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Imaging Hydrodynamic Electrons Flowing Without Landauer-Sharvin Resistance

C. Kumar, J. Birkbeck, J.A. Sulpizio, D. Perello, T. Taniguchi, K. Watanabe, O. Reuven, T. Scaffidi, Ady Stern, A.K. Geim, and S. Ilani

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conduction limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron-transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length-scale predicted by hydrodynamic theories – the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies.

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Spread and Erase - 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. Counter-intuitively, 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.

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Entropic evidence for a Pomeranchuk effect in magic angle graphene

A. Rozen, J.M. Park, U. Zondiner, Y. Cao, D. Rodan-Legrain,  T. Taniguchi, K. Watanabe, Y. Oreg,  Ady Stern, E. Berg, P. Jarillo-Herrero and S. Ilani

In the 1950's, Pomeranchuk predicted that, counterintuitively, liquid 3He may solidify upon heating, due to a high excess spin entropy in the solid phase. Here, using both local and global electronic entropy and compressibility measurements, we show that an analogous effect occurs in magic angle twisted bilayer graphene. Near a filling of one electron per moiré unit cell, we observe a dramatic increase in the electronic entropy to about 1kB per unit cell. 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 with magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump onsets at T~30K, the bandwidth of magnetic excitations is ~3K or smaller. The hybrid nature of the new correlated state and the large separation of energy scales have key implications for the physics of correlated states in twisted bilayer graphene.

News & Views:  Biao Lian, "Heating Freezes electrons in twisted bilayer graphene"

Condmat Journal Club: Paco Guinea, "Pomeranchuk effect in twisted bilayer graphene"

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Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene

U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, Ady Stern, E. Berg, P. Jarillo-Herrero and S. Ilani

Twisted bilayer graphene near the magic angle exhibits remarkably rich electron correlation physics, displaying insulating, magnetic, and superconducting phases. Here, using measurements of the local electronic compressibility, we reveal that these phases originate from a high-energy state with an unusual sequence of band populations. As carriers are added to the system, rather than filling all the four spin and valley flavors equally, we find that the population occurs through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. At each transition, a single spin/valley flavor takes all the carriers from its partially filled peers, "resetting" them back to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near the charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breakings.  The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state we reveal here, with its strongly broken electronic flavor symmetry and revived Dirac-like electronic character, is a key player in the physics of magic angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

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Atomic-like Charge Qubit in a Carbon Nanotube Enabling Electric and Magnetic field Nano-sensing

I.Khivrich and S. Ilani

Quantum sensing techniques have been successful in pushing the sensitivity limits in numerous fields, and hold great promise for scanning probes that study nano-scale devices and novel materials. However, forming a nano-scale qubit that is simple and robust enough to be placed on a scanning tip, and sensitive enough to detect various physical observables, is still a great challenge. Here we demonstrate a conceptually new qubit implementation in a carbon nanotube that achieves these requirements. In contrast to the prevailing semiconducting qubits that use electronic states in double quantum dots, our qubit utilizes the natural electronic wavefunctions in a single quantum dot. Using an ultraclean nanotube we construct a qubit from two wavefunctions with significantly different magnetic moments and spatial charge distributions, making it sensitive to both magnetic and electric fields. We use an array of gates to directly image these wavefunctions and demonstrate their localized moments. Owing to their different spatial structure, these wavefunctions also show radically different transport properties, giving us a simple transport-based qubit readout mechanism. Due to its narrow coherence-limited transition, the qubit demonstrates significantly better electric field detection sensitivity than a single electron transistor. Moreover, with the same qubit we demonstrate simultaneous probing of magnetic fields with DC sensitivity comparable to that of NV centers. Our technique has minimal requirements for device complexity, which can be implemented using a number of straightforward fabrication methods. These features make this atomic-like qubit a powerful new tool that enables a variety of new nanoscale imaging experiments.

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Visualizing Poiseuille flow of hydrodynamic electrons

J.A. Sulpizio†, L. Ella†, A. Rozen†, J. Birkbeck, D.J. Perello, D. Dutta, M. BenShalom, T. Taniguchi, K. Watanabe, T. Holder, R. Queiroz, A. Stern, T. Scaffidi, A.K. Geim, and S. Ilani

Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, 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 temperature 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 long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

News & Views: K. Ensslin, “Electrons in graphene go with the flow

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Imaging the Electronic Wigner Crystal in One Dimension

Shapir, I.*, Hamo, A.*, Pecker, S., Moca, C. P., Legeza, Ö., Zarand, G., & Ilani, S.

The quantum crystal of electrons, predicted more than eighty years ago by Eugene Wigner, is still one of the most elusive states of matter. Here, we present experiments that observe the one-dimensional Wigner crystal directly, by imaging its charge density in real-space. To measure this fragile state without perturbing it, we use a scanning probe platform that utilizes a pristine carbon nanotube as a scanning charge perturbation to image, with minimal invasiveness, the many-body electronic density within another nanotube. The obtained images, of few electrons confined in one-dimension, match those of strongly interacting crystals, with electrons ordered like pearls on a necklace. Comparison to theoretical modeling demonstrates the dominance of Coulomb interactions over kinetic energy and the weakness of exchange interactions. The quantum nature of the crystal emerges when we explore its tunneling through a potential barrier. Images of the density redistribution upon tunneling show that the tunneling involves the collective motion of multiple electrons. These experiments provide direct evidence of the formation of small Wigner crystals, and open the way for studying other fragile interacting states by imaging their many-body density in real space.

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

L. Ella, A. Rozen , J. Birkbeck, M. Ben-Shalom, D. Perello , J. Zultak , T. Taniguchi , K. Watanabe , A.K. Geim , S. Ilani , and J.A. Sulpizio*

Electron transport in nanoscale devices can often result in nontrivial spatial patterns of voltage and current that reflect a variety of physical phenomena, 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 magnetic field, across a broad range of temperatures, and beneath an insulating surface. Here we present such 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 both aid in understanding the physics of two-dimensional electronic devices, as well as enable new classes of experiments that image electron flow through buried nanostructures in the quantum and interaction-dominated regimes.

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

I. Khivrich, A. A. Clerk and S. Ilani

The quantum crystal of electrons, predicted more than eighty years ago by Eugene Wigner, is still one of the most elusive states of matter. Here, we present experiments that observe the one-dimensional Wigner crystal directly, by imaging its charge density in real-space. To measure this fragile state without perturbing it, we use a scanning probe platform that utilizes a pristine carbon nanotube as a scanning charge perturbation to image, with minimal invasiveness, the many-body electronic density within another nanotube. The obtained images, of few electrons confined in one-dimension, match those of strongly interacting crystals, with electrons ordered like pearls on a necklace. Comparison to theoretical modeling demonstrates the dominance of Coulomb interactions over kinetic energy and the weakness of exchange interactions. The quantum nature of the crystal emerges when we explore its tunneling through a potential barrier. Images of the density redistribution upon tunneling show that the tunneling involves the collective motion of multiple electrons. These experiments provide direct evidence of the formation of small Wigner crystals, and open the way for studying other fragile interacting states by imaging their many-body density in real space.

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Topological transitions and fractional charges induced by strain and magnetic field in carbon nanotubes

Y. Efroni, S. Ilani, E. Berg

Fractionalized excitations carrying half an electron charge were predicted many years ago to exist in conducting one-dimensional polymers, but so far have never been observed experimentally. Here we propose a rather simple experiment using a tensioned nanotube in a magnetic field that should finally enable the observation of these half-charge quasiparticles.

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Electron Attraction Mediated by Coulomb Repulsion

A. Hamo*, A. Benyamini*, I. Shapir*, I. Khivrich, J. Waissman, K. Kaasbjerg, Y. Oreg, F. von Oppen and S. Ilani

Can electrons be made to attract each other via their repulsion from other electrons?  In this work we demonstrate that this is in fact possible using a novel experimental platform consisting of pristine nanotube-based quantum devices and precision cryogenic manipulation.

News & Views: T. Kontos, “Attractive Electrons from Nanoengineering

Condmat Journal Club: Patrick A. Lee,"Can electrons attract each other without the help of  phonons?"

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Extreme Mobility Enhancement of Two-Dimensional Electron Gases at Oxide Interfaces via Charge Transfer Induced Modulation Doping

YZ Chen, Felix Trier, T Wijnands, RJ Green, N Gauquelin, R Egoavil, Dennis Valbjørn Christensen, G Koster, M Huijben, N Bovet, S Macke, F He, R Sutarto, Niels Hessel Andersen, GEDK Prawiroatmodjo, TS Jespersen, JA Sulpizio, M Honig, Søren Linderoth, S Ilani, Jo Verbeeck, G Van Tendeloo, Guus Rijnders, GA Sawatzky, Nini Pryds

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Nanotube Resound Better

I. Khivrich and S. Ilani

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Nanoscale Phenomena in Oxide Heterostructures

J. A. Sulpizio, S. Ilani, P. Irvin and J. Levy

Recent advances in complex oxide heterostructures, interfaces formed between two different transition-metal oxides, have heralded a new era of materials and physics research. We review the exciting developments in the physics of these systems, with a focus on the nanoscale probes employed to unravel their complex behavior.

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Competition Between Kondo Screening and Magnetism at the LaAlO3/SrTiO3 Interface

J. Ruhman, Arjun Joshua, S. Ilani and E. Altman

The prototypical oxide interface, LAO/STO, is composed of two insulating, nonmagnetic oxides, yet experiments have shown it plays host to a range of magnetic phenomena, including ferromagnetic domains and anisotropic magnetotransport.  We present a theory to unify these various magnetic phases which relies on the coupling between itinerant electrons and localized magnetic moments originating from interfacial charge traps

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Real-Space Tailoring of the Electron-Phonon Coupling in Ultra-Clean Nanotube Mechanical Resonators

A. Benyamini*, A. Hamo*, S. Viola Kusminskiy, F. von Oppen and S. Ilani

Despite tremendous advances in controlling electrons and phonons in engineered nanosystems, control over their coupling is still widely lacking. Here we demonstrate the ability to fully tailor electron-phonon interactions in a new class of nanotube-based mechanical resonators by creating gate-defined quantum dots along the length of the vibrating nanotube

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Local Electrostatic Imaging of Striped Domain Order in LaAlO3/SrTiO3

M. Honig*, J. A. Sulpizio*, J. Drori, A. Joshua, E Zeldov and S. Ilani

Through electrostatic imaging using a novel nanotube-based scanning single electron transistor, we unravel the microscopic origin for the anomalous piezoelectricity in strontium titanate (STO), the substrate used universally in the creation of complex oxide interfaces.  We further demonstrate how tetragonal domains in STO give rise to a striped potential landscape that can markedly influence the flow of electrons through complex oxide interfaces.

News & Views: Alexander Brinkman,  “Oxide interfaces: Streaks of conduction”

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Observation and Spectroscopy of a Two-Electron Wigner-Molecule State in an Ultra-Clean Carbon Nanotube

S. Pecker, F. Kuemmeth, A Secchi, M. Rontani, D. C. Ralph, P. L. McEuen and S. Ilani

In the presence of strong interactions, two electrons confined to a string are predicted to form a Wigner molecule and localize at the end of the string. We create such an electronic state within an ultraclean carbon nanotube, and use tunneling spectroscopy to explore its energy spectrum and quantum symmetry.

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Realization of Pristine and Locally-Tunable One-Dimensional Electron Systems in Carbon Nanotubes

J. Waissman*, M. Honig*, S. Pecker*, A. Benyamini*, A. Hamo* and S. Ilani

The creation of disorder-free and locally-tunable condensed matter systems has remained an outstanding challenge, limiting the ability to design quantum Hamiltonians for electrons.  In this work we establish a new technique for creating such tunable, pristine electron systems in carbon nanotubes suspended over complex electronic circuits, enabling a new era of experiments in quantum electronics and nanomechanics.

News&Views: Z. Zhong, “Pristine quantum devices on demand”.

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Gate-Tunable Polarized Phase of Two-Dimensional Electrons at the LaAlO3/SrTiO3 Interface

Arjun Joshua, J. Ruhman, S. Pecker, E. Altman, and S. Ilani

The LAO/STO interface hosts a novel system consisting of localized magnetic moments and extended 2D electrons.  Using anisotropic magnetotransport and anomalous Hall Effect measurements, we uncover an intrinsic, tunable coupling between the itinerant electrons and localized moments in this interface, resulting in a polarized electronic phase at high densities

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A Universal Critical Density Underlying the Physics of Electrons at the LaAlO3/SrTiO3 Interface

Arjun Joshua, S. Pecker, J. Ruhman, E. Altman, and S. Ilani

While the LAO/STO interface has fascinated researchers with its rich variety of phenomena, including ferromagnetism and superconductivity, the question of the key physical ingredients underlying its emergent properties has remained open.   We reveal here through magnetotransport that a universal Lifshitz transition between d-electron orbitals of different symmetry is fundamental to the multitude of observed effects in LAO/STO.

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Electron Transport in Carbon Nanotubes

S. Ilani and P. McEuen

 

Technological breakthroughs in nanotube device fabrication and electronic measurement have made possible experiments of unprecedented precision that reveal new and surprising phenomena. In this review, we present the fundamental properties of nanotubes along with recent discoveries and discuss the most exciting emerging research directions.

*Denotes equal contribution

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