arXiv subjects

Aaron Hui

Publications and source records attributed to Aaron Hui.

12 recordsLinked to original sources

arXiv2025

The Cosmological Constant from a Quantum Gravitational $\theta$-Vacua and the Gravitational Hall Effect

We provide a new perspective on the cosmological constant by exploring the background-independent Wheeler-DeWitt quantization of general relativity. The Chern-Simons-Kodama state of quantum gravity, a generalization of the Hartle-Hawking and Vilenkin states, has a striking structural similarity to the topological field theory of the quantum Hall effect. As a result, we study the gravitational topological $\theta$-sectors in analogy to Yang-Mills theory. We find that the cosmological constant $\Lambda$ is intimately linked to the $\theta$-parameter by $\theta=12\pi^2/(\Lambda \ell^2_{\rm Pl}) \mod 2\pi$ due to the fact that Chern-Simons-Kodama state must live in a particular $\theta$-sector. This result is shown in the canonical, non-perturbative formalism. Furthermore, we explain how the physics of the Hamiltonian constraint is analogous to the quantum Hall effect, with the cosmological constant playing the role of a quantum gravitational Hall resistivity. These relations suggest that $\Lambda$ is topologically protected against perturbative graviton loop corrections, analogous to the robustness of quantized Hall conductance against disorder in a metal.

gr-qc↗

arXiv2025

Hydrodynamics of the electronic Fermi liquid: a pedagogical overview

For over a hundred years, electron transport in conductive materials has been primarily described by the Drude model, which assumes that current flow is impeded primarily by momentum-relaxing collisions between electrons and extrinsic objects such as impurities or phonons. In the past decade, however, experiments have increasingly realized ultra-high quality electronic materials that demonstrate a qualitatively distinct method of charge transport called hydrodynamic flow. Hydrodynamic flow occurs when electrons collide much more frequently with each other than with anything else, and in this limit the electric current has long-wavelength collective behavior analogous to that of a classical fluid. While electron hydrodynamics has long been postulated theoretically for solid-state systems, the plethora of recent experimental realizations has reinvigorated the field. Here, we review recent theoretical and experimental progress in understanding hydrodynamic electrons using the (hydrodynamic) Fermi liquid as our prototypical example.

cond-mat.str-el↗

arXiv2024

Observation of Electronic Viscous Dissipation in Graphene Magneto-thermal Transport

Hydrodynamic transport effectively describes the collective dynamics of fluids with well-defined thermodynamic quantities. With enhanced electron-electron interactions at elevated temperatures, the collective behavior of electrons in graphene with minimal impurities can be depicted as a hydrodynamic flow of charges. In this new regime, the well-known rules of Ohmic transport based on a single electron picture no longer apply, necessitating the consideration of collective electron dynamics. In particular, the hydrodynamic analogues of Joule heating and thermal transport require consideration of the viscous motion of the electron fluid, which has a direct impact on energy dissipation and heat generation by the fluidic motion of charge. In this work, we probe graphene hydrodynamics with thermal transport and find two distinct, qualitative signatures: thermal conductivity suppression below the Wiedemann-Franz value and viscous heating leading to magnetically-induced redistribution of temperature. We find these two effects are coincident in temperature and density, providing robust qualitative signatures of hydrodynamics, despite arising from two distinct aspects of this new regime: microscopic momentum conservation due to electron-electron scattering, and geometry-dependent viscous dissipation. Our results mark the first observation of viscous electronic heating in an electron fluid, providing insight for thermal management in electronic hydrodynamic devices and offering a new methodology for identifying hydrodynamic states in other systems.

cond-mat.mes-hall↗

arXiv2024

Magnetothermopower of nodal line semimetals

The search for materials with large thermopower is of great practical interest. Dirac and Weyl semimetals have recently proven to exhibit superior thermoelectric properties, particularly when subjected to a quantizing magnetic field. Here we consider whether a similar enhancement arises in nodal line semimetals, for which the conduction and valence band meet at a line or ring in momentum space. We compute the Seebeck and Nernst coefficients for arbitrary temperature and magnetic field and we find a wealth of different scaling regimes. Most strikingly, when a sufficiently strong magnetic field is applied along the direction of a straight nodal line or in the plane of a nodal ring, the large degeneracy of states leads to a large, linear-in-$B$ thermopower that is temperature-independent even at low temperatures. Our results suggest that nodal line semimetals may offer significant opportunity for efficient, low-temperature thermoelectrics.

cond-mat.mtrl-sci↗

arXiv2023

Resolving the Corbino Shockley-Ramo Paradox for Hydrodynamic Current Noise

Johnson noise thermometry enables direct measurement of the electron temperature, a valuable probe of many-body systems. Practical use of this technique calls for non-equilibrium generalizations of the Johnson-Nyquist theorem. For a hydrodynamic Corbino device, however, a na\"ive use of the Shockley-Ramo theorem alongside the "Corbino paradox" leads to yet another paradox: bulk velocity fluctuations cannot be measured by the contacts. In this work, we resolve the unphysical "Corbino Shockley-Ramo paradox" by correctly formulating the hydrodynamic Shockley-Ramo problem. This allows us to properly formulate the problem of current noise in an hydrodynamic multi-terminal device of arbitrary geometry, as well as validate a previously unjustified assumption for rectangular geometry results. As an example, we compute the Johnson noise in a hydrodynamic Corbino device, where we find a suppression of Johnson noise with magnetic field. This unusual characteristic serves as a strong signature of viscous hydrodynamic behavior.

cond-mat.mes-hall↗

arXiv2023

Two-dimensional hydrodynamic electron flow through periodic and random potentials

We study the hydrodynamic flow of electrons through a smooth potential energy landscape in two dimensions, for which the electrical current is concentrated along thin channels that follow percolating equipotential contours. The width of these channels, and hence the electrical resistance, is determined by a competition between viscous and thermoelectric forces. For the case of periodic (moir\'{e}) potentials, we find that hydrodynamic flow provides a new route to linear-in-$T$ resistivity. We calculate the associated prefactors for potentials with $C_3$ and $C_4$ symmetry. On the other hand, for a random potential the resistivity has qualitatively different behavior because equipotential paths become increasingly tortuous as their width is reduced. This effect leads to a resistivity that grows with temperature as $T^{10/3}$.

cond-mat.str-el↗

arXiv2022

Current Noise of Hydrodynamic Electrons

A resistor at finite temperature produces white noise fluctuations of the current called Johnson-Nyquist noise. Measuring the amplitude of this noise provides a powerful primary thermometry technique to access the electron temperature. In practical situations, however, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogeneous temperature profiles. Recent work provided such a generalization for ohmic devices obeying the Wiedemann-Franz law, but there is a need to provide a similar generalization for hydrodynamic electron systems, since hydrodynamic electrons provide unusual sensitivity for Johnson noise thermometry but they do not admit a local conductivity nor obey the Wiedemann-Franz law. Here we address this need by considering low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. Unlike in the ohmic setting, we find that the Johnson noise is geometry-dependent due to non-local viscous gradients. Nonetheless, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the ohmic result.

cond-mat.mes-hall↗

arXiv2020

Beyond Ohm's law -- Bernoulli effect and streaming in electron hydrodynamics

Recent observations of non-local transport in ultraclean 2D materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of many-electron state. However, it has been pointed out that non-local transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e. Ohm's law, which cannot easily differentiate among different modes of transport. Here we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the non-linearity of the Navier-Stokes equation. Three experiments we propose will each manifest unique phenomenon well-known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical non-laminar flows, e.g. pattern formation and turbulence.

cond-mat.str-el↗

arXiv2019

Quantum aspects of "hydrodynamic" transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport. Here we demonstrate that even free fermion systems, in the presence of (inevitable) disorder, exhibit non-local conductivity effects such as those observed in experiment because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wavevector, $\sigma({\bf q})$, for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.

cond-mat.str-el↗

arXiv2019

Optical Signatures of the Chiral Anomaly in Mirror-Symmetric Weyl Semimetals

The chiral anomaly is a phenomenon characteristic of Weyl fermions, which has condensed matter realizations in Weyl semimetals. Efforts to observe smoking gun signatures of the chiral anomaly in Weyl semimetals have mostly focused on a negative longitudinal magnetoresistance in electronic transport. Unfortunately, disentangling the chiral anomaly contribution in transport or optical measurements has proven non-trivial. Recent works have proposed an alternative approach of probing pseudoscalar phonon dynamics for signatures of the chiral anomaly in non-mirror-symmetric crystals. Here, we show that such phonon signatures can be extended to scalar phonon modes and mirror-symmetric crystals, broadening the pool of candidate materials. We show that the presence of the background magnetic field can break mirror symmetry strongly enough to yield observable signatures of the chiral anomaly even in mirror-symmetric materials. Specifically for mirror-symmetric Weyl semimetals such as TaAs and NbAs, including the Zeeman interaction at $B \approx 10$T, we predict an IR reflectivity peak will develop with an $\mathbf{E}_\text{IR}\cdot\mathbf{B}$ dependence.

cond-mat.str-el↗

arXiv2017

Non-Abelian bosonization and modular transformation approach to superuniversality

Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents, i.e., the critical points are superuniversal. In apparent contradiction to these experiments, prior theoretical studies of quantum Hall phase transitions within the framework of Abelian Chern-Simons theory coupled to matter found correlation length exponents that depend on the value of the quantum critical Hall conductivity. Here, we use non-Abelian bosonization and modular transformations to theoretically study the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent $U(N)$ gauge symmetry with any $N > 1$ for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. We find the correlation length and dynamical critical exponents are independent of the particular transition within a controlled 't Hooft large $N$ expansion, i.e., superuniversal! We argue that this superuniversality could survive away from this controlled large $N$ limit using recent duality conjectures.

cond-mat.str-el↗

arXiv2017

Non-Abelian Fermionization and Fractional Quantum Hall Transitions

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields.

cond-mat.str-el↗