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We consider spin-vorticity coupling - the generation of spin polarization by vorticity - in viscous two-dimensional electron systems with spin-orbit coupling. We first derive hydrodynamic equations for spin and momentum densities in which their mutual coupling is determined by the rotational viscosity. We then calculate the rotational viscosity microscopically in the limits of weak and strong spin-orbit coupling. We provide estimates that show that the spin-orbit coupling achieved in recent experiments is strong enough for the spin-vorticity coupling to be observed. On the one hand, this coupling provides a way to image viscous electron flows by imaging spin densities. On the other hand, we show that the spin polarization generated by spin-vorticity coupling in the hydrodynamic regime can, in principle, be much larger than that generated, e.g. by the spin Hall effect, in the diffusive regime.

In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge.

We present a variational study of both unpaired and spin-singlet paired states induced in a two-dimensional electron gas at low density by a perpendicular magnetic field. It is based on an improved circular-cell approximation which leads to a number of closed analytical results. The ground-state energy of the Wigner crystal containing a single electron per cell in the lowest Landau level is obtained as a function of the filling factor $\nu$: the results are in good agreement with those of earlier approaches and predict $\nu_{c} \approx 0.25$ for the upper filling factor at which the solid-liquid transition occurs. A novel localized state of spin-singlet electron pairs is examined and found to be a competitor of the unpaired state for filling factor $\nu >1$. The corresponding phase boundary is quantitatively displayed in the magnetic field-electron density plane., Comment: 19 pages, 8 figures, submitted to Phys. Rev. B on 7th April 2001. to appear in Phys. Rev. B

Unlike any other material, graphene is all surface. This means that it is strongly affected by its surroundings, including the substrate it lays upon. In the past few years, it was understood that silicon oxide (SiO2), the most popular substrate material for graphene, limits the performance of graphene devices and obscures interesting physics. Hexagonal boron nitride (hBN) has emerged as “the perfect” substrate that results in graphene devices of astonishing electronic quality. In this Thesis, we explore some peculiar nonlocal effects that are found in such new devices due to quantum transport and electron-electron interactions in the coherent as well as the diffusive regime. Chapters 1-4 are devoted to the introduction of some basic concepts and to the main experimental facts that motivated our work. Since encapsulation in hBN crystals makes graphene practically insusceptible to the environment, electrons can travel micrometer distances without scattering. In Chapter 5, in the framework of the Landauer-Büttiker scattering theory, we have developed a scaling procedure for numerical simulations of tight-binding nonlocal transport in realistic graphene devices. We have tested our method against experimental data on transverse magnetic focusing (TMF). This comparison enables a clear physical interpretation of all the observed features of the TMF signal, including its oscillating sign. Moreover, in graphene/hBN superlattices and in bilayer graphene in a perpendicular electric field, which have broken inversion symmetry, topological currents originating from graphene’s two valleys flow in opposite directions and combine to produce long-range charge neutral flow. This effect translates into a nonlocal voltage at zero magnetic fields in a narrow energy range near Dirac points at distances as large as several micrometers. However, the behavior of the observed long-range nonlocality as a function of temperature, band gap, and carrier concentration remained to be understood. In Chapter 6 and 7, we have showen, using a diffusive theory, that this behavior can be explained with bulk topological transport and Coulomb drag between the electrons belonging to the two different valleys, in good agreement with experimental findings. Finally, in Chapter 8, we have studied the crossed Andreev reflection in a three-terminal hybrid graphene/superconductor system in the quantum Hall regime and its effect on the nonlocal resistances.

We investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction E(N) of energy stored in the B battery that can be extracted in order to perform thermodynamic work. We first demonstrate that E(N) is highly reduced by the presence of correlations between the charger and the battery or B between the two-level systems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N \to \infty limit., 5+4 pages

The energy charging of a quantum battery is analyzed in an open quantum setting, where the interaction between the battery element and the external power source is mediated by an ancilla system (the quantum charger) that acts as a controllable switch. Different implementations are analyzed putting emphasis on the interplay between coherent energy pumping mechanisms and thermalization.

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a given quantum system, termed charger, to another one, i.e. the proper battery. In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting them in the global energy balance of the model., 11 pages

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee, Nat. Phys. 13, 693 (2017)1745-247310.1038/nphys4084]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.

Berry curvature hot spots in two-dimensional materials with broken inversion symmetry are responsible for the existence of transverse valley currents, which give rise to giant nonlocal dc voltages. Recent experiments in high-quality gapped graphene have highlighted a saturation of the nonlocal resistance as a function of the longitudinal charge resistivity $\rho_{{\rm c}, xx}$, when the system is driven deep into the insulating phase. The origin of this saturation is, to date, unclear. In this work we show that this behavior is fully compatible with bulk topological transport in the regime of large valley Hall angles (VHAs). We demonstrate that, for a fixed value of the valley diffusion length, the dependence of the nonlocal resistance on $\rho_{{\rm c}, xx}$ weakens for increasing VHAs, transitioning from the standard $\rho^3_{{\rm c}, xx}$ power-law to a result that is independent of $\rho_{{\rm c}, xx}$., Comment: 5 pages, 3 figures

Ultra-clean graphene sheets encapsulated between hexagonal boron nitride crystals host two-dimensional electron systems in which low-temperature transport is solely limited by the sample size. We revisit the theoretical problem of carrying out microscopic calculations of non-local ballistic transport in such micron-scale devices. By employing the Landauer-Buttiker scattering theory, we propose a novel scaling approach to tight-binding non-local transport in realistic graphene devices. We test our numerical method against experimental data on transverse magnetic focusing (TMF), a textbook example of non-local ballistic transport in the presence of a transverse magnetic field. This comparison enables a clear physical interpretation of all the observed features of the TMF signal, including its oscillating sign., 12 pages, 12 multi-panel figures

[from the introduction]: This Thesis focusses on the physics of e-e interactions in single-layer graphene and on the role of interlayer e-e interactions in vertical heterostructures comprised of two closely spaced graphene sheets.

We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprising two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fails when the graphene sheet is heavily doped, i.e., when the Landau level spectrum of two-dimensional massless Dirac fermions is approximately harmonic. In this case we >integrate out> the Landau levels in valence band and obtain an effective Hamiltonian for the entire stack of Landau levels in conduction band, as dressed by strong light-matter interactions. © 2014 American Physical Society., We acknowledge support by the EC under Graphene Flagship (Contract No. CNECT-ICT-604391) (M.P.), the European Research Council Advanced Grant (Contract No. 290846) (L.C.), the Italian Ministry of Education, University, and Research (MIUR) through the programs “FIRB IDEAS”–Project ESQUI (Grant No. RBID08B3FM) (V.G.), “FIRB—Futuro in Ricerca 2010”—Project PLASMOGRAPH (Grant No. RBFR10M5BT) (M.P.) and PRIN Grant No. 2010LLKJBX (R.F.), and a 2012 SNS Internal Project (V.G.).

Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions., Comment: 18 pages, 8 figures

In the original work of this Thesis we use Time Dependent Density Matrix Renormalization Group (TDMRG) to follow and study the unitary dynamics of 1D strongly interacting quantum systems. In the rest part we present our work on the collision of spin polarized fermionic clouds. We study spin drag e ects immediately after the collision. This work is relevant to current experiments where pure spin currents have been realized with ultracold atomic gases. Several of our predictions can be veri ed in future experiments on strongly interacting few-fermion systems. In the second part the highly imbalanced case of an impurity immersed in a bath of bosonic atoms is considered. The interaction of the impurity with the bath manifests in the mass renormalization and in the damping of the oscillations of the breathing mode of the impurity in a harmonic potential. We compare the TDMRG results with an analytically tractable model in which the bath is treated as a Luttinger liquid and pinpoint striking deviations from this picture due to the nonlinear nature of the Lieb-Liniger gas. This results are relevant to current and future experiments on impurities coupled to one-dimensional ultracold gases. Finally, we employ DMRG to study spin-orbit coupled bosons in 1D optical lattices, following recent remarkable experimental advances on arti cially engineered gauge elds and spin-orbit coupling in ultracold atoms. We concentrate in the Mott insulator region of the phase diagram of pseudospin-1/2 bosons with spin-orbit coupling and anisotropic interaction terms that fully break spin rotational symmetry.