arXiv subjects

M. Franz

Publications and source records attributed to M. Franz.

At least 73 records · Page 4Linked to original sources

arXiv2009

Inverse Spin-Galvanic Effect in a Topological-Insulator/Ferromagnet Interface

When a ferromagnet is deposited on the surface of a topological insulator the topologically protected surface state develops a gap and becomes a 2-dimensional quantum Hall liquid. We demonstrate that the Hall current in such a liquid, induced by an external electric field, can have a large effect on the magnetization dynamics of the ferromagnet by changing the effective anisotropy field. This change is dissipationless and may be substantial even in weakly spin-orbit coupled ferromagnets. We study the possibility of dissipationless current-induced magnetization reversal in monolayer-thin, insulating ferromagnets with a soft perpendicular anisotropy and discuss possible applications of this effect.

cond-mat.mtrl-sci↗

arXiv2009

Interaction driven instabilities of a Dirac semi-metal

We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and pi-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic `quantum anomalous Hall' (Haldane) phase, we establish the existence of the dimerized Kekule phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the `spin Kekule' phase. On the pi-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekule phase is described by a Z3 order parameter whose singly quantized vortices carry fractional charge +/- e/2. On the pi-flux lattice the analogous dimerized phase is described by a Z4 order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear Z4 structure emerges with domain walls along the lattice diagonals.

cond-mat.str-el↗

arXiv2009

Topological insulator on the kagome lattice

Itinerant electrons in a two-dimensional Kagome lattice form a Dirac semi-metal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semi-metal is shown to spawn interesting non-magnetic insulating phases. These include a two-dimensional topological insulator with a non-trivial Z_2 invariant and robust gapless edge states, as well as dimerized and trimerized `Kekule' insulators. The latter two are topologically trivial but the Kekule phase possesses a complex order parameter with fractionally charged vortex excitations. A charge density wave is shown to couple to the Dirac fermions as an effective axial gauge field.

cond-mat.mes-hall↗

arXiv2009

Exciton condensation and charge fractionalization in a topological insulator film

An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a coherent exciton condensate, similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. Such a `topological' exciton condensate (TEC) exhibits a host of unusual properties; the most interesting among them is the fractional charge +-e/2 carried by a singly quantized vortex in the TEC order parameter.

cond-mat.str-el↗

arXiv2009

Quantum oscillations from Fermi arcs

When a metal is subjected to strong magnetic field B nearly all measurable quantities exhibit oscillations periodic in 1/B. Such quantum oscillations represent a canonical probe of the defining aspect of a metal, its Fermi surface (FS). In this study we establish a new mechanism for quantum oscillations which requires only finite segments of a FS to exist. Oscillations periodic in 1/B occur if the FS segments are terminated by a pairing gap. Our results reconcile the recent breakthrough experiments showing quantum oscillations in a cuprate superconductor YBCO, with a well-established result of many angle resolved photoemission (ARPES) studies which consistently indicate "Fermi arcs" -- truncated segments of a Fermi surface -- in the normal state of the cuprates.

cond-mat.supr-con↗

arXiv2009

Creation and manipulation of anyons in a layered superconductor-2DEG system

We describe and analyze in detail our recent theoretical proposal for the realization and manipulation of anyons in a weakly interacting system consisting of a two-dimensional electron gas in the integer quantum Hall regime adjacent to a type-II superconducting film with an artificial array of pinning sites. The anyon is realized in response to a defect in the pinned vortex lattice and carries a charge \pm e/2 and a statistical angle pi/4. We establish this result, both analytically and numerically, in three complementary approaches: (i) a continuum model of two-dimensional electrons in the vortex lattice of the superconducting film; (ii) a minimal tight-binding lattice model that captures the essential features of the system; and (iii) an effective theory of the superconducting vortex lattice superposed on the integer quantum Hall state. We propose a novel method to measure the fractional charge directly in a bulk transport experiment and an all-electric setup for an ``anyon shuttle'' implementing the braiding operations. We briefly discuss conditions for fabricating the system in the lab and its potential applications in quantum information processing with non-Abelian anyons.

cond-mat.mes-hall↗

arXiv2008

Giant proximity effect in a phase-fluctuating superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.

cond-mat.supr-con↗

arXiv2008

Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.

cond-mat.str-el↗

arXiv2008

Magnetic field evolution of the quasiparticle interference in a d-wave superconductor

Quasiparticle interference in a d-wave superconductor with weak disorder produces distinctive peaks in the Fourier-transformed local density of states measured by scanning tunneling spectroscopy. We predict that amplitudes of these peaks can be enhanced or suppressed by applied magnetic field according to a very specific pattern governed by the symmetry of the superconducting order parameter. This calculated pattern agrees with the recent experimental measurement and suggests that the technique could be useful for probing the underlying normal state at high fields.

cond-mat.supr-con↗

arXiv2007

Fractionalization in a square-lattice model with time-reversal symmetry

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.

cond-mat.str-el↗

arXiv2007

Fractional statistics of topological defects in graphene and related structures

We show that fractional charges bound to topological defects in the recently proposed time-reversal-invariant models on honeycomb and square lattices obey fractional statistics. The effective low-energy description is given in terms of a `doubled' level-2 Chern-Simons field theory, which is parity and time-reversal invariant and implies two species of semions (particles with statistical angle pi/2) labeled by a new emergent quantum number that we identify as the fermion axial charge.

cond-mat.str-el↗

arXiv2007

Vortex-boson duality in four space-time dimensions

A continuum version of the vortex-boson duality in (3+1) dimensions is formulated and its implications studied in the context of a pair Wigner crystal in underdoped cuprate superconductors. The dual theory to a phase fluctuating superconductor (or superfluid) is shown to be a theory of bosonic strings interacting through a Kalb-Ramond rank-2 tensorial gauge field. String condensation produces Higgs mass for the gauge field and the expected Wigner crystal emerges as an interesting space-time analog of the Abrikosov lattice.

cond-mat.str-el↗

arXiv2007

Anyons in a weakly interacting system

We describe a theoretical proposal for a system whose excitations are anyons with the exchange phase pi/4 and charge -e/2, but, remarkably, can be built by filling a set of single-particle states of essentially noninteracting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a 2D electron gas in the integer quantum Hall regime with unit filling fraction. The proposal rests on the observation that a vacancy in an otherwise periodic vortex lattice in the superconductor creates a bound state in the 2DEG with total charge -e/2. A composite of this fractionally charged hole and the missing flux due to the vacancy behaves as an anyon. The proposed setup allows for manipulation of these anyons and could prove useful in various schemes for fault-tolerant topological quantum computation.

cond-mat.mes-hall↗

arXiv2006

Duality and the vibrational modes of a Cooper-pair Wigner crystal

When quantum fluctuations in the phase of the superconducting order parameter destroy the off-diagonal long range order, duality arguments predict the formation of a Cooper pair crystal. This effect is thought to be responsible for the static checkerboard patterns observed recently in various underdoped cuprate superconductors by means of scanning tunneling spectroscopy. Breaking of the translational symmetry in such a Cooper pair Wigner crystal may, under certain conditions, lead to the emergence of low lying transverse vibrational modes which could then contribute to thermodynamic and transport properties at low temperatures. We investigate these vibrational modes using a continuum version of the standard vortex-boson duality, calculate the speed of sound in the Cooper pair Wigner crystal and deduce the associated specific heat and thermal conductivity. We then suggest that these modes could be responsible for the mysterious bosonic contribution to the thermal conductivity recently observed in strongly underdoped ultraclean single crystals of YBCO tuned across the superconductor-insulator transition.

cond-mat.supr-con↗

arXiv2006

4D-XY quantum criticality in a doped Mott insulator

A new phenomenology is proposed for the superfluid density of strongly underdoped cuprate superconductors based on recent data for ultra-clean single crystals of YBCO. The data feature a puzzling departure from Uemura scaling and a decline of the slope as the T_c = 0 quantum critical point is approached. We show that this behavior can be understood in terms of the renormalization of quasiparticle effective charge by quantum fluctuations of the superconducting phase as described by a (3+1)-dimensional XY model. We calculate the renormalization of the superfluid density and its slope, explain the new phenomenology, and predict its eventual demise close to the QCP.

cond-mat.supr-con↗

arXiv2005

Quasiparticle interference patterns as a test for the nature of the pseudogap phase in the cuprate superconductors

Electrons, when scattered by static random disorder, form standing waves that can be imaged using scanning tunneling microscopy. Such interference patterns, observable by the recently developed technique of Fourier transform scanning tunneling spectroscopy (FT-STS), are shown to carry unique fingerprints characteristic of the electronic order present in a material. We exploit this feature of the FT-STS technique to propose a test for the nature of the enigmatic pseudogap phase in the high-$T_c$ cuprate superconductors. Through their sensitivity to the quasiparticle spectra and coherence factors, the FT-STS patterns in principle carry enough information to unambiguously determine the nature of the condensate responsible for the pseudogap phenomenon. We argue that the next generation of FT-STS experiments, currently underway, should be able to distinguish between the pseudogap dominated by the remnants of superconducting order from the pseudogap dominated by some competing order in the particle-hole channel. Using general arguments and detailed numerical calculations, we point to certain fundamental differences between the two scenarios and discuss the prospects for future experiments.

cond-mat.supr-con↗

arXiv2004

Exact summation of vertex corrections to the penetration depth in d-wave superconductors

A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this result to be relevant to the $ab$-plane penetration depth in high-purity single crystals of underdoped YBCO.

cond-mat.supr-con↗

arXiv2004

Crystalline electron pairs

This is a nontechnical Perspective Commentary on the recent developments in cuprate STM and their ramifications for the theories of the pseudogap state, focusing on the paper by Hanaguri et al. [Nature 430, 1001 (2004)].

cond-mat.supr-con↗