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Christopher Mudry

Publications and source records attributed to Christopher Mudry.

At least 55 records · Page 3Linked to original sources
arXiv2014

Magnetic nano-fluctuations in a frustrated magnet

Frustrated systems exhibit remarkable properties due to the high degeneracy of their ground states. Stabilised by competing interactions, a rich diversity of typically nanometre-sized phase structures appear in polymer and colloidal systems, while the surface of ice pre-melts due to geometrically frustrated interactions. Atomic spin systems where magnetic interactions are frustrated by lattice geometry provide a fruitful source of emergent phenomena, such as fractionalised excitations analogous to magnetic monopoles. The degeneracy inherent in frustrated systems may prevail all the way down to absolute zero temperature, or it may be lifted by small perturbations or entropic effects. In the geometrically frustrated Ising--like magnet Ca3Co2O6, we follow the temporal and spatial evolution of nanoscale magnetic fluctuations firmly embedded inside the spin--density--wave magnetic structure. These fluctuations are a signature of a competing ferrimagnetic phase with an incommensurability that is different from, but determined by the host. As the temperature is lowered, the fluctuations slow down into a super-paramagnetic regime of stable spatiotemporal nano-structures.

cond-mat.str-el↗
arXiv2014

Spin-directed network model for the surface states of weak three-dimensional $\mathbb{Z}^{\,}_{2}$ topological insulators

A two-dimensional spin-directed $\mathbb{Z}^{\,}_{2}$ network model is constructed that describes the combined effects of dimerization and disorder for the surface states of a weak three-dimensional $\mathbb{Z}^{\,}_{2}$ topological insulator. The network model consists of helical edge states of two-dimensional layers of $\mathbb{Z}^{\,}_{2}$ topological insulators which are coupled by time-reversal symmetric interlayer tunneling. It is argued that, without dimerization of interlayer couplings, the network model has no insulating phase for any disorder strength. However, a sufficiently strong dimerization induces a transition from a metallic phase to an insulating phase. The critical exponent $ν$ for the diverging localization length at metal-insulator transition points is obtained by finite-size scaling analysis of numerical data from simulations of this network model. It is shown that the phase transition belongs to the two-dimensional symplectic universality class of Anderson transition.

cond-mat.mes-hall↗
arXiv2014

Erratum for "Elementary formula for the Hall conductivity of interacting systems"

When deriving a formula for the Hall conductivity of interacting electrons in Phys. Rev. B 86, 165133, we have relied on an unjustified implicit assumption that a certain gauge choice could be made. Only under this condition would the formula follow. If this condition fails, the formula we derived does not lead to the exactly quantized value of the Hall conductance in fractional Chern insulators.

cond-mat.str-el↗
arXiv2013

Fractional Chern insulators with strong interactions far exceeding bandgaps

We study two models for spinless fermions featuring topologically non-trivial bands characterized by Chern numbers $C=\pm1$ at fractional filling. Using exact diagonalization, we show that, even for infinitely strong nearest-neighbor repulsion, the ground states of these models belong to the recently discovered class of quantum liquids called fractional Chern insulators (FCI). We thus establish that FCI states can arise even if interaction strengths are arbitrarily larger than the noninteracting band gap, going beyond the limits in which FCI states have been previously studied. The strong-coupling FCI states therefore depart from the usual isolated-band picture that parallels the fractional quantum Hall effect in Landau levels and demonstrate how a topologically ordered state can arise in a truly multiband system.

cond-mat.str-el↗
arXiv2013

How to Measure the Quantum Geometry of Bloch Bands

Single-particle states in electronic Bloch bands form a Riemannian manifold whose geometric properties are described by two gauge invariant tensors, one being symmetric the other being antisymmetric, that can be combined into the so-called Fubini-Study metric tensor of the projective Hilbert space. The latter directly controls the Hall conductivity. Here we show that the symmetric part of the Fubini-Study metric tensor also has measurable consequences by demonstrating that it enters the current noise spectrum. In particular, we show that a non-vanishing equilibrium current noise spectrum at zero temperature is unavoidable whenever Wannier states have non-zero minimum spread, the latter being quantifiable by the symmetric part of the Fubini-Study metric tensor. We illustrate our results by three examples: (1) atomic layers of hexagonal boron nitride, (2) graphene, and (3) the surface states of three-dimensional topological insulators when gaped by magnetic dopants.

cond-mat.str-el↗
arXiv2012

Enhancing the stability of a fractional Chern insulator against competing phases

We construct a two-band lattice model whose bands can carry the Chern numbers C=0,pm1,pm2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number C=2 instead of C=1. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.

cond-mat.str-el↗
arXiv2012

Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension

The magnetic translation algebra plays an important role in the quantum Hall effect. Murthy and Shankar, arXiv:1207.2133, have shown how to realize this algebra using fermionic bilinears defined on a two-dimensional square lattice. We show that, in any dimension $d$, it is always possible to close the magnetic translation algebra using fermionic bilinears, whether in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the $f$-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare bandwidth of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra.

cond-mat.str-el↗
arXiv2012

Global phase diagram of two-dimensional Dirac fermions in random potentials

Anderson localization is studied for two flavors of massless Dirac fermions in 2D space perturbed by static disorder that is invariant under a chiral symmetry (chS) and a time-reversal symmetry (TRS) operation which, when squared, is equal either to plus or minus the identity. The former TRS (symmetry class BDI) can for example be realized when the Dirac fermions emerge from spinless fermions hopping on a 2D lattice with a linear energy dispersion such as the honeycomb lattice (graphene) or the square lattice with $π$-flux per plaquette. The latter TRS is realized by the surface states of 3D $\mathbb{Z}_{2}$-topological band insulators in symmetry class CII. In the phase diagram parametrized by the disorder strengths, there is an infrared stable line of critical points for both symmetry classes BDI and CII. Here we discuss a "global phase diagram" in which disordered Dirac fermion systems in all three chiral symmetry classes, AIII, CII, and BDI, occur in 4 quadrants, sharing one corner which represents the clean Dirac fermion limit. This phase diagram also includes symmetry classes AII [e.g., appearing at the surface of a disordered 3D $\mathbb{Z}_2$-topological band insulator in the spin-orbit (symplectic) symmetry class] and D (e.g., the random bond Ising model in two dimensions) as boundaries separating regions of the phase diagram belonging to the three chS classes AIII, BDI, and CII. Moreover, we argue that physics of Anderson localization in the CII phase can be presented in terms of a non-linear-sigma model (NLsM) with a $\mathbb{Z}_{2}$-topological term. We thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten terms in the NLsM description of disordered fermionic models in all 10 symmetry classes relevant to Anderson localization in two spatial dimensions.

cond-mat.mes-hall↗
arXiv2012

Masses and Majorana fermions in graphene

We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.

cond-mat.mes-hall↗
arXiv2012

Noncommutative geometry for three-dimensional topological insulators

We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.

cond-mat.str-el↗
arXiv2012

Topological Hubbard model and its high-temperature quantum Hall effect

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.

cond-mat.str-el↗
arXiv2011

Time-reversal symmetric hierarchy of fractional incompressible liquids

We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.

cond-mat.str-el↗
arXiv2011

Fractional topological liquids with time-reversal symmetry and their lattice realization

We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a Z_2 stability criterion for whether or not there exists a Kramers pair of edge modes that is robust against disorder. We also introduce an interacting electronic two-dimensional lattice model based on partially filled flattened bands of a Z_2 topological band insulator, which we study using numerical exact diagonalization. We show evidence for instances of the fractional topological liquid phase as well as for a time-reversal symmetry broken phase with a quantized (charge) Hall conductance in the phase diagram for this model.

cond-mat.str-el↗
arXiv2011

Fractional quantum Hall states at zero magnetic field

We present a simple prescription to flatten isolated Bloch bands with non-zero Chern number. We first show that approximate flattening of bands with non-zero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest neighbor hoppings in the Haldane model and, similarly, in the chiral-pi-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.

cond-mat.str-el↗
arXiv2011

Counting Majorana zero modes in superconductors

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.

cond-mat.supr-con↗
arXiv2010

Topological qubits in graphenelike systems

The fermion-doubling problem can be an obstacle to getting half-a-qubit in two-dimensional fermionic tight-binding models in the form of Majorana zero modes bound to the core of superconducting vortices. We argue that the number of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for a family of two-dimensional fermionic tight-binding models ranging from noncentrosymmetric materials to graphene. This charge depends on the dimension of the representation (i.e., the number of species of Dirac fermions -- where the doubling problem enters) and the parity of the Chern number induced by breaking time-reversal symmetry. We show that in graphene there are as many as ten order parameters that can be used in groups of four to change the topological number from even to odd.

cond-mat.mes-hall↗
arXiv2010

Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials

We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulators. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlets or pure triplets pairs of electrons in and out of the condensate, a corollary to the non-conservation of spin due to the spin-orbit coupling. We identify one single superconducting regime in the case of superconductivity in the topological surface states (Rashba-Dirac limit), irrespective of the relative strength between singlet and triplet pair potentials. In contrast, in the Fermi limit relevant to the noncentrosymmetric materials we find two regimes depending on the value of the chemical potential and the relative strength between singlet and triplet potentials. We construct explicitly the Majorana bound states in these regimes. In the single regime for the case of the Rashba-Dirac limit, there exist one and only one Majorana fermion bound to the core of an isolated vortex. In the Fermi limit, there are always an even number (0 or 2 depending on the regime) of Majorana fermions bound to the core of an isolated vortex. In all cases, the vorticity required to bind Majorana fermions is unity, in contrast to the half-flux in the case of two-dimensional $p_x \pm i p_y$ superconductors that break time-reversal symmetry.

cond-mat.supr-con↗