UC Berkeley

The Dirac fluid is a theoretical model describing the hot plasma of relativistic particles and antiparticles in the early universe right after the big bang. The main characteristics of the Dirac fluid are two parts: one is a equal number of relativistic particles and antiparticles with a linear energy-momentum dispersion; the second is a high particle-particle scattering rate resulting in hydrodynamic local equilibrium. The first characteristic corresponds to `Dirac' and the second corresponds to `fluid'. The `Dirac' part is straight forward, which can be achieved at very high energy where $E \approx pc$. The `fluid' part is similar to other hydrodynamic systems where the particle-particle scattering rate dominates all other time scales and locally the system forms thermal equilibrium on scales larger than the mean free path.

Although Dirac fluid is a model first proposed in high energy physics or astrophysics, it is rather difficult to observe it experimentally in any high energy or astrophysics scenario. Two main difficulties include the imbalance of particles and antiparticles in our universe and the difficulty of confining a large density of high-energy particles to achieve a high enough particle-particle scattering rate. This motivates researchers to think about alternative ways to investigate the properties of Dirac fluid in other scenario, which exhibits the same physics but is much more experimentally accessible. Condensed matter systems provide such an availability with the freedom of engineering effective particle dispersion with the freedom to engineer band structures of electrons in solids.

Monolayer graphene is a single-atomic-layer of carbon atoms with a 2D hexagonal honeycomb lattice. The band structure of monolayer graphene is linear within 1 eV of the charge neutral point due to the hexagonal lattice structure and the symmetry of the two carbon atoms within one unit cell. Besides the linear energy-momentum dispersion relation $E \approx p v_f$, where $v_f$ is the Fermi velocity $\approx 10^6$ m/s, the electrons and holes in graphene also have a `chirality' degree of freedom coming from sublattice wave functions. As a result, electrons and holes in monolayer graphene have an almost perfect correspondence with a 2D gas of Dirac particles and antiparticles. On the other hand, due to the lack of screening in 2D and the relatively low charge density ($< 10^{12} $/cm$^2$), the carrier-carrier scattering in monolayer graphene due to Coulomb interaction is much stronger compared with traditional metals or semi-metals. These low dimensional enhancement of Coulomb interaction are better demonstrated in 2D semiconductors like MoS$_{2}$, where the exciton binding energy is one order larger than traditional semiconductors like GaAs.

Due to the linear chiral band structure and the enhancement of Coulomb interaction, it is predicted that monolayer graphene is an ideal table-top simulator of the Dirac fluid physics with a much lower energy scale. However, the experimental realization of Dirac fluid physics in monolayer graphene remains challenging due to defect scattering, phonon scattering and spatial fluctuation of charge density etc. To realize the Dirac fluid regime we need all these effects to have energy scales much lower than the thermal excitation energy $k_B T$. The advances in the sample fabrication skills in recent years have facilitated our experiment. By using exfoliated graphene samples and encapsulating graphene within two pieces of hexagonal Boron nitride, we can obtain relatively clean graphene samples with all such irrelevant energy scales lower than $k_B T$. Under these conditions, the relevant energy scale of the Dirac fluid in graphene is on the order of $k_B T \sim$ 1 terahertz. We developed novel terahertz experiment techniques to probe the physical properties of the Dirac fluid.

In the first chapter of the dissertation, I will introduce the fundamental properties of monolayer graphene and discuss theoretical predictions of the quantum critical conductivity in graphene. I will then provide an introduction to on-chip terahertz time-domain spectroscopy, our main technique in probing the carrier dynamics in the Dirac fluid.

In the following chapters, I will discuss our findings achieved by applying this on-chip terahertz spectroscopy to monolayer graphene to investigate different peculiar properties of the Dirac fluid. In the second chapter, we measured the optical conductivity of hBN-encapsulated monolayer graphene in terahertz frequencies and obtained the temperature dependence of the carrier-carrier scattering rate. We observed the quantum-critical scattering rate characteristic of the Dirac fluid. We also detected two distinct current-carrying modes with zero and nonzero total momenta at nonzero doping. In the third chapter, we designed an optical-pump-terahertz-probe experiment to probe the collective energy excitation in the Dirac fluid, where energy propagates in the form of waves with velocity $v_f / \sqrt{2}$ instead of diffusion. Preliminary results correspond very well with simulations and qualitatively confirm a diffusive heat transport in the Fermi liquid regime and a wave-like heat transport in the Dirac fluid regime.