42 research outputs found
Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene
We study the realization in a model of graphene of the phenomenon whereby the
tendency of gauge-field mediated interactions to break chiral symmetry
spontaneously is greatly enhanced in an external magnetic field. We prove that,
in the weak coupling limit, and where the electron-electron interaction
satisfies certain mild conditions, the ground state of charge neutral graphene
in an external magnetic field is a quantum Hall ferromagnet which spontaneously
breaks the emergent U(4) symmetry to U(2)XU(2).
We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet
order parameter is given exactly by the leading order in perturbation theory.
On the other hand, the chiral condensate which is the order parameter for
chiral symmetry breaking generically obtains contributions at all orders. We
compute the leading correction to the chiral condensate. We argue that the
ensuing fermion spectrum resembles that of massive fermions with a vanishing
U(4)-valued chemical potential. We discuss the realization of parity and charge
conjugation symmetries and argue that, in the context of our model, the charge
neutral quantum Hall state in graphene is a bulk insulator, with vanishing
longitudinal conductivity due to a charge gap and Hall conductivity vanishing
due to a residual discrete particle-hole symmetry.Comment: 35 page
Thermally fluctuating superconductors in two dimensions
We describe the different regimes of finite temperature dynamics in the
vicinity of a zero temperature superconductor to insulator quantum phase
transition in two dimensions. New results are obtained for a low temperature
phase-only hydrodynamics, and for the intermediate temperature quantum-critical
region. In the latter case, we obtain a universal relationship between the
frequency-dependence of the conductivity and the value of the d.c. resistance.Comment: Presentation completely revised; 4 pages, 2 figure
Ripple Texturing of Suspended Graphene Atomic Membranes
Graphene is the nature's thinnest elastic membrane, with exceptional
mechanical and electrical properties. We report the direct observation and
creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene
sheets, using spontaneously and thermally induced longitudinal strains on
patterned substrates, with control over their orientations and wavelengths. We
also provide the first measurement of graphene's thermal expansion coefficient,
which is anomalously large and negative, ~ -7x10^-6 K^-1 at 300K. Our work
enables novel strain-based engineering of graphene devices.Comment: 15 pages, 4 figure
Pair-breaking quantum phase transition in superconducting nanowires
A quantum phase transition (QPT) between distinct ground states of matter is
a wide-spread phenomenon in nature, yet there are only a few experimentally
accessible systems where the microscopic mechanism of the transition can be
tested and understood. These cases are unique and form the experimentally
established foundation for our understanding of quantum critical phenomena.
Here we report the discovery that a magnetic-field-driven QPT in
superconducting nanowires - a prototypical 1d-system - can be fully explained
by the critical theory of pair-breaking transitions characterized by a
correlation length exponent and dynamic critical exponent . We find that in the quantum critical regime, the electrical
conductivity is in agreement with a theoretically predicted scaling function
and, moreover, that the theory quantitatively describes the dependence of
conductivity on the critical temperature, field magnitude and orientation,
nanowire cross sectional area, and microscopic parameters of the nanowire
material. At the critical field, the conductivity follows a
dependence predicted by phenomenological scaling theories and more recently
obtained within a holographic framework. Our work uncovers the microscopic
processes governing the transition: The pair-breaking effect of the magnetic
field on interacting Cooper pairs overdamped by their coupling to electronic
degrees of freedom. It also reveals the universal character of continuous
quantum phase transitions.Comment: 22 pages, 5 figure
Domain wall fermions for planar physics
In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations which preserve the global U(2N) symmetry present in the massless limit, and its breakdown to U(N)xU(N) implemented by three independent and parity-invariant fermion mass terms. I set out generalisations of the Ginsparg-Wilson relation, leading to a formulation of an overlap operator, and explore the remnants of the global symmetries which depart from the continuum form by terms of order of the lattice spacing. I also define a domain wall formulation in 2+1+1d, and present numerical evidence, in the form of bilinear condensate and meson correlator calculations in quenched non-compact QED using reformulations of all three mass terms, to show that U(2N) symmetry is recovered in the limit that the domain-wall separation L tends to infinity. The possibility that overlap and domain wall formulations of reducible fermions may coincide only in the continuum limit is discussed
Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
The flat bands in bilayer graphene(BLG) are sensitive to electric fields
E\bot directed between the layers, and magnify the electron-electron
interaction effects, thus making BLG an attractive platform for new
two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the
possibility of a variety of interesting broken symmetry states, some
characterized by spontaneous mass gaps, when the electron-density is at the
carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in
bilayer graphene are analogous[17,18] to the masses generated by broken
symmetries in particle physics and give rise to large momentum-space Berry
curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though
recent experiments[20-23] have provided convincing evidence of strong
electronic correlations near the CNP in BLG, the presence of gaps is difficult
to establish because of the lack of direct spectroscopic measurements. Here we
present transport measurements in ultra-clean double-gated BLG, using
source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the
CNP. The gap can be closed by an electric field E\bot \sim13 mV/nm but
increases monotonically with a magnetic field B, with an apparent particle-hole
asymmetry above the gap, thus providing the first mapping of the ground states
in BLG.Comment: 4 figure
Artificial graphene as a tunable Dirac material
Artificial honeycomb lattices offer a tunable platform to study massless
Dirac quasiparticles and their topological and correlated phases. Here we
review recent progress in the design and fabrication of such synthetic
structures focusing on nanopatterning of two-dimensional electron gases in
semiconductors, molecule-by-molecule assembly by scanning probe methods, and
optical trapping of ultracold atoms in crystals of light. We also discuss
photonic crystals with Dirac cone dispersion and topologically protected edge
states. We emphasize how the interplay between single-particle band structure
engineering and cooperative effects leads to spectacular manifestations in
tunneling and optical spectroscopies.Comment: Review article, 14 pages, 5 figures, 112 Reference
Inverse magnetic catalysis in dense holographic matter
We study the chiral phase transition in a magnetic field at finite
temperature and chemical potential within the Sakai-Sugimoto model, a
holographic top-down approach to (large-N_c) QCD. We consider the limit of a
small separation of the flavor D8-branes, which corresponds to a dual field
theory comparable to a Nambu-Jona Lasinio (NJL) model. Mapping out the surface
of the chiral phase transition in the parameter space of magnetic field
strength, quark chemical potential, and temperature, we find that for small
temperatures the addition of a magnetic field decreases the critical chemical
potential for chiral symmetry restoration - in contrast to the case of
vanishing chemical potential where, in accordance with the familiar phenomenon
of magnetic catalysis, the magnetic field favors the chirally broken phase.
This "inverse magnetic catalysis" (IMC) appears to be associated with a
previously found magnetic phase transition within the chirally symmetric phase
that shows an intriguing similarity to a transition into the lowest Landau
level. We estimate IMC to persist up to 10^{19} G at low temperatures.Comment: 42 pages, 11 figures, v3: extended discussion; new appendix D;
references added; version to appear in JHE
Spin and valley quantum Hall ferromagnetism in graphene
In a graphene Landau level (LL), strong Coulomb interactions and the fourfold
spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At
partial filling, exchange interactions can spontaneously break this symmetry,
manifesting as additional integer quantum Hall plateaus outside the normal
sequence. Here we report the observation of a large number of these quantum
Hall isospin ferromagnetic (QHIFM) states, which we classify according to their
real spin structure using temperature-dependent tilted field magnetotransport.
The large measured activation gaps confirm the Coulomb origin of the broken
symmetry states, but the order is strongly dependent on LL index. In the high
energy LLs, the Zeeman effect is the dominant aligning field, leading to real
spin ferromagnets with Skyrmionic excitations at half filling, whereas in the
`relativistic' zero energy LL, lattice scale anisotropies drive the system to a
spin unpolarized state, likely a charge- or spin-density wave.Comment: Supplementary information available at http://pico.phys.columbia.ed
Theory of Multidimensional Solitons
We review a number of topics germane to higher-dimensional solitons in
Bose-Einstein condensates. For dark solitons, we discuss dark band and planar
solitons; ring dark solitons and spherical shell solitons; solitary waves in
restricted geometries; vortex rings and rarefaction pulses; and multi-component
Bose-Einstein condensates. For bright solitons, we discuss instability,
stability, and metastability; bright soliton engineering, including pulsed atom
lasers; solitons in a thermal bath; soliton-soliton interactions; and bright
ring solitons and quantum vortices. A thorough reference list is included.Comment: review paper, to appear as Chapter 5a in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag