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Recent advances in materials science have made it possible to achieve conditions under which electrons in metals start behaving as highly viscous fluids, thicker than honey, and exhibit fascinating hydrodynamic effects. In this short review we provide a popular introduction to the emerging field of electron hydrodynamics.
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Graphene hosts a unique electron system in which electron-phonon scattering is extremely weak but electron-electron collisions are sufficiently frequent to provide local equilibrium above liquid nitrogen temperature. Under these conditions, electrons can behave as a viscous liquid and exhibit hydrodynamic phenomena similar to classical liquids. Here we report strong evidence for this transport regime. We find that doped graphene exhibits an anomalous (negative) voltage drop near current injection contacts, which is attributed to the formation of submicrometer-size whirlpools in the electron flow. The viscosity of graphenes electron liquid is found to be ~0.1 m$^2$ /s, an order of magnitude larger than that of honey, in agreement with many-body theory. Our work shows a possibility to study electron hydrodynamics using high quality graphene.
We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.
The properties of the isotropic incompressible $ u=5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+ip_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $ u=5/2$. This finding motivates us to consider an inhomogeneous paired state - a $p_x+ip_y$ pair-density-wave (PDW) - whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and anti-domain walls of the $p_x+i p_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy $E_{F}$ and the PDW pairing energy $E_{textrm{pdw}}$. The analysis of this interplay yields a rich set of topological states. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases - as well as transitions thereof - tuned by the strength of the paired liquid crystalline order.
Fermi liquid theory has been a foundation in understanding the electronic properties of materials. For weakly interacting two-dimensional (2D) electron or hole systems, electron-electron interactions are known to introduce quantum corrections to the Drude conductivity in the FL theory, giving rise to temperature dependent conductivity and magneto-resistance. Here we study the magneto-transport in a strongly interacting 2D hole system over a broad range of temperatures ($T$ = 0.09 to $>$1K) and densities $p=1.98-0.99times10^{10}$ cm$^{-2}$ where the ratio between Coulomb energy and Fermi energy $r_s$ = 20 - 30. We show that while the system exhibits a negative parabolic magneto-resistance at low temperatures ($lesssim$ 0.4K) characteristic of an interacting FL, the FL interaction corrections represent an insignificant fraction of the total conductivity. Surprisingly, a positive magneto-resistance emerges at high temperatures and grows with increasing temperature even in the regime $T sim E_F$, close to the Fermi temperature. This unusual positive magneto-resistance at high temperatures is attributed to the collective viscous transport of 2D hole fluid in the hydrodynamic regime where holes scatter frequently with each other. These findings highlight the collective transport in a strongly interacting 2D system in the $r_sgg 1$ regime and the hydrodynamic transport induced magneto-resistance opens up possibilities to new routes of magneto-resistance at high temperatures.
We study the transport through a molecular junction exhibiting interference effects. We show that these effects can still be observed in the presence of molecular vibrations if Coulomb repulsion is taken into account. In the Kondo regime, the conductance of the junction can be changed by several orders of magnitude by tuning the levels of the molecule, or displacing a contact between two atoms, from nearly perfect destructive interference to values of the order of 2e 2 /h expected in Kondo systems. We also show that this large conductance change is robust for reasonable temperatures and voltages for symmetric and asymmetric tunnel couplings between the source-drain electrodes and the molecular orbitals. This is relevant for the development of quantum interference effect transistors based on molecular junctions.
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