How Electron Hydrodynamics Can Eliminate the Landauer-Sharvin Resistance.

It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bound of resistance of hydrodynamic electrons. Here, we show that by a proper choice of device geometry, it is possible to spread the Landauer-Sharvin resistance throughout the bulk of the system, allowing its complete elimination by electron hydrodynamics. We trace the effect to the dynamics of electrons flowing in channels that terminate within the sample. For ballistic systems this termination leads to back-reflection of the electrons and creates resistance. Hydrodynamically, the scattering of these electrons off other electrons allows them to transfer to transmitted channels and avoid the resistance. Counterintuitively, we find that in contrast to the ohmic regime, for hydrodynamic electrons the resistance of a device with a given width can decrease with its length, suggesting that a long enough device may have an arbitrarily small total resistance.

Entropic evidence for a Pomeranchuk effect in magic-angle graphene.

In the 1950s, Pomeranchuk1 predicted that, counterintuitively, liquid 3He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1kB per unit cell (kB is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30 kelvin, the bandwidth of magnetic excitations is about 3 kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

Visualizing Poiseuille flow of hydrodynamic electrons.

Hydrodynamics, which generally describes the flow of a fluid, is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate1. Although various aspects of electron hydrodynamics have been revealed in recent experiments2-11, the fundamental spatial structure of hydrodynamic electrons-the Poiseuille flow profile-has remained elusive. Here we provide direct imaging of the Poiseuille flow of an electronic fluid, as well as a visualization of its evolution from ballistic flow. Using a scanning carbon nanotube single-electron transistor12, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperatures into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide direct confirmation of Poiseuille flow in the solid state, and enable exploration of the rich physics of interacting electrons in real space.

Simultaneous voltage and current density imaging of flowing electrons in two dimensions.

A variety of physical phenomena associated with nanoscale electron transport often results in non-trivial spatial voltage and current patterns, particularly in nonlocal transport regimes. While numerous techniques have been devised to image electron flows, the need remains for a nanoscale probe capable of simultaneously imaging current and voltage distributions with high sensitivity and minimal invasiveness, in a magnetic field, across a broad range of temperatures and beneath an insulating surface. Here we present a technique for spatially mapping electron flows based on a nanotube single-electron transistor, which achieves high sensitivity for both voltage and current imaging. In a series of experiments using high-mobility graphene devices, we demonstrate the ability of our technique to visualize local aspects of intrinsically nonlocal transport, as in ballistic flows, which are not easily resolvable via existing methods. This technique should aid in understanding the physics of two-dimensional electronic devices and enable new classes of experiments that image electron flow through buried nanostructures in the quantum and interaction-dominated regimes.

Nanomechanical pump-probe measurements of insulating electronic states in a carbon nanotube.

Transport measurements have been an indispensable tool in studying conducting states of matter. However, there exists a large set of interesting states that are insulating, often due to electronic interactions or topology, and are difficult to probe via transport. Here, through an experiment on carbon nanotubes, we present a new approach capable of measuring insulating electronic states through their back action on nanomechanical motion. We use a mechanical pump-probe scheme, allowing the detection of shifts in both frequency and dissipation rate of mechanical vibrational modes, in an overall insulating system. As an example, we use this method to probe the non-conducting configurations of a double quantum dot, allowing us to observe the theoretically predicted signature of nanomechanical back action resulting from a coherently tunnelling electron. The technique opens a new way for measuring the internal electronic structure of a growing variety of insulating states in one- and two-dimensional systems.

Topological Transitions and Fractional Charges Induced by Strain and a Magnetic Field in Carbon Nanotubes.

We show that carbon nanotubes (CNT) can be driven through a topological phase transition using either strain or a magnetic field. This can naturally lead to Jackiw-Rebbi soliton states carrying fractionalized charges, similar to those found in a domain wall in the Su-Schrieffer-Heeger model, in a setup with a spatially inhomogeneous strain and an axial field. Two types of fractionalized states can be formed at the interface between regions with different strain: a spin-charge separated state with integer charge and spin zero (or zero charge and spin ±â„/2), and a state with charge ±e/2 and spin ±â„/4. The latter state requires spin-orbit coupling in the CNT. We show that in our setup, the precise quantization of the fractionalized interface charges is a consequence of the symmetry of the CNT under a combination of a spatial rotation by π and time reversal.

Gate-tunable polarized phase of two-dimensional electrons at the LaAlO3/SrTiO3 interface.

Controlling the coupling between localized spins and itinerant electrons can lead to exotic magnetic states. A novel system featuring local magnetic moments and extended 2D electrons is the interface between LaAlO3 and SrTiO3. The magnetism of the interface, however, was observed to be insensitive to the presence of these electrons and is believed to arise solely from extrinsic sources like oxygen vacancies and strain. Here we show the existence of unconventional electronic phases in the LaAlO3/SrTiO3 system pointing to an underlying tunable coupling between itinerant electrons and localized moments. Using anisotropic magnetoresistance and anomalous Hall effect measurements in a unique in-plane configuration, we identify two distinct phases in the space of carrier density and magnetic field. At high densities and fields, the electronic system is strongly polarized and shows a response, which is highly anisotropic along the crystalline directions. Surprisingly, below a density-dependent critical field, the polarization and anisotropy vanish whereas the resistivity sharply rises. The unprecedented vanishing of the easy axes below a critical field is in sharp contrast with other coupled magnetic systems and indicates strong coupling with the moments that depends on the symmetry of the itinerant electrons. The observed interplay between the two phases indicates the nature of magnetism at the LaAlO3/SrTiO3 interface as both having an intrinsic origin and being tunable.

Localization of fractionally charged quasi-particles.

An outstanding question pertaining to the microscopic properties of the fractional quantum Hall effect is understanding the nature of the particles that participate in the localization but that do not contribute to electronic transport. By using a scanning single electron transistor, we imaged the individual localized states in the fractional quantum Hall regime and determined the charge of the localizing particles. Highlighting the symmetry between filling factors 1/3 and 2/3, our measurements show that quasi-particles with fractional charge e* = e/3 localize in space to submicrometer dimensions, where e is the electron charge.

Ab initio study of the alternating current impedance of a molecular junction.

The small-bias conductance of the C6 molecule, stretched between two metallic leads, is studied using time-dependent density functional theory within the adiabatic local density approximation. The leads are modeled by jellium slabs, the electronic density and the current density are described on a grid, whereas the core electrons and the highly oscillating valence orbitals are approximated using standard norm-conserving pseudopotentials. The jellium leads are supplemented by a complex absorbing potential that serves to absorb charge reaching the edge of the electrodes and hence mimic irreversible flow into the macroscopic metal. The system is rapidly exposed to a ramp potential directed along the C6 axis, which gives rise to the onset of charge and current oscillations. As time progresses, a fast redistribution of the molecular charge is observed, which translates into a direct current response. Accompanying the dc signal, alternating current fluctuations of charge and currents within the molecule and the metallic leads are observed. These form the complex impedance of the molecule and are especially strong at the plasmon frequency of the leads and the lowest excitation peak of C6. We study the molecular conductance in two limits: the strong coupling limit, where the edge atoms of the chain are submerged in the jellium and the weak coupling case, where the carbon atoms and the leads do not overlap spatially.