loose sense, "in-between" particles or anyons. The anyons are thought to be a promising platform for quantum computing. In a more exotic case, the excitations are not even quantum particles but strings --- one-dimensional, spatially extended objects that quantum mechanically expand, contract, and vibrate.

Selected Publications:

Non-equilibrium control of frustrated magnets

In some circumstances, the spins in a frustrated magnet do align in some specific pattern, or what experts call a magnetic order. However, the magnetic orders in geometrically frustrated magnets are often "fragile" in that the magnets often host other closely competing magnetic orders (spin patterns). The competing orders, being thermodynamically unstable or metastable, are not observed in thermal equilibrium. However, "kicking" the frustrated magnet with a magnetic field pulse or "shaking" the magnet with AC magnetic field can easily tip the balance in favor of these competing orders. Under non-equilibrium conditions, a frustrated magnet thus may exhibit magnetic orders that are different from the order seen in equilibrium.

Selected Publications:

2D coherent spectroscopy of quantum materials

Optical spectroscopy is a powerful probe of elementary excitations in quantum materials. The optical spectroscopy perturbs the system with electromagnetic (EM) waves, thereby exciting the elementary excitations in that system, and then measure how much energy is absorbed by the elementary excitations. Important properties of the elementary excitations, including their life time and mobility, can be inferred from such measurements.

Left: Conventional, or "one-dimensional" optical spectroscopy probes a many-body system with the electromagnetic (EW) wave at a given frequency and measures the system's response. Right: Two-dimensional coherent spectroscopy uses two EM waves at two frequencies and measures the cross-correlation induced by these two EM waves.

The conventional optical spectroscopy uses one "handle" that is the frequency of the probing EM waves --- it varies the probing frequency and examine the system's response at that frequency. This results in a "1D" spectrum of the response as a function of the probing frequency. One can significantly extend the utility of the optical spectroscopy by adding more “handles”, or more EM wave frequencies. The outcome is known as two-dimensional (if we use two frequencies) or multidimensional (if we use even more frequencies) coherent spectroscopy. In a loose sense, the two-dimensional coherent spectroscopy uses one EM wave to excite the material and another EM wave to probe the material’s response. This yields a two-dimensional spectrum with two frequency variables, namely the exciting frequency and the probing frequency. Since the two-dimensional coherent spectroscopy has more “handles”, one naturally expect that this technique can obtain more information about the material that is being investigated.

Two-dimensional coherent spectroscopy in the infrared and the radio frequency are well-established technique for investigating atoms and molecules. Extending this spectroscopy to the terahertz range put us in the right energy window to study the elementary excitations in quantum materials. As exciting as it sounds, applying this technique to quantum materials presents a challenge for theorists. The utility of this technique is rarely explored in the context of quantum materials such as quantum magnets and superconductors. We need to come up with clever ideas on how to make the most of this technique. Furthermore, the currently available theoretical tools used in analyzing the two-dimensional spectra are tailored for few-body systems represented by atoms and molecules. For quantum materials, we need to develop new tools and new languages that are more suitable for many-body systems.

Selected Publications: