arXiv subjects

Christopher Mudry

Publications and source records attributed to Christopher Mudry.

At least 73 records · Page 4Linked to original sources

arXiv2010

Deconfined fractional electric charges in graphene at high magnetic fields

The resistance at the charge neutral (Dirac) point was shown by Checkelsky et al in Phys. Rev. B 79, 115434 (2009) to diverge upon the application of a strong magnetic field normal to graphene. We argue that this divergence is the signature for a Kekule instability of graphene, which is induced by the magnetic field. We show that the strong magnetic field does not remove the zero modes that bind a fraction of the electron around vortices in the Kekule dimerization pattern, and that quenched disorder present in the system makes it energetically possible to separate the fractional charges. These findings, altogether, indicate that graphene can sustain deconfined fractionalized electrons.

cond-mat.mes-hall↗

arXiv2010

High-gradient operators in perturbed Wess-Zumino-Witten field theories in two dimensions

Many classes of non-linear sigma models (NLSMs) are known to contain composite operators with an arbitrary number 2s of derivatives ("high-gradient operators") which appear to become strongly relevant within RG calculations at one (or fixed higher) loop order, when the number 2s of derivatives becomes large. This occurs at many conventional fixed points of NLSMs which are perturbatively accessible within the usual epsilon-expansion in d=2+εdimensions. Since such operators are not prohibited from occurring in the action, they appear to threaten the very existence of such fixed points. At the same time, for NLSMs describing metal-insulator transitions of Anderson localization in electronic conductors, the strong RG-relevance of these operators has been previously related to statistical properties of the conductance of samples of large finite size ("conductance fluctuations"). In this paper, we analyze this question, not for perturbative RG treatments of NLSMs, but for 2d Wess-Zumino-Witten (WZW) models at level k, perturbatively in the current-current interaction of the Noether current. WZW models are special ("Principal Chiral") NLSMs on a Lie Group G with a WZW term at level k. In these models the role of high-gradient operators is played by homogeneous polynomials of order 2s in the Noether currents, whose scaling dimensions we analyze. For the Lie Supergroup G=GL(2N|2N) and k=1, this corresponds to time-reversal invariant problems of Anderson localization in the so-called chiral symmetry classes, and the strength of the current-current interaction, a measure of the strength of disorder, is known to be completely marginal (for any k). We find that all high-gradient (polynomial) operators are, to one loop order, irrelevant or relevant depending on the sign of that interaction.

cond-mat.mes-hall↗

arXiv2009

The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality

The quantum spin Hall effect shares many similarities (and some important differences) with the quantum Hall effect for the electric charge. As with the quantum (electric charge) Hall effect, there exists a correspondence between bulk and boundary physics that allows to characterize the quantum spin Hall effect in diverse and complementary ways. In this paper, we derive from the network model that encodes the quantum spin Hall effect, the so-called Z_2 network model, a Dirac Hamiltonian in two dimensions. In the clean limit of this Dirac Hamiltonian, we show that the bulk Kane-Mele Z_2 invariant is nothing but the SU(2) Wilson loop constructed from the SU(2) Berry connection of the occupied Dirac-Bloch single-particle states. In the presence of disorder, the non-linear sigma model (NLSM) that is derived from this Dirac Hamiltonian describes a metal-insulator transition in the standard two-dimensional symplectic universality class. In particular, we show that the fermion doubling prevents the presence of a topological term in the NLSM that would change the universality class of the ordinary two-dimensional symplectic metal-insulator transition. This analytical result is fully consistent with our previous numerical studies of the bulk critical exponents at the metal-insulator transition encoded by the Z_2 network model. Finally, we improve the quality and extend the numerical study of boundary multifractality in the Z_2 topological insulator. We show that the hypothesis of two-dimensional conformal invariance at the metal-insulator transition is verified within the accuracy of our numerical results.

cond-mat.mes-hall↗

arXiv2009

The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels

We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires perturbed by weak quenched disorder. Past works using this approach have considered a single chain. Here, we extend the formalism to treat a quasi-one-dimensional system: a quantum wire with an arbitrary number of channels coupled by random hopping amplitudes. The computations are carried out explicitly for the case of a chiral quasi-one-dimensional wire with broken time-reversal symmetry (chiral-unitary symmetry class). By treating the space direction along the chains as imaginary time, the effects of the disorder are encoded in the time evolution induced by a single site superspin (non-Hermitian) Hamiltonian. We obtain the density of states near the band center of an infinitely long quantum wire. Our results agree with those based on the Dorokhov-Mello-Pereyra-Kumar equation for the chiral-unitary symmetry class.

cond-mat.dis-nn↗

arXiv2009

Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics

We classify all possible 36 gap-opening instabilities in graphene-like structures in two dimensions, i.e., masses of Dirac Hamiltonian when the spin, valley, and superconducting channels are included. These 36 order parameters break up into 56 possible quintuplets of masses that add in quadrature, and hence do not compete and thus can coexist. There is additionally a 6th competing mass, the one added by Haldane to obtain the quantum Hall effect in graphene without magnetic fields, that breaks time-reversal symmetry and competes with all other masses in any of the quintuplets. Topological defects in these 5-dimensional order parameters can generically bind excitations with fractionalized quantum numbers. The problem simplifies greatly if we consider spin-rotation invariant systems without superconductivity. In such simplified systems, the possible masses are only 4 and correspond to the Kekulé dimerization pattern, the staggered chemical potential, and the Haldane mass. Vortices in the Kekulé pattern are topological defects that have Abelian fractional statistics in the presence of the Haldane term. We calculate the statistical angle by integrating out the massive fermions and constructing the effective field theory for the system. Finally, we discuss how one can have generically non-Landau-Ginzburg-type transitions, with direct transitions between phases characterized by distinct order parameters.

cond-mat.str-el↗

arXiv2009

Unconventional Fermi surface spin textures in the Bi_xPb_{1-x}/Ag(111) surface alloy

The Fermi and Rashba energies of surface states in the Bi_xPb_{1-x}/Ag(111) alloy can be tuned simultaneously by changing the composition parameter x. We report on unconventional Fermi surface spin textures observed by spin and angle-resolved photoemission spectroscopy {that are correlated with a topological transition of the Fermi surface occurring at x=0.5. We show that the surface states remain fully spin polarized upon alloying and that the spin polarization vectors are approximately tangential to the constant energy contours. We discuss the implications of the topological transition for the transport of spin.

cond-mat.mtrl-sci↗

arXiv2008

Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions

Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation symmetry is broken. The critical exponent $ν$ that characterizes the diverging localization length and the bulk multifractal scaling exponents that characterize the amplitudes of the critical wave functions at the metal-insulator transition do not depend on the topological nature of the insulating state, i.e., whether it is topologically trivial (ordinary insulator) or nontrivial (a $Z_2$ insulator supporting a quantum spin Hall effect). This is not true of the boundary multifractal scaling exponents which we show (numerically) to depend on whether the insulating state is topologically trivial or not.

cond-mat.mes-hall↗

arXiv2008

Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field

The effect of strong long-range disorder on the quantization of the Hall conductivity $σ_{xy}$ in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in $σ_{xy}$ except the plateaus at $σ_{xy}=\mp e^2/2h$ (per valley and per spin). The critical state at the charge-neutral Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.

cond-mat.mes-hall↗

arXiv2008

Irrational vs. rational charge and statistics in two-dimensional quantum systems

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-biding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge re-rationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).

cond-mat.str-el↗

arXiv2007

Electron fractionalization for two-dimensional Dirac fermions

Fermion-number fractionalization without breaking of time-reversal symmetry was recently demonstrated for a field theory in $(2+1)$-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued Higgs field carrying an axial gauge charge of 2, and a U(1) axial gauge field. Charge fractionalization occurs whenever the Higgs field either supports vortices by itself, or when these vortices are accompanied by half-vortices in the axial gauge field. The fractional charge is computed by three different techniques. A formula for the fractional charge is given as a function of a parameter in the Dirac Hamiltonian that breaks the spectral energy-reflection symmetry. In the presence of a charge $\pm1$ vortex in the Higgs field only, the fractional charge varies continuously and thus can take irrational values. The simultaneous presence of a half-vortex in the axial gauge field and a charge $\pm1$ vortex in the Higgs field re-rationalizes the fractional charge to the value 1/2.

hep-th↗

arXiv2007

Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization

We discuss, for a two-dimensional Dirac Hamiltonian with random scalar potential, the presence of a $Z_2$ topological term in the non-linear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The $Z_2$ topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This $Z_2$ topological effect can be relevant to graphene when the impurity potential is long-ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of $Z_2$ topological insulators in the symplectic symmetry class.

cond-mat.mes-hall↗

arXiv2007

Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect

The effects of static disorder on the Z_2 quantum spin-Hall effect for non-interacting electrons propagating in two-dimensional space is studied numerically. A two-dimensional time-reversal symmetric network model is constructed to account for the effects of static disorder on the propagation of non-interacting electrons subjected to spin-orbit couplings. This network model is different from past network models belonging to the symplectic symmetry class in that the propagating modes along the links of the network can be arranged into an odd number of Kramers doublet. It is found that (1) a two-dimensional metallic phase of finite extent is embedded in a Z_2 insulating phase in parameter space and (2) the quantum phase transitions between the metallic and Z_2 insulating phases belong to the conventional symplectic universality class in two space dimensions.

cond-mat.mes-hall↗

arXiv2007

Screening in (d+s)-wave superconductors: Application to Raman scattering

We study the polarization-dependent electronic Raman response of untwinned YBa$_2$Cu$_3$O$_{7-δ}$ superconductors employing a tight-binding band structure with anisotropic hopping matrix parameters and a superconducting gap with a mixing of $d$- and s-wave symmetry. Using general arguments we find screening terms in the $B^{\}_{1g}$ scattering channel which are required by gauge invariance. As a result, we obtain a small but measurable softening of the pair-breaking peak, whose position has been attributed for a long time to twice the superconducting gap maximum. Furthermore, we predict superconductivity-induced changes in the phonon line shapes that could provide a way to detect the isotropic s-wave admixture to the superconducting gap.

cond-mat.supr-con↗

arXiv2007

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero-modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.

cond-mat.mes-hall↗

arXiv2007

Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interactions that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.

cond-mat.str-el↗

arXiv2006

Scaling relations in quasi-two-dimensional Heisenberg antiferromagnet

The large-N expansion of the quasi-two-dimensional quantum nonlinear $σ$ model (QNLSM) is used in order to establish experimentally applicable universal scaling relations for the quasi-two-dimensional Heisenberg antiferromagnet. We show that, at $N=\infty$, the renormalized coordination number introduced by Yasuda \textit{et al.}, Phys. Rev. Lett. \textbf{94}, 217201 (2005), is a universal number in the limit of $J'/J\to 0$. Moreover, similar scaling relations proposed by Hastings and Mudry, Phys. Rev. Lett. \textbf{96}, 027215 (2006), are derived at $N=\infty$ for the three-dimensional static spin susceptibility at the wave vector $(π,π,0)$, as well as for the instantaneous structure factor at the same wave vector. We then use 1/N corrections to study the relation between interplane coupling, correlation length, and critical temperature, and show that the universal scaling relations lead to logarithmic corrections to previous mean-field results.

cond-mat.str-el↗

arXiv2006

Theory for Inelastic Neutron Scattering in Orthorhombic High-Tc Superconductors

Using a Fermi-liquid-based theory we calculate the in-plane anisotropy of the spin susceptibility for hole-doped high-T_c cuprates. Employing the two-dimensional one-band Hubbard model and a generalized RPA-type theory we consider anisotropic hopping matrix elements ($t_x \neq t_y$) and a mixing of d- and s-wave symmetry of the superconducting order parameter in order to describe orthorhombic superconductors. We compare our calculations with available inelastic neutron scattering data on untwinned YBa{2}Cu{3}O{7-δ} and find good agreement. Furthermore, we predict a strongly anisotropic in-plane dispersion of the resonance peak.

cond-mat.supr-con↗

arXiv2005

High-Temperature Criticality in Strongly Constrained Quantum Systems

The exotic nature of many strongly correlated materials at reasonably high temperatures, for instance cuprate superconductors in their normal state, has lead to the suggestion that such behavior occurs within a quantum critical region where the physics is controlled by the influence of a phase transition down at zero temperature. Such a scenario can be thought of as a bottom-up approach, with the zero temperature mechanisms finding a way to manifest critical behavior at high temperatures. Here we propose an alternative, top-down, mechanism by which strong kinematic constraints that can only be broken at extremely high temperatures are responsible for critical behavior at intermediate but still high temperatures. This critical behavior may extend all the way down to zero temperature, but this outcome is not one of necessity, and the system may order at low temperatures. We provide explicit examples of such high-temperature criticality when additional strong interactions are introduced in quantum Heisenberg, transverse field Ising, and some bosonic lattice models.

cond-mat.str-el↗