Two-dimensional Electron Liquid Research Articles

Electronic rotons and Wigner crystallites in a two-dimensional dipole liquid.

A key concept proposed by Landau to explain superfluid liquid helium is the elementary excitation of quantum particles called rotons1-8. The irregular arrangement of atoms in a liquid leads to the aperiodic dispersion of rotons, which played a pivotal role in understanding fractional quantum Hall liquids (magneto-rotons)9,10 and the supersolidity of Bose-Einstein condensates11-13. Even for a two-dimensional electron or dipole liquid, in the absence of a magnetic field, the repulsive interactions have been predicted to form a roton minimum14-19, which can be used to trace the transition to Wigner crystals20-24 and superconductivity25-27, although this has not yet been observed. Here, we report the observation of such electronic rotons in a two-dimensional dipole liquid of alkali-metal ions donating electrons to surface layers of black phosphorus. Our data reveal the striking aperiodic dispersion of rotons, which is characterized by a local minimum of energy at finite momentum. As the density of dipoles decreases so that interactions dominate over the kinetic energy, the roton gap reduces to 0, as in a crystal, signalling Wigner crystallization. Our model shows the importance of short-range order arising from repulsion between dipoles, which can be viewed as the formation of Wigner crystallites (bubbles or stripes) floating in the sea of a Fermi liquid. Our results reveal that the primary origin of electronic rotons (and the pseudogap) is strong correlations.

Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices

Stacking and twisting graphene layers allows to create and control a two-dimensional electron liquid with strong correlations. Experiments indicate that these systems exhibit strong tendencies towards both magnetism and triplet superconductivity. Motivated by this phenomenology, we study a 2D model of fluctuating triplet pairing and spin magnetism. Individually, their respective order parameters, d and N, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-4e superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite d ⋅ N, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi level can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This provides a possible explanation for recent tunneling experiments in the superconducting phase of graphene moiré systems.

Shear Bernstein modes in a two-dimensional electron liquid

Shear Bernstein modes in a two-dimensional electron liquid

Scale-dependent theory of the disordered electron liquid

We review the scaling theory of disordered itinerant electrons with e−e interactions. We first show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions (Finkel’stein’s model). This model is closely connected to the Fermi liquid, but is more generally applicable, since it can also be viewed as a minimal effective functional describing disordered interacting electrons. Our discussion emphasizes the general structure of the theory, and the connection of the scaling parameters to conservation laws. We then move on to discuss the metal–insulator transition (MIT) in the disordered electron liquid in two and three dimensions. Generally speaking, this MIT is a non-trivial example of a quantum phase transition. The NLSM approach allows to identify the dynamical exponent connecting the spatial and energy scales, which is central for the description of the kinetic and thermodynamic behavior of the system in the critical region of the MIT in three dimensions. In two dimensions, the system can be discussed in terms of a flow in the disorder-interaction phase plane, which is controlled by a fixed point. We demonstrate that the two-parameter RG-equations accurately describe electrons in Si-MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The theory can also be applied to systems with an attractive interaction in the Cooper channel, where it describes the suppression of superconductivity in disordered amorphous films. We extend our discussion to heat transport in the two-dimensional electron liquid. Similar to the electric conductivity, the thermal conductivity also acquires logarithmic corrections induced by the interplay of the electron interaction and disorder. The resulting thermal conductivity can be calculated in the NLSM formalism after introducing so-called gravitational potentials. It may be concluded that the combined effect of disorder and e−e interactions determines all aspects of the physics of itinerant electrons in the presence of disorder.

Fermiology of Topological Metals

The modern scope of fermiology encompasses not just the classical geometry of Fermi surfaces but also the geometry of quantum wave functions over the Fermi surface. This enlarged scope is motivated by the advent of topological metals—metals whose Fermi surfaces are characterized by a robustly nontrivial Berry phase. We review the extent to which topological metals can be diagnosed from magnetic-field-induced quantum oscillations of transport and thermodynamic quantities. A holistic analysis of the oscillatory wave form is proposed, in which different characteristics of the wave form (e.g., phase offset, high-harmonic amplitudes, temperature-dependent frequency) encode different aspects of a topologically nontrivial Fermi surface. Which characteristic to focus on depends on ( a) the orientation of the magnetic field relative to certain crystallographic axes, ( b) the symmetry class of the topological metal, and ( c) the separation of Fermi-surface pockets in quasimomentum [Formula: see text] space. Closely proximate pockets arise when (1) spin–split pockets are nearly overlapping due to a weak spin–orbit force or when (2) two pockets touch at an isolated [Formula: see text] point, which can be a topological band-touching point or a saddlepoint in the energy-momentum dispersion. The emergence of a pseudospin degree of freedom (in case 1) and the implications of magnetic breakdown (in case 2) are reviewed, with emphasis on new aspects originating from the (nonabelian) Berry connection of the Fermi surface. Future extensions of topofermiology are suggested in the directions of interaction-induced Fermi-liquid instabilities and two-dimensional electron liquids.

Acoustic plasmons and isotropic short-range interaction in two-component electron liquids

Dispersion of acoustic plasmons and isotropic Landau parameters are calculated in three- and two-dimensional two-component electron-electron and electron-hole liquids at various concentration and mass ratios using Landau-Silin kinetic equation and the random phase approximation for the self-energy. It is shown that the mode propagation and the strength of quasiparticle interaction are determined by the intercomponent screening and are asymmetric with respect to charge composition of two-component liquid. The well-defined acoustic plasmon-zero sound mode arises at strong difference in concentrations between components and its renormalization by the short-range exchange-correlation interaction is negligible. The acoustic plasmon mediated interparticle effective interaction in the fast component is weak in both the three- and two-dimensional electron liquids with parabolic dispersion, so the associated plasmonic superconductivity and the formation of acoustic plasmarons are unfavorable.

Many-body correction to the intrinsic anomalous and spin Hall conductivities

Broken Galilean invariance in a spin-orbit coupled system can amplify many-body effects on its different responses. We study the anomalous Hall and spin Hall conductivities of a magnetic two-dimensional electron gas with Rashba spin-orbit coupling. We show that both of these conductivities in the intrinsic limit are fully specified in terms of the longitudinal and transverse spin-spin response functions. We include the effect of electron-electron interaction in the spin-spin linear response functions, going beyond the random-phase approximation. We do this by incorporating the local-field correction in the response functions, which takes into account the many-body exchange-correlation effects. We observe a significant enhancement of the static anomalous Hall conductivity due to the electron-electron interaction. The many-body correction on the spin Hall effects is more non-trivial, and strong electron-electron interaction can even reverse the sign of the static spin Hall conductivity.

Decoupling the conduction from redox reaction and electronic reconstruction at polar oxide interfaces

The physical properties of oxide heterointerfaces depend crucially on the electronic and ionic reconstructions across the interface. For the formation of a two-dimensional electron liquid (2DEL) at the interface of ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ (LAO/STO) systems, although it is well accepted that the conduction of amorphous-LAO/STO samples comes exclusively from the oxygen vacancies due to interfacial redox reactions, the relative contribution of ionic reconstruction and electronic reconstruction to the conduction at the polar crystalline LAO/STO interface has been a topic of debate. Herein, by resonant x-ray photoemission spectroscopy and x-ray absorption spectroscopy measurements, we investigated the evolution of the Ti $2p$ signal as well as the in-gap states at the diluted oxide interface of $\mathrm{La}{\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{O}}_{3}/\mathrm{STO}$ $(0\ensuremath{\le}x\ensuremath{\le}0.3)$, where the doping of Mn into LAO gradually decreases the carrier density of the interfacial 2DEL but does not change the interface polarity. The spectroscopic results present direct evidence that the conduction from redox reaction at polar LAO/STO interfaces is suppressed by increasing the Mn doping level without the need of oxygen postannealing. A pure polarity discontinuity induced electronic reconstruction can be achieved by deliberately controlling the Mn doping level in LAO, which results in low-carrier, high-mobility, and spin-polarized 2DELs at $x=0.3$.

Intrinsic versus extrinsic orbital and electronic reconstructions at complex oxide interfaces

The interface between the insulators ${\mathrm{LaAlO}}_{3}$ (LAO) and ${\mathrm{SrTiO}}_{3}$ accommodates a two-dimensional electron liquid (2DEL)---a high-mobility electron system exhibiting superconductivity as well as indications of magnetism and correlations. While this flagship oxide heterostructure shows promise for electronics applications, the origin and microscopic properties of the 2DEL remain unclear. The uncertainty remains in part because the electronic structures of such nanoscale-buried interfaces are difficult to probe and is compounded by the variable presence of oxygen vacancies and coexistence of both localized and delocalized charges. These various complications have precluded decisive tests of intrinsic electronic and orbital reconstruction at this interface. Here we overcome prior difficulties by developing an interface analysis based on the inherently interface-sensitive resonant x-ray reflectometry. We discover a high-charge density of 0.5 electrons per interfacial unit cell (u.c.) for samples above the critical LAO thickness and extract the depth dependence of both the orbital and the electronic reconstructions near the buried interface. We find that the majority of the reconstruction phenomena are confined to within 2 u.c. of the interface, and we quantify how oxygen vacancies significantly affect the electronic system. Our results provide strong support for the existence of polarity-induced electronic reconstruction, clearly separating its effects from those of oxygen vacancies.

Transition from a uni- to a bimodal interfacial charge distribution in hbox {LaAlO}_3/hbox {SrTiO}_3 upon cooling

We present a combined resonant soft X-ray reflectivity and electric transport study of hbox {LaAlO}_3/hbox {SrTiO}_3 field effect devices. The depth profiles with atomic layer resolution that are obtained from the resonant reflectivity reveal a pronounced temperature dependence of the two-dimensional electron liquid at the hbox {LaAlO}_3/hbox {SrTiO}_3 interface. At room temperature the corresponding electrons are located close to the interface, extending down to 4 unit cells into the hbox {SrTiO}_3 substrate. Upon cooling, however, these interface electrons assume a bimodal depth distribution: They spread out deeper into the hbox {SrTiO}_3 and split into two distinct parts, namely one close to the interface with a thickness of about 4 unit cells and another centered around 9 unit cells from the interface. The results are consistent with theoretical predictions based on oxygen vacancies at the surface of the hbox {LaAlO}_3 film and support the notion of a complex interplay between structural and electronic degrees of freedom.

Hydrodynamic inverse Faraday effect in a two-dimensional electron liquid

We show that a small conducting object, such as a nanosphere or a nanoring, embedded into or placed in the vicinity of the two-dimensional electron liquid (2DEL) and subjected to a circularly polarized electromagnetic radiation induces ``twisted'' plasmonic oscillations in the adjacent 2DEL. The oscillations are rectified due to the hydrodynamic nonlinearities leading to the helicity sensitive circular dc current and to a magnetic moment. This hydrodynamic inverse Faraday effect (HIFE) can be observed at room temperature in different materials. The HIFE is dramatically enhanced in a periodic array of the nanospheres forming a resonant plasmonic coupler. Such a coupler exposed to a circularly polarized wave converts the entire 2DEL into a vortex state. Hence, the twisted plasmonic modes support resonant plasmonic-enhanced gate-tunable optical magnetization. Due to the interference of the plasmonic and Drude contributions, the resonances have an asymmetric Fano-like shape. These resonances present a signature of the 2DEL properties not affected by contacts and interconnects and, therefore, providing the most accurate information about the 2DEL properties. In particular, the widths of the resonances encode direct information about the momentum relaxation time and viscosity of the 2DEL.

Mobility of a spatially modulated electron liquid on the helium surface

We present the results of large-scale numerical simulations of the mobility of a two-dimensional electron liquid on the helium surface in the presence of a one-dimensional periodic potential. Even where the potential is much weaker than the electron-electron interaction, it can strongly change the mobility. The effect depends on the interrelation between the potential period and the mean interelectron distance. It is most pronounced where the period is close to the period of the Wigner crystal that would form if the liquid were cooled to a lower temperature. The results suggest, in particular, that the correlation length in the electron liquid can be found by measuring the mobility in a weak periodic potential. The simulations are based on the microscopic model of the electron scattering by the excitations in helium.

Stokes flow around an obstacle in viscous two-dimensional electron liquid

The electronic analog of the Poiseuille flow is the transport in a narrow channel with disordered edges that scatter electrons in a diffuse way. In the hydrodynamic regime, the resistivity decreases with temperature, referred to as the Gurzhi effect, distinct from conventional Ohmic behaviour. We studied experimentally an electronic analog of the Stokes flow around a disc immersed in a two-dimensional viscous liquid. The circle obstacle results in an additive contribution to resistivity. If specular boundary conditions apply, it is no longer possible to detect Poiseuille type flow and the Gurzhi effect. However, in flow through a channel with a circular obstacle, the resistivity decreases with temperature. By tuning the temperature, we observed the transport signatures of the ballistic and hydrodynamic regimes on the length scale of disc size. Our experimental results confirm theoretical predictions.

Optical excitations in compressible and incompressible two-dimensional electron liquids

Optically generated electron-hole pairs can probe strongly correlated electronic matter, or, by forming exciton-polaritons within an optical cavity, give rise to photonic nonlinearities. The present paper theoretically studies the properties of electron-hole pairs in a two-dimensional electron liquid in the fractional quantum Hall regime. In particular, we quantify the effective interactions between optical excitations by numerically evaluating the system's energy spectrum under the assumption of full spin and Landau level polarization. Optically most active are those pair excitations which do not modify the correlations of the electron liquid, also known as multiplicative states. In the case of spatial separation of electrons and holes, these excitations interact repulsively with each other. However, when the electron liquid is compressible, other non-multiplicative configurations occur at lower energies. The interactions of such dark excitations strongly depend on the liquid, and can also become attractive. For the case of a single excitation, we also study the effect of Landau level mixing in the valence band which can dramatically change the effective mass of an exciton.

Role of point and line defects on the electronic structure of LaAlO3/SrTiO3 interfaces

Realization of heterostructures containing multiple two-dimensional electron liquids requires a fine control of the fabrication process. Here, we report a structural and spectroscopy study of LaAlO3/SrTiO3/LaAlO3 trilayers grown on the SrTiO3 substrate by pulsed-laser deposition. Scanning transmission electron microscopy with the help of ab initio calculations reveals that antisite defects associated with oxygen vacancies are primarily present in the SrTiO3 film (STO-f) close to the p-type interface (STO-f/LaAlO3), while oxygen vacancies prevail close to the top n-type interface (LaAlO3/STO-f). At the same interface, misfit dislocations relax the tensile strain of the top LaAlO3 layer. Combining x-ray absorption spectroscopy, x-ray linear dichroism, resonant photoemission spectroscopy, and electron energy loss spectroscopy, we observe that the 3d orbital reconstruction at the interface between LaAlO3 and the SrTiO3 substrate is confined over a few interfacial Ti planes while, at the top n-type interface (LaAlO3/STO-f), the absence of a dichroic signal can be related to the blurring of the interfacial orbital reconstruction due to the heterogeneity of defects.

Magnetic two-dimensional electron liquid at the surface of Heusler semiconductors

Conducting and magnetic properties of a material often change in some confined geometries. However, a situation where a non-magnetic semiconductor becomes both metallic and magnetic at the surface is quite rare, and to the best of our knowledge has never been observed in experiment. In this work, we employ first-principles electronic structure theory to predict that such a peculiar magnetic state emerges in a family of quaternary Heusler compounds. We investigate magnetic and electronic properties of CoCrTiP, FeMnTiP and CoMnVAl. For the latter material, we also analyse the magnetic exchange interactions and use them for parametrizing an effective spin Hamiltonian. According to our results, magnetism in this material should persist at temperatures at least as high as 155 K.

Dynamic response of partially spin- and valley-polarised two-dimensional electron liquids

The growing field of valleytronics provides new promising physics. Here, we focus on the collective modes of an infinitely thin electron layer with a binary valley degree of freedom that is unequally occupied. The spin populations are allowed to be imbalanced, too. This system can support four collective modes and two anti-resonances emerge. We study this copious dynamics in the spin- and valley-sensitive random phase approximation (RPA) and explain the uncommon behaviour by building a bridge from the many-fermion system to its bosonic counterpart. For completeness, we also report the RPA exchange and correlation energies for arbitrary spin and valley polarisation. A phase transition occurs at from the four-component to the ferro-magnetic, single-valley-occupation state.

Metamorphoses of Electron Systems Hosting a Fermion Condensate

We present a unified theory of strongly correlated electron systems with a fermion condensate. This theoretical framework facilitates quantitative analysis and explanation, on an equal footing, of (i) non-Fermi-liquid behavior of high-Tc superconductors in which the critical temperature for superconductivity is proportional to the Fermi energy TF and (ii) the so-called quantum electron solid state in the two-dimensional electron liquid of MOSFETs and SiGe/Si/SiGe quantum wells. In this framework, low-temperature chaotic-like behavior that is documented in experimental studies of these systems is attributed to a spontaneous topological rearrangement of the conventional Landau state, quite in contrast to models in which the chaotic element is introduced deliberately in terms of a chaotic distribution of interaction matrix elements.

Growing a LaAlO3/SrTiO3 heterostructure on Ca2Nb3O10 nanosheets

The two-dimensional electron liquid which forms between the band insulators LaAlO3 (LAO) and SrTiO3 (STO) is a promising component for oxide electronics, but the requirement of using single crystal SrTiO3 substrates for the growth limits its applications in terms of device fabrication. It is therefore important to find ways to deposit these materials on other substrates, preferably Si, or Si-based, in order to facilitate integration with existing technology. Interesting candidates are micron-sized nanosheets of Ca2Nb3O10 which can be used as seed layers for perovskite materials on any substrate. We have used low-energy electron microscopy (LEEM) with in-situ pulsed laser deposition to study the subsequent growth of STO and LAO on such flakes which were deposited on Si. We can follow the morphology and crystallinity of the layers during growth, as well as fingerprint their electronic properties with angle resolved reflected electron spectroscopy. We find that STO layers, deposited on the nanosheets, can be made crystalline and flat; that LAO can be grown in a layer-by-layer fashion; and that the full heterostructure shows the signature of the formation of a conducting interface.

Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions

Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall effect. Effective theory approach and exact diagonalization in a disk and torus geometries proves the existence of the counter-propagating edge modes with opposite spin polarizations at the boundary between the two neighboring regions of the two-dimensional electron liquid in spin-polarized and spin-unpolarized phases. By analytical and numerical analysis, we argue that these systems can host parafermions when coupled to an s-wave superconductor and are experimentally feasible. We investigate settings based on $\nu=\frac{2}{3}$, $\nu=\frac{4}{3}$ and $\nu=\frac{5}{3}$ spin transitions and analyze spin-flipping interactions that hybridize counter-propagating modes. Finally, we discuss spin-orbit interactions of composite fermions.