More stuff: personal thoughts about what is potentially interesting/useful to study in condensed matter physics, particularly experiments in low-dimensional quantum materials.

As a PhD freshman, I do hold some long-term goals to achieve during my PhD career i.e. some “big” topics to study. I hope these topics would stimulate some discussion and may be beneficial to other readers, if possible.

Currently, the academia of condensed matter physics is reaching or has already reached its “Golden Age”, where dozens of new topics are emerging and dozens of old topics are consolidating into fancy formalisms/paradigms or refreshing themselves and leading physicists moving forward reversely, both in the area of theories and experiments. Meanwhile, theorists, computationists and experimentalists are working together more and more tightly to create an abundant future of quantum technologies based on condensed matter physics. This is because the very fundamental physical philosophy of condensed matter is about creating to more, not about reducing to less. Thus, under the context of emergentism, any new materials that are discovered experimentally, thanks to the generosity of the Nature itself, will be abstracted into a quantum many-body system with a well-defined Hamiltonian or wavefunction phenomenologically immediately, and then will be studied extensively via modern computational tools and algorithms, and the deep mathematics or physics behind the observed phenomena will be soon uncovered. The process can be then reversed back and stimulate the growing of the experiments and the related techniques in materials sciences and electrical engineerings. There are several examples I’d love to raise. 

1. First, the study of superconductivity of normal metals, originated from the invention of refrigration technology below hellium temperature, through various cryogenic electrical transport, magnetotransport, therml transport and infrared opics as well as phononics study, finally condensed into the BCS theory of all 3D Fermi liquids, and soon stimulate the formulation of Landau-Ginzberg framework with Anderson-Higgs mechanism, eventually lead to the abundant study of unconventional superconductors as well as studies in the high energy physics community nowadays. With the increasement of Tc, physicists are moving closer and closer towards the discovery of room temperature superconductors in the application field, as well as the uncovery of the deep mystery of strongly-correlated quantum many-body physics.
2. Second, the study of quantum Hall effect in 2DEG and 2D electron liquids, originated from the prediction of Landau levels in 2DEG placed in a strong magnetic field, firstly observed in GaAs system experimentally through magnetotransport technique, has leaded to the various family of QHE including QAHE, QSHE, FQHE, FQAHE, etc., and is further abstracted into fields of topogical insulators, topological orders, with topologically robust collective excitations often featured with fractionalization as a formidable task to understand in modern strongly-correlated-topological physics. New maths, physics, and experimental tools have emerge in this big field, with a new framework called topological order and other theories with the same spirit that aim to build a new languange to describe these quantum many-body physics with robust long-range order in their ground states. 
3. Third, the study of Kondo effect in magnetially doped non-magnetic alloys, also orginated from cryognetic transport measurements, stimulate the formulation of renormalization group which is a modern powerful scheme in both condensed matter physics as well as high energy physics, in tandem with DMFT, DMRG algorithms and heavy fermion systems, which, may be a path to solve the mystery of high-Tc superconductivity as the core of modern quantum many-body physics. The associated Wilsonian renormalization group scheme has reformed both the condensed matter and the high energy physics communities.

From the discussion above, we shall believe that it is the right time for us to choose a right topic to study so as to facilitate this progress, eventually make the future physicists be able to understant the fundamental structure of quantum many-body systems beyond perturbative symmetry-breaking scheme, and then to apply these new physics in building new technologies to improve the producivity of human-beings. What is the “right” path? As Steven Weinburg said, “Go for the chaos!” The path towards chaos is always the right path. In condensed matter physics, the current and at least future-10-years chaos is the field of strongly correlated electronic systems.

The study of strongly correlated electrons has become more and more abundant, both theoretically and computationally. Theoretically, many theories as well as formalisms have been proposed to build the new paradigm of many-body electrons outside the Landau paradigm, such as the study of 2D Hubbard model and beyond, has leaded to the investigation of strongly correlated quantum magnetism, various competing instabilities, emergent gauge fields, disorder, etc.; the study of 1D spin chain model and beyond, has leaded to the investigation of Bethe Ansatz, bosonization, strongly entangled electrons, DQCP, etc.; the study of quantum Hall liquids and beyond, has leaded to the investigation of topological orders, fractionalization, generalized symmetries, etc. Computationally, such theories have boosted the widly usage of ED, DFT+U, QMC, DMFT, DMRG plus tensor network, even Al4S, etc. Since I am not a professionist in both areas, I will stop here and I would like to talk a little more about experiments.

Nowdays, tons of experiments in strongly correlated electronic systems have been done, in 3D bulk thin-film systems, 3D thin-film heterostructures, doped Mott insulators, Kagome lattices, perovskites, heavy fermion materials, 2D heterostructures (moire or non-moire) spanning from graphene to transition metal dichalcogenides, 1D quantum wires and junctions, and 0D quantum dots, etc., with many useful probe techniques from materials growing (MBE, CVD, etc.), nanodevice fabrication, transport measurements (electromagnetic, thermal, phononic, etc.), tip scanning spectroscopy (STM/STS, SQUID, STEM, MIM, etc.), optical spectroscopy (ultrafast-laser, magnetoptical, optoelectronic, etc.), covering a wide spatial (down to sub-nm) and temporal domain (down to sub-fs). Yet, the true “smoking-gun” like experiments are very few. As an experimentalist, I want to think about what experiments are right, both interesting and useful to push the understanding of strongly correlated electroic systems.

I will narrow the discussion into the low-dimensional quantum materials, especially for moire heterostructurs. These systems have firstly established a highly tunable experimental platform for physicists to probe, tune, and even create strongly correlated electrons in labs. Unlike bulk thin-film materials, the quantum confinement effect is more strong in 2D or 1D materials, yet the growing and fabrication techniques for these low-dimensional structures are still mature. What’s more, the extremely high freedom of stacking, squeezing, stretching, and twisting these 2D flakes or 1D tubes offer physicists a bigger space to tune the physical parameters of the electronic systems in situ from the very first device architechture. To our suprise, these physical knobs, just like the doping, temperature, pressure or external fields, are directly related to the strongly correlated structures of electrons, yet more easily and freely to controll. The best example is the discovering of twistronics, which, liberated the angles of different 2D materials as a knob to diretly tune the correlations of microscopic electrons at a mesoscopic or even macroscopic level. It is a true renormalization group machine, since the smallest energy scale of the system is directly related to the angles between two thin flakes and is now in full control of our hands. Currently, many afore-predicted strongly correlated phemoena, have been observed in this platform, including unconventional SC, FQHE, FQAHE, chiral Luttinger liquid, correlated Chern insulators beyond Mottness, Wigner crystal, etc. In light of this, there are several things (“big” topics) I think we can expect to do to facilitate this field, as the facilitation of the study of strongly correlated electronic systems:

1. A systematic experimental scheme, including probing methods, tools and corresponding engineering techniques as a whole, to probe topological orders.
2. A delicate strategy to control the twist angle in situ of the devices, or more broadly speacking, the reconfigurability of low-dimensional quantum devices.
3. The study and control of the pseudogap inside these materials near superconducting region.
4. A general paradigm of 2D electronic fluids with long-range Coulomb interactions (weak screening limit), including its phase and phase transition properties.
5. A general paradigm of 1D electronic fluids with long-range Coulomb interactions (interacting Luttinger liquid), a better investigation of bosonization.
6. A delicate investigation of local real space imaging of fractionalized excitations in quantum Hall liquids, to build theories beyond the composite quasi-particle theory (latter as a semi-Landau theory in strongly correlated physics, as the semi-classical theory in quantum physics).
7. Connection with quantum computing hardware using fully controllabe strongly correlated electrons, for example, 2D materials arrays or circuits?
8. …