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Here we review a universal model for chirally induced spin-selectivity (CISS) as a standalone effect occurring in chiral molecules. We tie together the results of forward scattering in the gas phase to the results for photoelectrons in chiral self-assembled monolayers and the more contemporary results in two terminal transport setups. We discuss the ingredients that are necessarily present in all experiments to date, which we identify as: i) chirality, be it point, helical or configurational, ii) the spin-orbit coupling as the spin active coupling of atomic origin, iii) decoherence as a time-reversal symmetry breaking mechanism that avoids reciprocity relations in the linear regime and finally iv) tunneling that accounts for the magnitude of the spin polarization effect. This proposal does not discard other mechanisms that can yield comparable spin effects related to interactions of the molecule to contacts or substrates that have been proposed but that are less universal or apply to particular situations. Finally, we discuss recent results suggesting CISS as a molecular phenomenon in the real of enantiomer selectivity, coherent electron transfer, and spin effects in chiroptical activity.

A very famous ``test'' of the General Theory of Relativity (GTR) is the advance of Mercury's perihelion (and of other planets too). To be more precise, this is not a prediction of General Relativity, since the anomaly was known in the XIXth century, but no consistent explanation had been found yet at the time GTR was elaborated. Einstein came up with a solution to the problem in 1914. In the case of Mercury, the closest planet to the Sun, the effect is more pronounced than for other planets, and observed from Earth; there is an advance of the perihelion of Mercury of about 5550~arc seconds per century (as/cy). Among these, about $5000$ are due to the equinox precession (the precise value is {$5025.645$}~as/cy) and about $500$ ({$531.54$}) to the influence of the external planets. The remaining, about $50$~as/cy ({$42.56$}), are not understood within Newtonian mechanics. Here, we revisit the problem in some detail for a presentation at the undergraduate level.

Chirally Induced Spin Selectivity (CISS) is a transport phenomenon observed in both linear and non-linear regimes, where the spin-orbit coupling (SOC) acts as the key driver and electron tunneling serves as the dominant mechanism for charge transfer. Despite SOC's inherent time-reversal symmetry (TRS) preservation, conventional reciprocity relations limit spin polarization and the differential treatment of spin species. In experimental systems, an additional factor, spin-independent decoherence, disrupts TRS and reciprocity. We introduce decoherence using the Buttiker voltage probe within the scattering matrix framework. Our results reveal the importance of under-the-barrier decoherence as an order-of-magnitude polarization enhancement mechanism. Polarization arises by the disruption of spin precession around the spin-orbit magnetic field with a new spin component along the field direction. The alignment of polarization depends on interference effects produced by the voltage probe. We discuss the connection of our model to a more realistic decoherence mechanism in molecular systems., Comment: arXiv admin note: text overlap with arXiv:2301.02156

Chiral structures, breaking spatial inversion symmetry, exhibit non-zero chiroptical activity (COA) due to the interaction between their electric and magnetic responses under external electromagnetic fields, an effect that is otherwise absent in achiral systems. Non-magnetic chiral structures also exhibit Chiral Induced Spin Selectivity (CISS), where spin-polarization (SP) emerges without external magnetic influence. We have obtained a COA-SP connection for a model system of an electron constrained to a helix including spin-orbit coupling (SOC), and in the presence of an external electromagnetic field. Despite its simplicity, this model captures the relevant physics required to address the problem. In particular, our results reveal that the norm of the SP vector can be used as a predictor of COA. In addition to SOC and the breaking of space inversion, a non-vanishing SP requires the breaking of time-reversal symmetry (TRS), as demanded by Onsager's reciprocity. Beyond the relationship between SP and COA, we obtain the novel result that TRS breaking is also necessary to yield a non-vanishing contribution of the SOC to the COA., Comment: 23 pages, 6 figures

The spin activity in macromolecules such as DNA and oligopeptides, in the context of the Chiral Induced Spin Selectivity (CISS) has been proposed to be due to the atomic Spin-Orbit Coupling (SOC) and the associated chiral symmetry of the structures. This coupling, associated with carbon, nitrogen and oxygen atoms in biological molecules, albeit small (meV), can be enhanced by the geometry, and strong local polarization effects such as hydrogen bonding (HB). A novel way to manipulate the spin degree of freedom is by modifying the spectrum using a coupling to the appropriate electromagnetic radiation field. Here we use the Floquet formalism in order to show how the half filled band Hamiltonian for DNA, can be modulated by the radiation to produce a up to a tenfold increase of the effective SOC once the intrinsic coupling is present. On the other hand, the chiral model, once incorporating the orbital angular momentum of electron motion on the helix, opens a gap for different helicity states (helicity splitting) that chooses spin polarization according to transport direction and chirality, without breaking time reversal symmetry. The observed effects are feasible in physically reasonable parameter ranges for the radiation field amplitude and frequency., Comment: 8 pages, 6 figures

The comment by O. Entin-Wohlman, A. Aharony, and Y. Utsumi, on our paper S. Varela, I. Zambrano, B. Berche, V. Mujica, and E. Medina, Phys. Rev. B 101, 241410(R) (2020) makes a few points related to the validity of our model, especially in the light of the interpretation of Bardarson's theorem: "in the presence of time reversal symmetry and for half-integral spin the transmission eigenvalues of the two terminal scattering matrix come in (Kramers) degenerate pairs". The authors of the comment first propose an ansatz for the wave function in the spin active region and go on to show that the resulting transmission does not show spin dependence, reasoning that spin dependence would violate Bardarson's assertion. Here we clearly show that the ansatz presented assumes spin-momentum independence from the outset and thus just addresses the spinless particle problem. We then find the appropriate eigenfunction contemplating spin-momentum coupling and show that the resulting spectrum obeys Bardarson's theorem. Finally we show that the allowed wavevectors are the ones assumed in the original paper and thus the original conclusions follow. We recognize that the Hamiltonian in our paper written in local coordinates on a helix was deceptively simple and offer the expressions of how it should be written to more overtly convey the physics involved. The relation between spin polarization and torque becomes clear, as described in our paper. This response is a very important clarification in relation to the implications of Bardarson's theorem concerning the possibility of spin polarization in one dimensional systems in the linear regime.

Chiral degrees of freedom occur in matter and in electromagnetic fields and constitute an area of research that is experiencing renewed interest driven by recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials. The CISS effect underpins the fact that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision. Any technology that relies on optimal charge transport, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which is presently lacking. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking perspective provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects, and presents a vision for their future roles in enabling room-temperature quantum technologies.

Recently experiments have shown very significant spin activity in biological molecules such as DNA, proteins, oligopeptides and aminoacids. Such molecules have in common their chiral structure, time reversal symmetry and the absence of magnetic exchange interactions. The spin activity is then assumed to be due to either the pure Spin-orbit (SO) interaction or SO coupled to the presence of strong local sources of electric fields. Here we derive an analytical tight-binding Hamiltonian model for Oligopeptides that contemplates both intrinsic SO and Rashba interaction induced by hydrogen bond. We use a lowest order perturbation theory band folding scheme and derive the reciprocal space intrinsic and Rashba type Hamiltonian terms to evaluate the spin activity of the oligopeptide and its dependence of molecule uniaxial deformations. SO strengths in the tens of meV are found and explicit spin active deformation potentials. We find a rich interplay between responses to deformations both to enhance and diminish SO strength that allow for experimental testing of the orbital model. Qualitative consistency with recent experiments shows the role of hydrogen bonding in spin activity., Comment: 9 pages, 4 figures

Electron transfer (ET) in biological molecules such as peptides and proteins consists of electrons moving between well defined localized states (donors to acceptors) through a tunneling process. Here we present an analytical model for ET by tunneling in DNA, in the presence of Spin-Orbit (SO) interaction, to produce a strong spin asymmetry with the intrinsic atomic SO strength in meV range. We obtain a Hamiltonian consistent with charge transport through $\pi$ orbitals on the DNA bases and derive the behavior of ET as a function of the injection state momentum, the spin-orbit coupling and barrier length and strength. A highly consistent scenario arises where two concomitant mechanisms for spin selection arises; spin interference and differential spin amplitude decay. High spin filtering can take place at the cost of reduced amplitude transmission assuming realistic values for the spin-orbit coupling. The spin filtering scenario is completed by addressing the spin dependent torque under the barrier, with a consistent conserved definition for the spin current.

We introduce a $p_{z}-d$ coupling model Hamiltonian for the $\pi$-graphene/Au bands that predicts a rather large intrinsic spin-orbit (SO) coupling as are being reported in recent experiments and DFT studies. Working within the analytical Slater-Koster tight-binding approach we were able to identify the overlapping orbitals of relevance in the enhancement of the SO coupling for both, the sublattice symmetric (BC), and the ATOP (AC) stacking configurations. Our model effective Hamiltonian reproduces quite well the experimental spectrum for the two registries, and in addition, its shows that the hollow site configuration (BC), in which the A/B sites remain symmetric, yields the larger increase of the SO coupling. We also explore the Au-diluted case keeping the BC configuration and showed that it renders the preservation of the SO-gap with a similar SO interaction enhancement as the undiluted case but with a smaller graphene-gold distance., Comment: 13 pages, 8 figures

The induced-proximity effects of nearly commensurate lattice structure of a graphene layer on Ni(111) and Co(0001) substrates in the AC stacking configuration are addressed through an analytical tight-binding approach within the Slater-Koster method. A minimal Hamiltonian is constructed by considering the hybridizations of the magnetic $3d$-orbitals of Ni(Co) atoms with the $p_z$-orbitals of graphene, in addition to the atomic spin-orbit coupling and the magnetization of the Ni(Co) atoms. A low-energy effective Hamiltonian for graphene/Ni(Co) describing the perturbed $\pi$-bands in the vicinity of the Dirac points is derived which enable us to get further insight on the physical nature of the induced-effective couplings to the graphene layer. It is shown that a magneto-spin-orbit type effect may emerge through two competing mechanisms simultaneously present, namely the proximity induced exchange and Rashba spin-orbit interaction. Such effects results in giant exchange splittings and robust Rashba spin-orbit coupling transferred to the graphene layer in agreement with recent density functional theory calculations and experimental observations. We further analyze the physical conditions for the appearance of intact Dirac cones in the minority spin bands as observed by recent photoemission measurements with spin resolution., Comment: 13 pages, 7 figures

The strength of the spin-orbit interaction relevant to transport in a low dimensional structure depends critically on the relative geometrical arrangement of current carrying orbitals. Recent tight-binding orbital models for spin transport in DNA-like molecules, have surmised that the band spin-orbit coupling arises from the particular angular relations between orbitals of neighboring bases on the helical chain. Such arrangement could be probed by inducing deformations in the molecule in a conductive probe AFM type setup, as it was recently reported by Kiran, Cohen and Naaman\cite{Kiran}. Here we report deformation dependent spin selectivity when a double strand DNA model is compressed or stretched. We find that the equilibrium geometry is not optimal with respect to the SO coupling strength and thus spin selectivity can be tuned by deformations. The latter can be increased by stretching the helical structure taking into account its elastic properties through the Poisson ratio. The spin filtering gap is also found to be tunable with uniaxial deformations., Comment: 6 pages, 4 figures, Submitted to PRB

We study the effect of grain polydispersity on the bulk modulus in non-cohesive two dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of {\it branch vector/contact length}. Classifying the contact lengths and forces by their size compared to the average length and average force respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three dimensional experiments., Comment: 9 pages, 9 Figures, Submitted to Physical Review E

We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a single screw dislocation, whose Burgers vector measures the torsion amplitude. The problem, first treated in the relativistic limit describing fermions that couple minimally to torsion, is then analysed in the Pauli limit We show that torsion induces a geometric potential and also that it couples generically to the phase of the wave function, giving rise to the possibility of using torsion to manipulate spin currents in the case of spinor wave functions. These results emerge as an alternative strategy for using screw dislocations in the design of spintronic-based devices.

We build a tight-binding Hamiltonian describing Co/Ni over graphene, contemplating ATOP (a Co/Ni atom on top of each Carbon atom of one graphene sublattice) and HCP (one Co/Ni atom per Graphene plaquette) configurations. For the ATOP configuration the orbitals involved, for the Co/Ni, are the $d_{z^2-r^2}$ which most strongly couple to one graphene sublattice and the $d_{xz}$, $d_{yz}$ orbitals that couple directly to the second sublattice site. Such configuration is diagonal in pseudo-spin and spin space, yielding electron doping of the graphene and antiferro-magnetic ordering in the primitive cell in agreement with DFT calculations. The second, HCP configuration is symmetric in the graphene sublattices and only involves coupling to the $d_{xz}$, $d_{yz}$ orbitals. The register of the lattices in this case allows for a new coupling between nearest neighbour sites, generating non-diagonal terms in the pseudo-spin space and novel spin-kinetic couplings mimicking a spin-orbit coupling generated by a magnetic coupling. The resulting proximity effect in this case yields ferromagnetic order in the graphene substrate. We derive the band structure in the vicinity of the K points for both configurations, the Bloch wavefunctions and their spin polarization.

We study the relationship between the granular contact angle distribution and local particle friction on the macroscopic friction and bulk modulus in non-cohesive disk packings. Molecular dynamics in two dimensions are used to simulate uniaxial loading-unloading cycles imposed on the granular packings. While macroscopic Mohr-friction depends on the granular pack geometric details, it reaches a stationary limit after a finite number of loading-unloading cycles that render well-defined values for bulk modulus, grain coordination, porosity, and friction. For random packings and for all polydispersities analyzed, we found that as inter-particle friction increases, the bulk modulus for the limit cycle decreases linearly, while the mean coordination number is reduced and the porosity increased, also as approximately linear functions. On the other hand, the macroscopic Mohr-friction increases in a monotonous trend with inter-particle friction. The latter result is compared to a theoretical model which assumes the existence of sliding planes corresponding to definite Mohr-friction values. The simulation results for macroscopic friction are well described by the theoretical model that incorporates the local neighbour angle distribution that can be quantified through the contact angle entropy. As local friction is increased, the limit entropy of the neighbour angle distribution is reduced, thus introducing the geometric component to granular friction. Surprisingly, once the limit cycle is reached, the Mohr-friction seem to be insensitive to polydispersity as has been recently reported., Comment: 14 pages, 16 figures, Accepted in Physical Review E

We derive optimal-work finite time protocols for a colloidal particle in a Gaussian well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behaviour of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quais-static processes. When measurements are performed protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below the predicted by the Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements., Comment: 10 pages, 7 figures

We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not preserved in the usual manner; (ii) non-gauge-invariant quantities can be associated with physical observables; and (iii) there are changes in the physical boundary conditions of the wave function that render it non-single-valued. We give worked examples that illustrate these points, in contrast to general opinions from classic texts. We also give a historical perspective on the development of Abelian gauge theory in relation to our particular points. Our aim is to provide a discussion of these issues at the graduate level.

Inclusion of spin-dependent interactions in graphene in the vicinity of the Dirac points can be posed in terms of non-Abelian gauge potentials. Such gauge potentials being surrogates of physical electric fields and material parameters, only enjoy a limited gauge freedom. A general gauge transformation thus in general changes the physical model. We argue that this property can be useful in connecting reference physical situations, such as free particle or Rashba interactions to non-trivial physical Hamiltonians with a new set of spin-orbit interactions, albeit constrained to being isoenergetic. We analyse different combinations of spin-orbit interactions in the case of monolayer graphene and show how they are related by means of selected non-Abelian gauge transformations.

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented $p_z$ type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the SOC opens up an effective $\pi_z-\pi_z$ coupling via interbase $p_{x,y}-p_z$ hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry, nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts which spin orientation is selected depending on chirality and bias, changes in spin preference as a function of input Fermi level and scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov- Anandan phase. To describe room temperature transport we assume that the total transmission is the result of a product of coherent steps limited by the coherence length.

The electronic states of a mesoscopic ring are assessed in the presence of Rashba Spin Orbit coupling and a $U(1)$ gauge field. Spin symmetric coupling to an ideal lead is implemented following B\"uttiker's voltage probe. The exact density of states is derived using the reservoir uncoupled eigenstates as basis functions mixed by the reservoir coupling. The decay time of uncoupled electron eigenstates is derived by fitting the broadening profiles. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but nonuniformly in temperature, the latter due to the fact that currents emerge from different depths of the Fermi sea, and thus for some regimes of flux, they are provided with a protective gap. Such flux regimes can be tailored by the SO coupling for both charge and spin currents.

We address the problem of persistent charge and spin currents on a Corbino disk built from a graphene sheet. We consistently derive the Hamiltonian including kinetic, intrinsic (ISO) and Rashba spin-orbit interactions in cylindrical coordinates. The Hamiltonian is carefully considered to reflect hermiticity and covariance. We compute the energy spectrum and the corresponding eigenfunctions separately for the intrinsic and Rashba spin-orbit interactions. In order to determine the charge persistent currents we use the spectrum equilibrium linear response definition. We also determine the spin and pseudo spin polarizations associated with such equilibrium currents. For the intrinsic case one can also compute the correct currents by applying the bare velocity operator to the ISO wavefunctions or alternatively the ISO group velocity operator to the free wavefunctions. Charge currents for both SO couplings are maximal in the vicinity of half integer flux quanta. Such maximal currents are protected from thermal effects because contributing levels plunge ($\sim$1K) into the Fermi sea at half integer flux values. Such a mechanism, makes them observable at readily accessible temperatures. Spin currents only arise for the Rashba coupling, due to the spin symmetry of the ISO spectrum. For the Rashba coupling, spin currents are cancelled at half integer fluxes but they remain finite in the vicinity, and the same scenario above protects spin currents.

We study the spin polarization of mixed and entangled electron states in a four probe/beam splitter geometry with local Rashba and Dresselhaus interactions. A pair of maximally entangled electrons collides with the beam splitter and enters into two perpendicular branches of length L, composed of spin-orbit active materials (gate confined 2D electron gas). One of the branches is connected to an electron reservoir that acts as a source of decoherence by either behaving as a voltage probe or as a controlled source or sink of current at fixed voltage. Such decoherence source is used to modify the entropy of an unpolarized incoming state in order to generate electron polarization at one or both output branches. The degree of entanglement of the global state and the spin polarization is computed for the outgoing electrons as a function of the coupling to the electron reservoir. Experimentally available spin-orbit strength at the beam splitter arms, for arm lengths of a few micrometers, is able to modulate spin polarization up to 80% in particular spin axes proportional to the decoherence current. The Dresselhaus and Rashba coefficients play a symmetric role in modulating the polarization. Significantly less polarization is achieved for incoming mixed states due to the local operation of the reservoir.

Recently, gauge field theory approaches were extensively used in order to discuss the physical consequences of spin-orbit interactions in condensed matter physics. An SU(2)$\times$U(1) gauge theory is very naturally borne out and provides an illustrative example of a classical Yang-Mills field theory at work. This approach may serve as an exemplification of non-Abelian field theories for students in general physics curriculum. It allows to introduce discussions on fundamental ideas like Noether currents, gauge symmetry principle, gauge symmetry breaking and non linear Yang Mills equations in very concrete physical situations that makes it accessible to a broad audience.

The Hamiltonian describing 2D electron gas, in a spin-orbit active medium, can be cast into a consistent non-Abelian gauge field theory leading to a proper definition of the spin current. The generally advocated gauge symmetric version of the theory results in current densities that are gauge covariant, a fact that poses severe concerns on their physical nature. We show that in fact the problem demands gauge fixing, leaving no room to ambiguity in the definition of physical spin currents. Gauge fixing also allows for polarized edge excitations not present in the gauge symmetric case. The scenario here is analogous to that of superconductivity gauge theory. We develop a variational formulation that accounts for the constraints between U(1) physical fields and SU(2) gauge fields and show that gauge fixing renders a physical matter and radiation currents and derive the particular consequences for the Rashba SO interaction., Comment: to appear in EPL

Recent experiments on electron scattering through molecular films have shown that chiral molecules can be efficient sources of polarized electrons even in the absence of heavy nuclei as source of a strong spin-orbit interaction. We show that self-assembled monolayers (SAMs) of chiral molecules are strong electron polarizers due to the high density effect of the monolayers and explicitly compute the scattering amplitude off a helical molecular model of carbon atoms. Longitudinal polarization is shown to be the signature of chiral scattering. For elastic scattering, we find that at least double scattering events must take place for longitudinal polarization to arise. We predict energy windows for strong polarization, determined by the energy dependences of spin-orbit strength and multiple scattering probability. An incoherent mechanism for polarization amplification is proposed, that increases the polarization linearly with the number of helix turns, consistent with recent experiments on DNA SAMs., Comment: 5 Pages, 4 figures

A spin filtering device using quantum spin interference is theoretically proposed in a GaAs/AlGaAs electron gas that has both Rashba and Dresselhaus spin-orbit couplings. The device achieves polarized electron currents by separating spin up and spin down components without a magnetic field gradient. We find two broad spin filtering regimes, one where the interferometer has symmetrical arms, where a small magnetic flux is needed to achieve spin separation, and the other with asymmetric arms where the change in path length renders an extra phase emulating the effects of a magnetic field. We identify operating points for the device where optimal electron polarization is achieved within value ranges found in a 2D electron gas. Both device setups apply for arbitrary incoming electron polarization and operate at broad energy ranges within the incoming electron band.

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground state properties. Spin currents are derived following an intuitive definition and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin 1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate Condensed Matter Physics course.

Spin filtering through quantum spin interference is addressed exactly, in two dimensions, in a medium that has both Rashba and Dresselhaus spin-orbit couplings and an applied external magnetic field. The problem is addressed from the fully non-Abelian Gauge formulation. We propose an experimentally feasible electronic Mach Zehnder Interferometer and solve for the perfect spin filtering conditions. We find two broad solutions, one where filtering is achieved in the original incoming basis, that is purely a non-Abelian solution, and the other where one needs a tilted axis to observe the polarized output spinor. The latter solution is well approximated by an Abelianized approximation. Both solutions apply for arbitrary incoming polarization, and are only limited by the randomness of the incoming spinor state., Comment: published version, one figure added

In a recent paper [Phys. Rev. Lett. 101, 106601], I. V. Tokatly addresses a non Abelian formulation of spin orbit interaction in condensed matter, restricting to a gauge symmetric scenario. In this comment we draw attention on the relevance of gauge symmetry breaking on such formulation and point out why this is a necessary ingredient for properly describing the associated diamagnetic color currents., Comment: 2 pages, no figures

We discuss the Pauli Hamiltonian within a ${SU(2)}$ gauge theory interpretation, where the gauge symmetry is broken. This interpretation carries directly over to the structural inversion asymmetric spin-orbit interactions in semiconductors and offers new insight into the problem of spin currents in the condensed matter environment. The central results is that symmetry breaking leads to zero spin conductivity in contrast to predictions of Gauge symmetric treatments. Computing the translation operator commutation relations comprising the simplest possible structural inversion asymmetry due to an external electric field, we derive a new condition for orbit quantization. The relation between the topological nature of this effect is consistent with our non-Abelian gauge symmetry breaking scenario., Comment: 7 pages, 1 figure

We analyze the role of resonances in two-fermion entanglement production for a quasi one-dimensional two channel scattering problem. We solve exactly for the problem of a two-fermion antisymmetric product state scattering off a double delta well potential. It is shown that the two-particle concurrence of the post-selected state has an oscillatory behavior where the concurrence vanishes at the values of momenta for virtual bound states in the double well. These concurrence zeros are interpreted in terms of the uncertainty in the knowledge of the state of the one particle subspace reduced one particle density matrix. Our results suggest manipulation of fermion entanglement production through the resonance structure of quantum dots., Comment: 4 pages, 3 figures

The incidence of cementation processes on the acoustical properties of sands is studied via molecular dynamics simulation techniques. In our simulations, we consider samples with different degrees of compaction and cementing materials with distinct elastic properties. The microstructure of cemented sands is taken into account while adding cement at specific locations within the pores, such as grain-to-grain contacts. Results show that acoustical properties of cemented sands are strongly dependent on the amount of cement, its relative stiffness with respect to the hosting medium, and its location within pores. Simulation results are in good correspondence available experimental data and compare favourably with some theoretical predictions for the sound velocity within a range of cement saturation, porosity and confining pressure., Comment: Research paper. 13 pages and 13 figures

We study a device for entangling electrons as cotunneling occurs through a quantum dot where on-site electron-electron interactions $U$ are in place. The main advantage of this device is that single particle processes are forbidden by energy conservation as proposed by Oliver et al\cite{oli02}. Within this model we calculated two electron transition amplitude, in terms of the T-matrix, to all orders in the coupling to the dot, and consider a finite lead bandwidth. The model filters singlet entangled pairs with the sole requirement of Pauli principle. Feynman paths involving consecutive and doubly occupied dot interfere destructively and produce a transition amplitude minimum at a critical value of the onsite repulsion $U$. Singlet filtering is demonstrated as a function of a gate voltage applied to the dot with a special resonance condition when the dot levels are symmetrically placed about the input lead energy., Comment: 5 pages, 5 figures

We perform a brief but critical review of the Landauer picture of transport that clarifies how decoherence appears in this approach. On this basis, we present different models that allow the study of the coherent and decoherent effects of the interaction with the environment in the electronic transport. These models are particularly well suited for the analysis of transport in molecular wires. The effects of decoherence are described through the D'Amato-Pastawski model that is explained in detail. We also consider the formation of polarons in some models for the electron-vibrational interaction. Our quantum coherent framework allows us to study many-body interference effects. Particular emphasis is given to the occurrence of anti-resonances as a result of these interferences. By studying the phase fluctuations in these soluble models we are able to identify inelastic and decoherence effects. A brief description of a general formulation for the consideration of time-dependent transport is also presented., Comment: 32 pages, 11 eps figures. To appear in Chemical Physics (Special Molecular Electronics Number)

We give a detailed and rigorous picture of the mesoscopic conductance fluctuations in the deep insulating regime (DIR) within the Nguyen, Spivak and Shklovskii model including spin-orbit coupling (SO). Without SO, we find that fluctuations of the log-conductance are persistent above a saturation field $% B_s$, where one has that the log-conductance is approximately a stationary random process. In contrast, in the SO case the saturation field $B_s$ is negligible and the stationarity is well realized. We find non-vanishing disorder fluctuations of the field average of the log-conductance as a quantitative measure of the lack of ergodicity in the mean square sense. As a consequence the commonly used criterion to test the ergodicity based on the equivalence of the variance in disorder and the variance in the field is not fulfilled. Using the replica approach, we derive the weak localization analogs of the `cooperon and diffuson.

We discuss the steady-state electronic transport in solid-state and molecular devices in the quantum regime. The decimation technique allows a comprehensive description of the electronic structure. Such a method is used, in conjunction with the generalizations of Landauer's tunneling formalism, to describe a wide range of transport regimes. We analize mesoscopic and semiclassical metallic transport, the metal-insulator transition, and the resonant tunneling regime. The effects of decoherence on transport is discussed in terms of the D'Amato-Pastawski model. A brief presentation of the time dependent phenomena is also included., Comment: 25 pages 20 figures

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition'' using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments $$ always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($n\to 0$) to obtain $<\ln J>$ for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic'' structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities., Comment: 20 pages, 12 figures