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We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields (B), of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, Bc2. Our higher-disorder samples undergo a B-induced transition into a strongly insulating state, which terminates at higher B's forming an insulating peak. We demonstrate that the B terminating this peak coincides with Bc2 of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime. [ABSTRACT FROM AUTHOR]

We report a novel method for the fabrication of superconducting nano-devices based on niobium. The well-known difficulties of lithographic patterning of high-quality niobium are overcome by replacing the usual organic resist mask by a metallic one. The quality of the fabrication procedure is demonstrated by the realization and characterization of long and narrow superconducting lines and niobium-gold-niobium proximity SQUIDs. [ABSTRACT FROM AUTHOR]

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the 'superinsulating' phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T < 0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator. [ABSTRACT FROM AUTHOR]

We report the coexistence of charge puddles and topographic ripples in graphene decoupled from the Ir( 111) substrate it was grown on. We show the topographic and the charge disorder to be locally correlated as a result of the intercalation of molecular species. From the analysis of quasiparticle scattering interferences, we find a linear dispersion relation, demonstrating that graphene on a metal can recover its intrinsic electronic properties. The measured Fermi velocity VF = 0.9 ± 0.04×106 m/s is lower than in graphene on dielectric substrates, pointing to a strong screening of electron-electron interactions in graphene by the nearby metallic substrate. [ABSTRACT FROM AUTHOR]

We study the response of high-critical-current proximity Josephson junctions to a microwave excitation. Electron overheating in such devices is known to create hysteretic dc voltage-current characteristics. Here we demonstrate that it also strongly influences the ac response. The interplay of electron overheating and ac Josephson dynamics is revealed by the evolution of the Shapiro steps with the microwave drive amplitude. Extending the resistively shunted Josephson junction model by including a thermal balance for the electronic bath coupled to phonons, a strong electron overheating is obtained. [ABSTRACT FROM AUTHOR]

Thin films of amorphous indium oxide undergo a magnetic field driven superconducting to insulator quantum phase transition. In the insulating phase, the current-voltage characteristics show large current discontinuities due to overheating of electrons. We show that the onset voltage for the discontinuities vanishes as we approach the quantum critical point. As a result, the insulating phase becomes unstable with respect to any applied voltage making it, at least experimentally, immeasurable. We emphasize that unlike previous reports of the absence of linear response near quantum phase transitions, in our system, the departure from equilibrium is discontinuous. Because the conditions for these discontinuities are satisfied in most insulators at low temperatures, and due to the decay of all characteristic energy scales near quantum phase transitions, we believe that this instability is general and should occur in various systems while approaching their quantum critical point. Accounting for this instability is crucial for determining the critical behavior of systems near the transition. [ABSTRACT FROM AUTHOR]

We report a study of the relaxation time of the restoration of the resistive superconducting state in single crystalline boron-doped diamond using amplitude-modulated absorption of (sub-)THz radiation (AMAR). The films grown on an insulating diamond substrate have a low carrier density of about 2.5?1021cm-3 and a critical temperature of about 2K. By changing the modulation frequency we find a high-frequency rolloff which we associate with the characteristic time of energy relaxation between the electron and the phonon systems or the relaxation time for nonequilibrium superconductivity. Our main result is that the electron-phonon scattering time varies clearly as T-2, over the accessible temperature range of 1.7 to 2.2 K. In addition, we find, upon approaching the critical temperature Tc, evidence for an increasing relaxation time on both sides of Tc. [ABSTRACT FROM AUTHOR]

The pairing of electrons is ubiquitous in electronic systems featuring attractive inter-electron interactions, as exemplified in superconductors. Counterintuitively, it can also be mediated in certain circumstances by the repulsive Coulomb interaction alone. Quantum Hall (QH) Fabry-Pérot interferometers (FPIs) tailored in a two-dimensional electron gas under a perpendicular magnetic field have been argued to exhibit such an unusual electron pairing, seemingly without attractive interactions. Here, we show evidence in graphene QH FPIs, revealing not only a similar electron pairing at bulk filling factor ν B  = 2, but also an unforeseen emergence of electron tripling characterized by a fractional Aharonov-Bohm flux period of h/3e (h is the Planck constant and e the electron charge) at ν B  = 3. Leveraging plunger-gate spectroscopy, we demonstrate that electron pairing (tripling) involves correlated charge transport on two (three) entangled QH edge channels. This spectroscopy indicates a quantum interference flux periodicity determined by the sum of the phases acquired by the distinct QH edge channels having slightly different interfering areas. Phase jumps observed in the pajama maps can be accounted for by the frequency beating between pairing/tripling modes and the outer interfering edge., Competing Interests: Competing interests: The authors declare no competing interests., (© 2024. The Author(s).)

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, e.g. , snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers., (Creative Commons Attribution license.)

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation 1-3 . However, despite recent experimental progress towards this hybridization 4-15 , concrete evidence for a chiral QH Josephson junction 16 -the elemental building block for coherent superconducting QH circuits-is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ 0 magnetic flux periodicity 16-19 (ϕ 0  = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e 2  ≈ 12.9 kΩ. We observe reproducible 2ϕ 0 -periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface 19-22 . Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes 23-32 ., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

Abstarct: When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy 1-5 . The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders 6-11 . Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy 12 or by dielectric screening of the Coulomb interaction 13 . However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders 14 . Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition 15,16 . Under dielectric screening, a sublattice-unpolarized ground state 13 emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions 6-10 . This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Electron interferometry with quantum Hall (QH) edge channels in semiconductor heterostructures can probe and harness the exchange statistics of anyonic excitations. However, the charging effects present in semiconductors often obscure the Aharonov-Bohm interference in QH interferometers and make advanced charge-screening strategies necessary. Here we show that high-mobility monolayer graphene constitutes an alternative material system, not affected by charging effects, for performing Fabry-Pérot QH interferometry in the integer QH regime. In devices equipped with gate-tunable quantum point contacts acting on the edge channels of the zeroth Landau level, we observe-in agreement with theory-high-visibility Aharonov-Bohm interference widely tunable through electrostatic gating or magnetic fields. A coherence length of 10 μm at a temperature of 0.02 K allows us to further achieve coherently coupled double Fabry-Pérot interferometry. In future, QH interferometry with graphene devices may enable investigations of anyonic excitations in fractional QH states.

The ground state of charge-neutral graphene under perpendicular magnetic field was predicted to be a quantum Hall topological insulator with a ferromagnetic order and spin-filtered, helical edge channels. In most experiments, however, an insulating state is observed that is accounted for by lattice-scale interactions that promote a broken-symmetry state with gapped bulk and edge excitations. We tuned the ground state of the graphene zeroth Landau level to the topological phase through a suitable screening of the Coulomb interaction with the high dielectric constant of a strontium titanate (SrTiO 3 ) substrate. Robust helical edge transport emerged at magnetic fields as low as 1 tesla and withstanding temperatures up to 110 kelvin over micron-long distances. This versatile graphene platform may find applications in spintronics and topological quantum computation., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

For more than two decades, there have been reports on an unexpected metallic state separating the established superconducting and insulating phases of thin-film superconductors. To date, no theoretical explanation has been able to fully capture the existence of such a state for the large variety of superconductors exhibiting it. Here, we show that for two very different thin-film superconductors, amorphous indium oxide and a single crystal of 2H-NbSe 2 , this metallic state can be eliminated by adequately filtering external radiation. Our results show that the appearance of temperature-independent, metallic-like transport at low temperatures is sufficiently described by the extreme sensitivity of these superconducting films to external perturbations. We relate this sensitivity to the theoretical observation that, in two dimensions, superconductivity is only marginally stable.

In most superconductors, the transition to the superconducting state is driven by the binding of electrons into Cooper pairs [1]. The condensation of these pairs into a single, phase coherent, quantum state takes place at the same time as their formation at the transition temperature, T c . A different scenario occurs in some disordered, amorphous, superconductors: Instead of a pairing-driven transition, in-coherent Cooper pairs first pre-form above T c , causing the opening of a pseudogap, and then, at T c , condense into the phase coherent superconducting state [2-11]. Such a two-step scenario implies the existence of a new energy scale, Δ c , driving the collective superconducting transition of the preformed pairs [2-6]. Here we unveil this energy scale by means of Andreev spectroscopy [5, 12] in superconducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at ± Δ c that develop only below T c and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper-pairs., Competing Interests: Competing Interests The authors declare that they have no competing financial interests.

We report on the evolution of the coherent electronic transport through a gate-defined constriction in a high-mobility graphene device from ballistic transport to quantum Hall regime upon increasing the magnetic field. At a low field, the conductance exhibits Fabry-Pérot resonances resulting from the npn cavities formed beneath the top-gated regions. Above a critical field B* corresponding to the cyclotron radius equal to the npn cavity length, Fabry-Pérot resonances vanish, and snake trajectories are guided through the constriction with a characteristic set of conductance oscillations. Increasing further the magnetic field allows us to probe the Landau level spectrum in the constriction and unveil distortions due to the combination of confinement and deconfinement of Landau levels in a saddle potential. These observations are confirmed by numerical calculations.

Strongly disordered superconductors in a magnetic field display many characteristic properties of type-II superconductivity-except at low temperatures, where an anomalous linear temperature dependence of the resistive critical field B c 2 is routinely observed. This behavior violates the conventional theory of superconductivity, and its origin has posed a long-standing puzzle. Here we report systematic measurements of the critical magnetic field and current on amorphous indium oxide films with various levels of disorder. Surprisingly, our measurements show that the B c 2 anomaly is accompanied by mean-field-like scaling of the critical current. Based on a comprehensive theoretical study we argue that these observations are a consequence of the vortex-glass ground state and its thermal fluctuations. Our theory further predicts that the linear-temperature anomaly occurs more generally in both films and disordered bulk superconductors, with a slope that depends on the normal-state sheet resistance, which we confirm experimentally., Competing Interests: Competing Interests The authors declare that they have no competing financial interests.

Charge carriers in the quantum Hall regime propagate via one-dimensional conducting channels that form along the edges of a two-dimensional electron gas. Controlling their transmission through a gate-tunable constriction, also called quantum point contact, is fundamental for many coherent transport experiments. However, in graphene, tailoring a constriction with electrostatic gates remains challenging due to the formation of p-n junctions below gate electrodes along which electron and hole edge channels co-propagate and mix, short circuiting the constriction. Here we show that this electron-hole mixing is drastically reduced in high-mobility graphene van der Waals heterostructures thanks to the full degeneracy lifting of the Landau levels, enabling quantum point contact operation with full channel pinch-off. We demonstrate gate-tunable selective transmission of integer and fractional quantum Hall edge channels through the quantum point contact. This gate control of edge channels opens the door to quantum Hall interferometry and electron quantum optics experiments in the integer and fractional quantum Hall regimes of graphene.

Three-dimensional topological insulators are characterized by the presence of a bandgap in their bulk and gapless Dirac fermions at their surfaces. New physical phenomena originating from the presence of the Dirac fermions are predicted to occur, and to be experimentally accessible via transport measurements in suitably designed electronic devices. Here we study transport through superconducting junctions fabricated on thin Bi(2)Se(3) single crystals, equipped with a gate electrode. In the presence of perpendicular magnetic field B, sweeping the gate voltage enables us to observe the filling of the Dirac fermion Landau levels, whose character evolves continuously from electron- to hole-like. When B=0, a supercurrent appears, whose magnitude can be gate tuned, and is minimum at the charge neutrality point determined from the Landau level filling. Our results demonstrate how gated nano-electronic devices give control over normal and superconducting transport of Dirac fermions at an individual surface of a three-dimensional topological insulators.

We report transport measurements through graphene on SrTiO(3) substrates as a function of magnetic field B, carrier density n, and temperature T. The large dielectric constant of SrTiO(3) very effectively screens long-range electron-electron interactions and potential fluctuations, making Dirac electrons in graphene virtually noninteracting. The absence of interactions results in an unexpected behavior of the longitudinal resistance in the N=0 Landau level and in a large suppression of the transport gap in nanoribbons. The "bulk" transport properties of graphene at B=0 T, on the contrary, are completely unaffected by the substrate dielectric constant.

We report on a study of magnetotransport in LaAlO3 /SrTiO3 interfaces characterized by mobilities of the order of several thousands cm2/V s. We observe Shubnikov-de Haas oscillations whose period depends only on the perpendicular component of the magnetic field. This observation directly indicates the formation of a two-dimensional electron gas originating from quantum confinement at the interface. From the temperature dependence of the oscillation amplitude we extract an effective carrier mass m* ≃ 1.45 m(e). An electric field applied in the back-gate geometry increases the mobility, the carrier density, and the oscillation frequency.

A superconducting state is characterized by the gap in the electronic density of states, which vanishes at the superconducting transition temperature T(c). It was discovered that in high-temperature superconductors, a noticeable depression in the density of states, the pseudogap, still remains even at temperatures above T(c). Here, we show that a pseudogap exists in a conventional superconductor, ultrathin titanium nitride films, over a wide range of temperatures above T(c). Our study reveals that this pseudogap state is induced by superconducting fluctuations and favoured by two-dimensionality and by the proximity to the transition to the insulating state. A general character of the observed phenomenon provides a powerful tool to discriminate between fluctuations as the origin of the pseudogap state and other contributions in the layered high-temperature superconductor compounds.

The current-voltage characteristics measured in the insulating state terminating the superconducting phase in disordered superconductors exhibit sharp threshold voltages, where the current abruptly changes by as much as 5 orders of magnitude. We analyze the current-voltage characteristics of an amorphous indium oxide film in the field-tuned insulating state, and show that they are consistent with a bistability of the electron temperature, and with a significant overheating of the electron system above the lattice temperature. An analysis of these current jumps indicates that, in the insulating state, the electrons are thermally decoupled from the phonon bath.

Scanning tunneling spectroscopy at very low temperatures on homogeneously disordered superconducting titanium nitride thin films reveals strong spatial inhomogeneities of the superconducting gap Delta in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature Tc towards zero, enhancement of spatial fluctuations in Delta, and growth of the Delta/Tc ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.

We present the first scanning tunneling spectroscopy study of single-crystalline boron-doped diamond. The measurements were performed below 100 mK with a low temperature scanning tunneling microscope. The tunneling density of states displays a clear superconducting gap. The temperature evolution of the order parameter follows the weak-coupling BCS law with Delta(0)/kBTc approximately 1.74. Vortex imaging at low magnetic field also reveals localized states inside the vortex core that are unexpected for such a dirty superconductor.