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Hybrid superconductor/semiconductor devices constitute a powerful platform where intriguing topological properties can be investigated. Here we present fabrication methods and analysis of Josephson junctions formed by a high-mobility InAs quantum-well bridging two Nb superconducting contacts. We demonstrate supercurrent flow with transport measurements, critical temperature of 8.1 K, and critical fields of the order of 3 T. Modulation of supercurrent amplitude can be achieved by acting on two side gates lithographed close to the two-dimensional electron gas. Low-temperature measurements reveal also well-developed quantum Hall plateaus, showing clean quantization of Hall conductance. Here the side gates can be used to manipulate channel width and electron carrier density in the device. These findings demonstrate the potential of these hybrid devices to investigate the coexistence of superconductivity and Quantum Hall effect and constitute the first step in the development of new device architectures hosting topological states of matter.

We study energy transport in the integrable $\mathbb Z_3$ parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the non-equilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge $c=4/5$, which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with $c=1$. By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a novel framework, where it can be profitably used for exploring new physical phenomena., Comment: 13 pages, 12 figures

We propose a device based on a topological Josephson junction where the helical edge states of a two-dimensional topological insulator are in close proximity to two superconducting leads. The presence of a magnetic flux through the junction leads to a Doppler shift in the spectrum of Andreev bound states, and affects the quantum interference between proximized edge states. We inspect the emergent features, accessing the density of states through a tunnel-coupled metallic probe, thus realizing a Topological Superconducting Quantum Interference Proximity Transistor (TSQUIPT). We calculate the expected performances of this new device, concluding that it can be used as a sensitive, absolute magnetometer due to the voltage drop across the junction decaying to a constant value as a function of the magnetic flux. Contrary to conventional SQUID and SQUIPT designs, no ring structure is needed. The findings pave the way for novel and sensitive devices based on hybrid devices that exploit helical edge states., Comment: 8 pages, 7 figures

It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law $\propto t^{-2}$ in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour $\propto t^{-2}$ is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour., Comment: 22 pages, 5 figures. Submission to SciPost

We discuss the quasiparticle entropy and heat capacity of a dirty superconductor-normal metal-superconductor junction. In the case of short junctions, the inverse proximity effect extending in the superconducting banks plays a crucial role in determining the thermodynamic quantities. In this case, commonly used approximations can violate thermodynamic relations between supercurrent and quasiparticle entropy. We provide analytical and numerical results as a function of different geometrical parameters. Quantitative estimates for the heat capacity can be relevant for the design of caloritronic devices or radiation sensor applications., Comment: 7 pages, 5 figures

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay in system spectral properties $ \propto t^{-2} $, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay $ \propto t^{-2} $ induced by entanglement and represents a novel way to study the corresponding relaxation mechanism., Comment: 11 pages, 3 figures

Charge and energy fractionalization are among the most intriguing features of interacting onedimensional fermion systems. In this work we determine how these phenomena are modified in the presence of an interaction quench. Charge and energy are injected into the system suddenly after the quench, by means of tunneling processes with a non-interacting one-dimensional probe. Here, we demonstrate that the system settles to a steady state in which the charge fractionalization ratio is unaffected by the pre-quenched parameters. On the contrary, due to the post-quench nonequilibrium spectral function, the energy partitioning ratio is strongly modified, reaching values larger than one. This is a peculiar feature of the non-equilibrium dynamics of the quench process and it is in sharp contrast with the non-quenched case, where the ratio is bounded by one., Comment: 12 pages, 4 figures

The possibility to inject a single electron into ballistic conductors is at the basis of the new field of electron quantum optics. Here, we consider a single electron injection into the helical edge channels of a topological insulator. Their counterpropagating nature and the unavoidable presence of electron-electron interactions dramatically affect the time evolution of the single wavepacket. Modeling the injection process from a mesoscopic capacitor in presence of non-local tunneling, we focus on the time resolved charge and energy packet dynamics. Both quantities split up into counterpropagating contributions whose profiles are strongly affected by the interactions strength. In addition, stronger signatures are found for the injected energy, which is also affected by the finite width of the tunneling region. Indeed, the energy flow can be controlled by tuning the injection parameters and we demonstrate that, in presence of non-local tunneling, it is possible to achieve situation in which charge and energy flow in opposite directions., Comment: 13 pages, 8 figures

The time-dependent energy transfer in a driven quantum system strongly coupled to a heat bath is studied within an influence functional approach. Exact formal expressions for the statistics of energy dissipation into the different channels are derived. The general method is applied to the driven dissipative two-state system. It is shown that the energy flows obey a balance relation, and that, for strong coupling, the interaction may constitute the major dissipative channel. Results in analytic form are presented for a particular value of strong Ohmic dissipation. The energy flows show interesting behaviors including driving-induced coherences and quantum stochastic resonances., Comment: 7 pages, 2 figures

We consider thermoelectric transport properties of the edge states of a two dimensional topological insulator in a double quantum point contact geometry coupled to two thermally biased reservoirs. Both spin-preserving and spin-flipping tunneling processes between opposite edges are analyzed in the presence of electron-electron interactions. We demonstrate that the simultaneous presence of spin-flipping processes and interactions gives rise to a finite longitudinal spin current. Moreover, its sign and amplitude can be tuned by means of gate voltages with the possibility to generate a pure spin current, with a vanishing charge current., Comment: 9 pages, 7 figures

We consider a two level system coupled to a thermal bath and we investigate the variation of energy transferred to the reservoir as a function of time. The physical quantity under investigation is the time-dependent quantum average power. We compare quantum master equation approaches with functional influence method. Differences and similarities between the methods are analyzed, showing deviations at low temperature between the functional integral approach and the predictions based on master equations., Comment: 13 pages, 2 figures, proceeding of the conference UPoN 2015

We analyze the time evolution of spin-polarized electron wave packets injected into the edge states of a two-dimensional topological insulator. In the presence of electron interactions, the system is described as a helical Luttinger liquid and injected electrons fractionalize. However, because of the presence of metallic detectors, no evidences of fractionalization are encoded in dc measurements, and in this regime the system do not show deviations from its non-interacting behavior. Nevertheless, we show that the helical Luttinger liquid nature emerges in the transient dynamics, where signatures of charge/spin fractionalization can be clearly identified., Comment: Contribution for the special issue of Physica E in memory of Markus B\"uttiker. 4 figures

Helical Luttinger liquids, appearing at the edge of two-dimensional topological insulators, represent a new paradigm of one-dimensional systems, where peculiar quantum phenomena can be investigated. Motivated by recent experiments on charge fractionalization, we propose a setup based on helical Luttinger liquids that allows to time-resolve, in addition to charge fractionalization, also spin-charge separation and pure spin fractionalization. This is due to the combined presence of spin-momentum locking and interactions. We show that electric time-resolved measurements can reveal both charge and spin properties, avoiding the need of magnetic materials. Although challenging, the proposed setup could be achieved with nowadays technologies, promoting helical liquids as interesting playgrounds to explore the effects of interactions in one dimension., Comment: main text + supplementary material

Interference represents one of the most striking manifestation of quantum physics in low-dimensional systems. Despite evidences of quantum interference in charge transport have been known for a long time, only recently signatures of interference induced thermal properties have been reported, paving the way for the phase-coherent manipulation of heat in mesoscopic devices. In this work we show that anomalous thermoelectric properties and efficient heat rectification can be achieved by exploiting the phase-coherent edge states of quantum Hall systems. By considering a tunneling geometry with multiple quantum point contacts, we demonstrate that the interference paths effectively break the electron-hole symmetry, allowing for a thermoelectric charge current flowing either from hot to cold or viceversa, depending on the details of the tunnel junction. Correspondingly, an interference induced heat current is predicted, and we are able to explain these results in terms of an intuitive physical picture. Moreover, we show that heat rectification can be achieved by coupling two quantum Hall systems with different filling factors, and that this effect can be enhanced by exploiting the interference properties of the tunnel junction., Comment: 9 pages, 7 figures

Hydrodynamic flow occurs in an electron liquid when the mean free path for electron-electron collisions is the shortest length scale in the problem. In this regime, transport is described by the Navier-Stokes equation, which contains two fundamental parameters, the bulk and shear viscosities. In this Article we present extensive results for these transport coefficients in the case of the two-dimensional massless Dirac fermion liquid in a doped graphene sheet. Our approach relies on microscopic calculations of the viscosities up to second order in the strength of electron-electron interactions and in the high-frequency limit, where perturbation theory is applicable. We then use simple interpolation formulae that allow to reach the low-frequency hydrodynamic regime where perturbation theory is no longer directly applicable. The key ingredient for the interpolation formulae is the "viscosity transport time" $\tau_{\rm v}$, which we calculate in this Article. The transverse nature of the excitations contributing to $\tau_{\rm v}$ leads to the suppression of scattering events with small momentum transfer, which are inherently longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as $-1/[T^2 \ln(T/T_{\rm F})]$, in the low temperature limit we find $\tau_{\rm v} \sim 1/T^2$., Comment: 27 pages, 6 figures, 5 appendices

Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this letter we exploit near-field microscopy to image propagating plasmons in high quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine dispersion and particularly plasmon damping in real space. We find unprecedented low plasmon damping combined with strong field confinement, and identify the main damping channels as intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key for the development of graphene nano-photonic and nano-optoelectronic devices.

Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs display superb electronic properties due to very limited scattering from extrinsic disorder sources such as Coulomb impurities and corrugations. Such samples are therefore expected to be ideal platforms for highly-tunable low-loss plasmonics in a wide spectral range. In this Article we present a theory of collective electron density oscillations in a graphene sheet encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes. We focus on scattering of these modes against graphene's acoustic phonons and hBN optical phonons, two sources of scattering that are expected to play a key role in hBN/G/hBN stacks. We find that at room temperature the scattering against graphene's acoustic phonons is the dominant limiting factor for hBN/G/hBN stacks, yielding theoretical inverse damping ratios of hybrid plasmon-phonon modes of the order of $50$-$60$, with a weak dependence on carrier density and a strong dependence on illumination frequency. We confirm that the plasmon lifetime is not directly correlated with the mobility: in fact, it can be anti-correlated., Comment: 14 pages, 4 figures

Recent scattering-type scanning near-field optical spectroscopy (s-SNOM) experiments on single-layer graphene have reported Dirac plasmon lifetimes that are substantially shorter than the dc transport scattering time \tau_{tr}. We highlight that the plasmon lifetime is fundamentally different from \tau_{tr} since it is controlled by the imaginary part of the current-current linear response function at finite momentum and frequency. We first present the minimal theory of the extrinsic lifetime of Dirac plasmons due to scattering against impurities. We then show that a very reasonable concentration of charged impurities yields a plasmon damping rate which is in good agreement with s-SNOM experimental results., Comment: 5 pages, 2 figures, to be submitted to Phys. Rev. B

Dirac plasmons in a doped graphene sheet have recently been shown to enable confinement of light to ultrasmall volumes. In this work we calculate the intrinsic lifetime of a Dirac plasmon in a doped graphene sheet by analyzing the role of electron-electron interactions beyond the random phase approximation. The damping mechanism at work is intrinsic since it operates also in disorder-free samples and in the absence of lattice vibrations. We demonstrate that graphene's sublattice-pseudospin degree of freedom suppresses intrinsic plasmon losses with respect to those that occur in ordinary two-dimensional electron liquids. We relate our findings to a microscopic calculation of the homogeneous dynamical conductivity at energies below the single-particle absorption threshold., Comment: 5 pages and 3 figures (main text), 6 pages and 4 figures in appendices

We show that the plasmon spectrum of an ordinary two-dimensional electron gas (2DEG) hosted in a GaAs heterostructure is significantly modified when a graphene sheet is placed on the surface of the semiconductor in close proximity to the 2DEG. Long-range Coulomb interactions between massive electrons and massless Dirac fermions lead to a new set of optical and acoustic intra-subband plasmons. Here we compute the dispersion of these coupled modes within the Random Phase Approximation, providing analytical expressions in the long-wavelength limit that shed light on their dependence on the Dirac velocity and Dirac-fermion density. We also evaluate the resistivity in a Coulomb-drag transport setup. These Dirac/Schroedinger hybrid electron systems are experimentally feasible and open new research opportunities for fundamental studies of electron-electron interaction effects in two spatial dimensions., Comment: 7 pages, 4 figures