SCSam T. Carr

Sam T. Carr

University of Kent
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Sam T. Carr has a total of 41 co-authors. Here are the top co-authors by number of shared publications:

Latest Publications

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    The Widom line in the Ising model on a decorated bilayer lattice

    by Joseph Chapman, Justas Gidziunas, Bruno Tomasello, Sam Carr

    There has been much recent interest devoted to a class of frustrated one-dimensional statistical mechanics lattice models which exhibit sharp thermodynamics. In this work, we study an extension of one of these models to two dimensions, the Ising model on a decorated bilayer lattice. We show that the pseudo-transitions of the one-dimensional models become a real first order phase transition in this two-dimensional analogue. Moreover, the pseudo-transition behaviour is found to still exist above a bi-critical point. This can be characterised as a Widom line, which allows a reinterpretation of the physics in the previously studied one-dimensional models.

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    Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole

    by J. Martin, A. Baskerville, V. L. Campo, J. Minns, J. Pooley, S. T. Carr, C. A. Hooley, G. Möller, J. Quintanilla

    In three-dimensional space, an electron moving in the field of a magnetic monopole has no bound states. In this paper, we explore the physics when the electron is restricted to a two-dimensional plane adjacent to a magnetic monopole. We find bound states in the classical version of the problem and quasi-bound states in the quantum one, in addition to a continuum of scattering states. We calculate the lifetimes of the quasi-bound states using several complementary approximate methods, which agree well. The threshold monopole magnetic charge required to realize a single quasi-bound state is approximately 18 Q D , where Q D is the magnetic charge of a Dirac monopole. We examine the feasibility of achieving this magnetic charge in currently available monopole analogues: spin ice, artificial spin ice, magnetic needles, image charges in magnetoelectric materials and emergent quantum excitations in Josephson junction arrays or superconducting films.

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    Bifurcation in correlation length of the Ising model on a ‘Toblerone’ lattice

    by Joseph Chapman, Bruno Tomasello, Sam Carr

    The classical Ising chain is a paradigm for the non-existence of phase transitions in one-dimensional systems and was solved by Ernst Ising 100 years ago. More recently, a decorated two-leg Ising ladder has received interest due to its curious thermodynamics that resemble a phase transition; a sharp peak in the specific heat at low, but finite temperature. We use this model to reveal a bifurcation in the correlation lengths due to a crossing of the sub-leading eigenvalues of the transfer matrix, which results in two distinct length scales necessary to describe the decay of correlations. We discuss this phenomenon in the context of the geometric frustration in the model. We also provide additional results to aid in the understanding of the curious thermodynamics of the model through a study of the magnetic susceptibilities.

    Cited by 6
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    Weakly interacting one-dimensional topological insulators: A bosonization approach

    by Polina Matveeva, Dmitri Gutman, Sam T. Carr

    We investigate the topological properties of one-dimensional weakly interacting topological insulators using bosonization. To do that we study the topological edge states that emerge at the edges of a model realized by a strong impurity or at the boundary between topologically distinct phases. In the bosonic model, the edge states are manifested as degenerate bosonic kinks at the boundaries. We first illustrate this idea on the example of the interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization length of the edge states as the width of an edge soliton that occurs in the SSH model in the presence of a strong impurity. Next, we examine models of two capacitively coupled SSH chains that can be either identical or in distinct topological phases. We find that weak Hubbard interaction reduces the ground-state degeneracy in the topological phase of identical chains. We then prove that, similarly to the noninteracting model, the degeneracy of the edge states in the interacting case is protected by chiral symmetry. We then study topological insulators built from two SSH chains with interchain hopping that represent models of different chiral symmetric universality classes. We demonstrate in bosonic language that the topological index of a weakly coupled model is determined by the type of interchain coupling, invariant under one of two possible chiral symmetry operators. Finally, we show that a general one-dimensional model in a phase with topological index ν is equivalent at low energies to a theory of at least ν SSH chains. We illustrate this idea on the example of an SSH model with longer-range hopping.

    Cited by 8
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    Elementary models of three-dimensional topological insulators with chiral symmetry

    by Donghao Liu, Polina Matveeva, Dmitri Gutman, Sam T. Carr

    We construct a set of lattice models of noninteracting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of Z classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For Z topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in Z classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in Z2 topological classes, we show that class CII and AII are distinct, and cannot be adiabatically connected.

    Cited by 11
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    Local density of states of the interacting resonant level model at zero temperature

    by G. Camacho, P. Schmitteckert, S. T. Carr

    The Anderson single impurity model, including its Kondo limit, can be seen as the hydrogen atom for correlated systems. Its most striking feature is the universal scaling of its low-energy properties governed by the appearance of a single emergent scale, the Kondo temperature TK. In this work, we demonstrate the emergence of a second independent energy scale in a quantum impurity model, the interacting resonant level model, which is equivalent to the anisotropic Kondo model. We study the local density of states at the impurity site in the ground state (zero temperature limit) of the model. We see collapse of data onto universal curves at low energies, however this is only achieved by defining a second low-energy scale with a different power law dependence on model parameters than the Kondo temperature. We provide an exact expression for this second critical exponent. We also report on a splitting of the central resonance as the interaction strength is increased in the absence of any external magnetic field in the model.

    Cited by 4
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    Helical quantum Hall edge modes in bilayer graphene: a realization of quantum spin-ladders

    by Victoria Mazo, Efrat Shimshoni, Chia-Wei Huang, Sam T Carr, H A Fertig

    Cited by 5
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    Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

    by Nikolaos Kainaris, Sam T. Carr

    We present analysis of a single-channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is then a two-band model with a difference of Fermi velocities δv. Using bosonization and a two-loop renormalization group procedure, we show that electron-electron interactions can open a gap in the spin sector of the theory when the interaction strength U is smaller than δv in appropriate units. For repulsive interactions, the resulting strong coupling phase is of the spin-density-wave type. We show that this phase has peculiar emergent topological properties. The gapped spin sector behaves as a topological insulator, with zero-energy edge modes with fractional spin. On the other hand, the charge sector remains critical, meaning the entire system is metallic. However, this bulk electron liquid as a whole exhibits properties commonly associated with the one-dimensional edge states of two-dimensional spin Hall insulators, in particular, the conduction of 2e2/h is robust against nonmagnetic impurities.

    Cited by 77
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    Effect of paramagnetic fluctuations on a Fermi-surface topological transition in two dimensions

    by Sergey Slizovskiy, Joseph J. Betouras, Sam T. Carr, Jorge Quintanilla

    We study the Fermi-surface topological transition of the pocket-opening type in a two-dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second-order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in light of our results.

    Cited by 10
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    Conductivity of a generic helical liquid

    by Nikolaos Kainaris, Igor V. Gornyi, Sam T. Carr, Alexander D. Mirlin

    A quantum spin Hall insulator is a two-dimensional state of matter consisting of an insulating bulk and one-dimensional helical edge states. While these edge states are topologically protected against elastic backscattering in the presence of disorder, interaction-induced inelastic terms may yield a finite conductivity. By using a kinetic equation approach, we find the backscattering rate τ−1 and the semiclassical conductivity in the regimes of high (ω≫τ−1) and low (ω≪τ−1) frequency. By comparing the two limits, we find that the parametric dependence of conductivity is described by the Drude formula for the case of a disordered edge. On the other hand, in the clean case where the resistance originates from umklapp interactions, the conductivity takes a non-Drude form with a parametric suppression of scattering in the dc limit as compared to the ac case. This behavior is due to the peculiarity of umklapp scattering processes involving necessarily the state at the “Dirac point.” In order to take into account Luttinger liquid effects, we complement the kinetic equation analysis by treating interactions exactly in bosonization and calculating conductivity using the Kubo formula. In this way, we obtain the frequency and temperature dependence of conductivity over a wide range of parameters. We find the temperature and frequency dependence of the transport scattering time in a disordered system as τ∼[max(ω,T)]−2K−2, for K>2/3 and τ∼[max(ω,T)]−8K+2 for K<2/3.

    Cited by 170
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