170 research outputs found
Quantum phase transitions from topology in momentum space
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
physics which emerges in the low-energy corner does not depend on the
complicated details of the system and is relatively simple. It is determined by
the nodes in the fermionic spectrum, which are protected by topology in
momentum space (in some cases, in combination with the vacuum symmetry). Close
to the nodes the behavior of the system becomes universal; and the universality
classes are determined by the toplogical invariants in momentum space. When one
changes the parameters of the system, the transitions are expected to occur
between the vacua with the same symmetry but which belong to different
universality classes. Different types of quantum phase transitions governed by
topology in momentum space are discussed in this Chapter. They involve Fermi
surfaces, Fermi points, Fermi lines, and also the topological transitions
between the fully gapped states. The consideration based on the momentum space
topology of the Green's function is general and is applicable to the vacua of
relativistic quantum fields. This is illustrated by the possible quantum phase
transition governed by topology of nodes in the spectrum of elementary
particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum
Simulations via Analogues: From Phase Transitions to Black Holes", to appear
in Springer lecture notes in physics (LNP
Quasiparticle spectrum of d-wave superconductors in the mixed state: a large Fermi-velocity anisotropy study
The quasiparticle spectrum of a two-dimensional d-wave superconductor in the
mixed state, H_c1 << H << H_c2, is studied for large values of the ``anisotropy
ratio'' alpha_D = v_F/v_Delta. For a square vortex lattice rotated by 45
degrees from the quasiparticle anisotropy axes (and the usual choice of
Franz--Tesanovic singular gauge transformation) we determine essential features
of the band structure asymptotically for large alpha_D, using an effective
one-dimensional model, and compare them to numerical calculations. We find that
several features of the band structure decay to zero exponentially fast for
large alpha_D. Using a different choice of singular gauge transformation, we
obtain a different band structure, but still find qualitative agreement between
the 1D and full 2D calculations. Finally, we distort the square lattice into a
non-Bravais lattice. Both the one- and two-dimensional numerical calculations
of the energy spectra show a gap around zero-energy, with our gauge choice, and
the two excitation spectra agree reasonably well.Comment: 14 pages, 13 figures, revte
Spontaneous symmetry breaking and the limit
We point out a basic ambiguity in the limit of the connected
propagator in a spontaneously broken phase. This may represent an indication
that the conventional singlet Higgs boson, rather than being a purely massive
field, might have a gap-less branch. This would dominate the energy spectrum
for and give rise to a very weak, long-range force. The
natural interpretation is in terms of density fluctuations of the `Higgs
condensate': in the region of very long wavelengths, infinitely larger than the
Fermi scale, it cannot be treated as a purely classical c-number field.Comment: 17 pages, LaTex, small changes and some comments adde
Electronic state around vortex in a two-band superconductor
Based on the quasiclassical theory, we investigate the vortex state in a
two-band superconductor with a small gap on a three dimensional Fermi surface
and a large gap on a quasi-two dimensional one, as in MgB_2. The field
dependence of zero-energy density of states is compared for fields parallel and
perpendicular to the ab plane, and the anisotropy of the vortex core shape is
discussed for a parallel field. The Fermi surface geometry of two-bands,
combining the effect of the normal-like electronic state on the small gap band
at high fields, produces characteristic behavior in the anisotropy of c- and
ab-directions.Comment: 6 pages, 6 figures, to appear in Phys. Rev.
as parameter of Minkowski metric in effective theory
With the proper choice of the dimensionality of the metric components, the
action for all fields becomes dimensionless. Such quantities as the vacuum
speed of light c, the Planck constant \hbar, the electric charge e, the
particle mass m, the Newton constant G never enter equations written in the
covariant form, i.e., via the metric g^{\mu\nu}. The speed of light c and the
Planck constant are parameters of a particular two-parametric family of
solutions of general relativity equations describing the flat isotropic
Minkowski vacuum in effective theory emerging at low energy:
g^{\mu\nu}=diag(-\hbar^2, (\hbar c)^2, (\hbar c)^2, (\hbar c)^2). They
parametrize the equilibrium quantum vacuum state. The physical quantities which
enter the covariant equations are dimensionless quantities and dimensionful
quantities of dimension of rest energy M or its power. Dimensionless quantities
include the running coupling `constants' \alpha_i; topological and geometric
quantum numbers (angular momentum quantum number j, weak charge, electric
charge q, hypercharge, baryonic and leptonic charges, number of atoms N, etc).
Dimensionful parameters include the rest energies of particles M_n (or/and mass
matrices); the gravitational coupling K with dimension of M^2; cosmological
constant with dimension M^4; etc. In effective theory, the interval s has the
dimension of 1/M; it characterizes the dynamics of particles in the quantum
vacuum rather than geometry of space-time. We discuss the effective action, and
the measured physical quantities resulting from the action, including
parameters which enter the Josepson effect, quantum Hall effect, etc.Comment: 18 pages, no figures, extended version of the paper accepted in JETP
Letter
Zel'dovich-Starobinsky Effect in Atomic Bose-Einstein Condensates: Analogy to Kerr Black Hole
We consider circular motion of a heavy object in an atomic Bose-Einstein
condensate (BEC) at . Even if the linear velocity of the object is
smaller than the Landau critical velocity, the object may radiate
quasiparticles and thus experience the quantum friction. The radiation process
is similar to Zel'dovich-Starobinskii (ZS) effect -- the radiation by a
rotating black hole. This analogy emerges when one introduces the effective
acoustic metric for quasiparticles. In the rotating frame this metric has an
ergosurface, which is similar to the ergosurface in the metric of a rotating
black hole. In a finite size BEC, the quasiparticle creation takes place when
the ergosurface is within the condensate and occurs via quantum tunneling from
the object into the ergoregion. The dependence of the radiation rate on the
position of the ergosurface is investigated.Comment: 6 pages, 3 figures,submitted to JLT
Cosmology, Particle Physics and Superfluid 3He
Many direct parallels connect superfluid 3He with the field theories
describing the physical vacuum, gauge fields and elementary fermions.
Superfluid He exhibits a variety of topological defects which can be
detected with single-defect sensitivity. Modern scenarios of defect-mediated
baryogenesis can be simulated by the interaction of the 3He vortices and domain
walls with fermionic quasiparticles. Formation of defects in a
symmetry-breaking phase transition in the early Universe, which could be
responsible for large-scale structure formation and for microwave-background
anisotropy, also may be modelled in the laboratory. This is supported by the
recent observation of vortex formation in neutron-irradiated 3He-B where the
"primordial fireball" is formed in an exothermic nuclear reaction.Comment: Invited talk at LT-21 Conference, 20 pages, 3 figures available at
request, compressed ps file of the camera-ready format with 3 figures is at
ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96006.ps.g
Vortex with Fractional Quantum Numbers in Chiral p-Wave Superconductor
We show that a vortex in a chiral p-wave superconductor, which has the p_{x}+
i p_{y}-wave pairing state and breaks U(1), parity and time reversal symmetry
simultaneously, has fractional charge -{n e}/{4} and fractional angular
momentum -n^{2}/{16} (n; vorticity). This suggests that the vortex could be
anyon and could obey fractional statistics. Electromagnetic property of the
vortex is also discussed and we find that an electric field is induced near the
vortex core.Comment: 10 pages, 3 figures, accepted for publication in Phys. Rev.
Wavefunction topology of two-dimensional time-reversal symmetric superconductors
We discuss the topology of the wavefunctions of two-dimensional time-reversal
symmetric superconductors. We consider (a) the planar state, (b) a system with
broken up-down reflection symmetry, and (c) a system with general spin-orbit
interaction. We show explicitly how the relative sign of the order parameter on
the two Fermi surfaces affects this topology, and clarify the meaning of the
classification for these topological states.Comment: only the Introduction has been modified from v
Singular current response from isolated impurities in d-wave superconductors
The current response of a d-wave superconductor containing a single impurity
is calculated and shown to be singular in the low-temperature limit, leading in
the case of strong scattering to a 1/T term in the penetration depth
similar to that induced by Andreev surface bound states. For a
small number of such impurities, we argue this low- upturn could be
observable in cuprate superconductors.Comment: 4 pages, 2 .eps figures. Minor changes to match the published versio
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