arXiv subjects

I. Snyman

Publications and source records attributed to I. Snyman.

17 recordsLinked to original sources

arXiv2023

The structure of quasiparticles in a local Fermi liquid

Conduction electrons interacting with a dynamic impurity can give rise to a local Fermi liquid. The latter has the same low energy spectrum as an ideal Fermi gas containing a static impurity. The Fermi liquids's elementary excitations are however not bare electrons. In the vicinity of the impurity, they are dressed by virtual particle-hole pairs. Here we study this dressing. Among other things, we construct a mode-resolved measure of dressing. To evaluate it in position representation, we have to circumvent the limitations of the Numerical Renormalization Group, which discretizes the conduction band logarithmically. We therefore extend Natural Orbital methods, that successfully characterize the ground state, to describe excitations. We demonstrate that the dressing profile shows nontrivial powerlaw decay at large distances. Our Natural Orbital methodology could lay the foundation for calculating the properties of local Fermi liquid quasiparticles in nontrivial geometries such as disordered hosts or mesoscopic devices.

cond-mat.str-el↗

arXiv2018

Ground state overlap knows about ultraviolet dynamics: results for the Kondo model

We consider a quantum quench from the strongly correlated ground state of the Kondo model to a Fermi sea. We calculate the overlap between the ground states before and after the quench, as well as the Loschmidt echo, that is, the transition amplitude between the initial state and the evolved state at a time $t$ after the quench. The overlap is known to determine the dynamics of the echo at large times. We show in addition that the overlap depends algebraically on the emergent Kondo length with a power law exponent equal to the difference of long and short time contributions that appear in the echo. Our result suggests that there may in general be more information contained in the overlap than previously recognized.

cond-mat.str-el↗

arXiv2013

Linear response of a one-dimensional conductor coupled to a dynamical impurity with a Fermi edge singularity

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport set-up in which the impurity can be realised in a double quantum dot. The same Hamiltonian describes tunnelling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e. many fermion correlations result in an impurity decay rate with a non-trivial power law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand, and the linear response of the Fermi sea to external perturbations on the other. This results in a power law singularity in the space and time dependence of the non-local polarisability of the Fermi sea, which can be detected in transport experiments.

cond-mat.str-el↗

arXiv2012

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a non-trivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

cond-mat.str-el↗

arXiv2012

Fermi edge singularity and finite frequency spectral features in a semi-infinite 1D wire

We theoretically study a charge qubit interacting with electrons in a semi-infinite 1D wire. The system displays the physics of the Fermi edge singularity. Our results generalize known results for the Fermi-edge system to the regime where excitations induced by the qubit can resolve the spatial structure of the scattering region. We find resonant features in the qubit tunneling rate as a function of the qubit level splitting. They occur at integer multiples of h times v_F/l. Here v_F is the Fermi velocity of the electrons in the wire, and l is the distance from the tip of the wire to the point where it interacts with the qubit. These features are due to a single coherent charge fluctuation in the electron gas, with a half-wavelength that fits into l an integer number of times. As the coupling between the qubit and the wire is increased, the resonances are washed out. This is a clear signature of the increasingly violent Fermi-sea shake-up that accompanies strong coupling.

cond-mat.str-el↗

arXiv2011

Hall conductance from Berry curvature in carbon nanotubes

We analytically show that a gap is induced around the Dirac point in the electronic spectrum of a previously metallic nanotube, in the presence of electric and magnetic fields perpendicular to the tube axis. For realistic values of the fields, a gap of at least a few meV can appear. Despite the quasi-one dimensional nature of the system, the gapped state is associated with a non-zero topological invariant and supports a Hall effect. This is revealed when the flux through the tube is varied by one flux quantum, which leads to exactly one electron per spin being transported between the ends of the tube.

cond-mat.mes-hall↗

arXiv2011

Polarons in suspended carbon nanotubes

We prove theoretically the possibility of electric-field controlled polaron formation involving flexural (bending) modes in suspended carbon nanotubes. Upon increasing the field, the ground state of the system with a single extra electron undergoes a first order phase transition between an extended state and a localized polaron state. For a common experimental setup, the threshold electric field is only of order $\simeq 10^{-2}$ V/$μ$m.

cond-mat.mes-hall↗

arXiv2009

The gapped state of a carbon mono-layer in periodic magnetic and electric fields

When smooth, zero-on-average, periodic magnetic and electric fields are applied to a carbon mono-layer (graphene), a gap between the valence and conduction band is introduced. Here this gapped state is studied analytically. It is found that it does not correspond to a band insulator: a constant electric field induces a quantized Hall current even though the magnetic flux through the sample is zero and there are no Landau levels. The phenomenon is of the same type as that discovered by Haldane for a graphene sample in a periodic magnetic field that is not smooth, i.e. varies rapidly on the scale of the graphene lattice constant. The effect can be explained in terms of the topological theory of Thouless, Kohmoto, Nightingale and den Nijs. For the system studied in this paper, an explanation in terms of simple physical principles is also presented. Thus some of the mystery is taken out of the apparently strange phenomenon of a Hall effect without magnetic flux. Furthermore, Haldane's model requires control over external magnetic fields on length scales less than an angstrom and is therefore hard to realize experimentally. For the model studied here, control over external fields on length scales that are larger by two orders of magnitude or more is sufficient. The model is therefore more amenable to experimental realization.

cond-mat.mes-hall↗

arXiv2008

Bi-stability in voltage-biased NISIN structures

As a generic example of a voltage-driven superconducting structure we study a short superconductor connected to normal leads by means of low transparency tunnel junctions, with a voltage bias $V$ between the leads. The superconducting order parameter $Δ$ is to be determined self-consistently. We study the stationary states of the system as well as the dynamics after a perturbation. We find a region in parameter space where there are two stable stationary states at a given voltage. These bi-stable states are distinguished by distinct values of the superconducting order parameter $Δ$ and of the current between the leads. We have evaluated (1) the multi-valued superconducting order parameter $Δ$ at given $V$; (2) the current between the leads at a given V; and (3) the critical voltage at which superconductivity in the island ceases. With regards to dynamics, we find numerical evidence that the stationary states are stable and that no complicated non-stationary regime can be induced by changing the voltage. This result is somewhat unexpected and by no means trivial, given the fact that the system is driven out of equilibrium. The response to a change in the voltage is always gradual, even in the regime where changing the interaction strength induces rapid anharmonic oscillations of the order parameter.

cond-mat.supr-con↗

arXiv2008

Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

The Chalker-Coddington network model (introduced originally as a model for percolation in the quantum Hall effect) is known to map onto the two-dimensional Dirac equation. Here we show how the network model can be used to solve a scattering problem in a weakly doped graphene sheet connected to heavily doped electron reservoirs. We develop a numerical procedure to calculate the scattering matrix with the aide of the network model. For numerical purposes, the advantage of the network model over the honeycomb lattice is that it eliminates intervalley scattering from the outset. We avoid the need to include the heavily doped regions in the network model (which would be computationally expensive), by means of an analytical relation between the transfer matrix through the weakly doped region and the scattering matrix between the electron reservoirs. We test the network algorithm by calculating the conductance of an electrostatically defined quantum point contact and comparing with the tight-binding model of graphene. We further calculate the conductance of a graphene sheet in the presence of disorder in the regime where intervalley scattering is suppressed. We find an increase in conductance that is consistent with previous studies. Unlike the tight-binding model, the network model does not require smooth potentials in order to avoid intervalley scattering.

cond-mat.mes-hall↗

arXiv2008

The Keldysh action of a multi-terminal time-dependent scatterer

We present a derivation of the Keldysh action of a general multi-channel time-dependent scatterer in the context of the Landauer-Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering Full Counting Statistics and the Fermi Edge Singularity.

cond-mat.mes-hall↗

arXiv2007

Valley-isospin dependence of the quantum Hall effect in a graphene p-n junction

We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the high-magnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e^2/h. In the absence of intervalley scattering, the result G=(e^2/h)(1-cos Phi) depends only on the angle Phi between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.

cond-mat.mes-hall↗

arXiv2006

Exciting half-integer charges in a quantum point contact

We study a voltage-driven quantum point contact (QPC) strongly coupled to a qubit. We predict pronounced observable features in the QPC current that can be interpreted in terms of half-integer charge transfers. Our analysis is based on the Keldysh generating functional approach and contains general results, valid for all coherent conductors.

cond-mat.mes-hall↗

arXiv2006

Ballistic transmission through a graphene bilayer

We calculate the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length $L\ll$ width $W$), and compare with known results for a monolayer. At the Dirac point of charge neutrality, the bilayer transmits as two independent monolayers in parallel: Both current and noise are resonant at twice the monolayer value, so that their ratio (the Fano factor) has the same 1/3 value as in a monolayer -- and the same value as in a diffusive metal. The range of Fermi energies around the Dirac point within which this pseudo-diffusive result holds is smaller, however, in a bilayer than in a monolayer (by a factor $l_{\perp}/L$, with $l_{\perp}$ the interlayer coupling length).

cond-mat.mes-hall↗

arXiv2006

Analysis of the Strong Coupling Limit of the Richardson Hamiltonian using the Dyson Mapping

The Richardson Hamiltonian describes superconducting correlations in a metallic nanograin. We do a perturbative analysis of this and related Hamiltonians, around the strong pairing limit, without having to invoke Bethe Ansatz solvability. Rather we make use of a boson expansion method known as the Dyson mapping. Thus we uncover a selection rule that facilitates both time-independent and time-dependent perturbation expansions. In principle the model we analise is realised in a very small metalic grain of a very regular shape. The results we obtain point to subtleties sometimes neglected when thinking of the superconducting state as a Bose-Einstein condensate. An appendix contains a general presentation of time-independent perturbation theory for operators with degenerate spectra, with recursive formulas for corrections of arbitrarily high orders.

cond-mat.str-el↗

arXiv2005

Quantum Tunneling Detection of Two-photon and Two-electron Processes

We analyze the operation of a quantum tunneling detector coupled to a coherent conductor. We demonstrate that in a certain energy range the output of the detector is determined by two-photon processes, two-electron processes and the interference of the two. We show how the individual contributions of these processes can be resolved in experiments.

cond-mat.mes-hall↗

arXiv2004

Analysis and Applications of the Generalised Dyson Mapping

Generalised Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalised Dyson boson-fermion mapping is a one-to-one linear but non-unitary operator that can be applied to vectors representing the states of a many-fermion system. A vector representing a fermion system maps onto a vector that represents a state of a many-body system that contains both bosons and fermions. The motivation for doing such a mapping is the hope that it will reveal some property of the system that simplifies its analysis and that was hidden in the original form. The aims of this text are to review the theory of generalized Dyson boson-fermion mappings and to find a useful application for a generalized Dyson boson-fermion mapping, by considering a non-trivial model, namely the Richardson model for superconductivity. It is the first time that a boson expansion technique is implemented for a system where the roles of both collective and non-collective fermion pairs are important. The Dyson mapping uncovers non-trivial properties of the system that aid the construction of time-independent as well as time-dependent perturbation expansions. The time-independent expansions agree with results that other authors have obtained through methods other than boson expansions. The time-dependent expansions might in future prove useful in understanding aspects of the dynamics of ultra-cold fermi gases, when time-dependent magnetic fields are used to vary the atom-atom interaction strenght.

nucl-th↗