13,813 research outputs found
Composite fermi liquids in the lowest Landau level
We study composite fermi liquid (CFL) states in the lowest Landau level (LLL)
limit at a generic filling . We begin with the old
observation that, in compressible states, the composite fermion in the lowest
Landau level should be viewed as a charge-neutral particle carrying vorticity.
This leads to the absence of a Chern-Simons term in the effective theory of the
CFL. We argue here that instead a Berry curvature should be enclosed by the
fermi surface of composite fermions, with the total Berry phase fixed by the
filling fraction . We illustrate this point with the CFL of
fermions at filling fractions and (single and two-component) bosons
at . The Berry phase leads to sharp consequences in the transport
properties including thermal and spin Hall conductances, which in the RPA
approximation are distinct from the standard Halperin-Lee-Read predictions. We
emphasize that these results only rely on the LLL limit, and do not require
particle-hole symmetry, which is present microscopically only for fermions at
. Nevertheless, we show that the existing LLL theory of the composite
fermi liquid for bosons at does have an emergent particle-hole
symmetry. We interpret this particle-hole symmetry as a transformation between
the empty state at and the boson integer quantum hall state at .
This understanding enables us to define particle-hole conjugates of various
bosonic quantum Hall states which we illustrate with the bosonic Jain and
Pfaffian states. The bosonic particle-hole symmetry can be realized exactly on
the surface of a three-dimensional boson topological insulator. We also show
that with the particle-hole and spin rotation symmetries, there is no
gapped topological phase for bosons at .Comment: 16 pages, 1 figure, new version with minor change
Dual Dirac liquid on the surface of the electron topological insulator
We discuss a non-fermi liquid gapless metallic surface state of the
topological band insulator. It has an odd number of gapless Dirac fermions
coupled to a non-compact U(1) gauge field. This can be viewed as a vortex dual
to the conventional Dirac fermion surface state. This surface duality is a
reflection of a bulk dual description discussed recently for the gauged
topological insulator. All the other known surface states can be conveniently
accessed from the dual Dirac liquid, including the surface quantum hall state,
the Fu-Kane superconductor, the gapped symmetric topological order and the
"composite Dirac liquid". We also discuss the physical properties of the dual
Dirac liquid, and its connection to the half-filled Landau level.Comment: 5+2 page
Time-reversal symmetric U(1) quantum spin liquids
We study possible quantum spin liquids in three dimensions with
time-reversal symmetry. We find a total of 7 families of such spin
liquids, distinguished by the properties of their emergent electric/magnetic
charges. We show how these spin liquids are related to each other. Two of these
classes admit nontrivial protected surface states which we describe. We show
how to access all of the 7 spin liquids through slave particle (parton)
constructions. We also provide intuitive loop gas descriptions of their ground
state wave functions. One of these phases is the `topological Mott insulator'
conventionally described as a topological insulator of an emergent fermionic
`spinon'. We show that this phase admits a remarkable dual description as a
topological insulator of emergent fermionic magnetic monopoles. This results in
a new (possibly natural) surface phase for the topological Mott insulator and a
new slave particle construction. We describe some of the continuous quantum
phase transitions between the different spin liquids. Each of these
seven families of states admits a finer distinction in terms of their surface
properties which we determine by combining these spin liquids with symmetry
protected topological phases. We discuss lessons for materials such as
pyrochlore quantum spin ices which may harbor a spin liquid. We suggest
the topological Mott insulator as a possible ground state in some range of
parameters for the quantum spin ice Hamiltonian.Comment: 25 pages, 11 figures, 1 tabl
Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
We synthesize and partly review recent developments relating the physics of
the half-filled Landau level in two dimensions to correlated surface states of
topological insulators in three dimensions. The latter are in turn related to
the physics of certain three dimensional quantum spin liquid states. The
resulting insights provide an interesting answer to the old question of how
particle-hole symmetry is realized in composite fermion liquids. Specifically
the metallic state at filling - described originally in
pioneering work by Halperin , Lee, and Read as a liquid of composite fermions -
was proposed recently by Son to be described by a particle-hole symmetric
effective field theory distinct from that in the prior literature. We show how
the relation to topological insulator surface states leads to a physical
understanding of the correctness of this proposal. We develop a simple picture
of the particle-hole symmetric composite fermion through a modification of
older pictures as electrically neutral "dipolar" particles. We revisit the
phenomenology of composite fermi liquids (with or without particle-hole
symmetry), and show that their heat/electrical transport dramatically violates
the conventional Wiedemann-Franz law but satisfies a modified one. We also
discuss the implications of these insights for finding physical realizations of
correlated topological insulator surfaces.Comment: 22 pages, 7 figures; (v2) Added some clarifications and corrected
typo
Interacting fermionic topological insulators/superconductors in three dimensions
Symmetry Protected Topological (SPT) phases are a minimal generalization of
the concept of topological insulators to interacting systems. In this paper we
describe the classification and properties of such phases for three
dimensional(3D) electronic systems with a number of different symmetries. For
symmetries representative of all classes in the famous 10-fold way of free
fermion topological insulators/superconductors, we determine the stability to
interactions. By combining with results on bosonic SPT phases we obtain a
classification of electronic 3D SPT phases for these symmetries. In cases with
a normal U(1) subgroup we show that this classification is complete. We
describe the non-trivial surface and bulk properties of these states. In
particular we discuss interesting correlated surface states that are not
captured in a free fermion description. We show that in many, but not all
cases, the surface can be gapped while preserving symmetry if it develops
intrinsic topological order.Comment: 14+1 pages, an erratum is added at the end, the original paper is
unchange
Topological Paramagnetism in Frustrated Spin-One Mott Insulators
Time reversal protected three dimensional (3D) topological paramagnets are
magnetic analogs of the celebrated 3D topological insulators. Such paramagnets
have a bulk gap, no exotic bulk excitations, but non-trivial surface states
protected by symmetry. We propose that frustrated spin-1 quantum magnets are a
natural setting for realising such states in 3D. We describe a physical picture
of the ground state wavefunction for such a spin-1 topological paramagnet in
terms of loops of fluctuating Haldane chains with non-trivial linking phases.
We illustrate some aspects of such loop gases with simple exactly solvable
models. We also show how 3D topological paramagnets can be very naturally
accessed within a slave particle description of a spin-1 magnet. Specifically
we construct slave particle mean field states which are naturally driven into
the topological paramagnet upon including fluctuations. We propose bulk
projected wave functions for the topological paramagnet based on this slave
particle description. An alternate slave particle construction leads to a
stable U(1) quantum spin liquid from which a topological paramagnet may be
accessed by condensing the emergent magnetic monopole excitation of the spin
liquid.Comment: 16 pages, 5 figure
Symmetry enriched U(1) quantum spin liquids
We classify and characterize three dimensional quantum spin liquids
(deconfined gauge theories) with global symmetries. These spin liquids
have an emergent gapless photon and emergent electric/magnetic excitations
(which we assume are gapped). We first discuss in great detail the case with
time reversal and spin rotational symmetries. We find there are 15
distinct such quantum spin liquids based on the properties of bulk excitations.
We show how to interpret them as gauged symmetry-protected topological states
(SPTs). Some of these states possess fractional response to an external
gauge field, due to which we dub them "fractional topological paramagnets". We
identify 11 other anomalous states that can be grouped into 3 anomaly classes.
The classification is further refined by weakly coupling these quantum spin
liquids to bosonic Symmetry Protected Topological (SPT) phases with the same
symmetry. This refinement does not modify the bulk excitation structure but
modifies universal surface properties. Taking this refinement into account, we
find there are 168 distinct such quantum spin liquids. After this
warm-up we provide a general framework to classify symmetry enriched
quantum spin liquids for a large class of symmetries. As a more complex
example, we discuss quantum spin liquids with time reversal and
symmetries in detail. Based on the properties of the bulk excitations, we find
there are 38 distinct such spin liquids that are anomaly-free. There are also
37 anomalous quantum spin liquids with this symmetry. Finally, we
briefly discuss the classification of quantum spin liquids enriched by
some other symmetries.Comment: 24 pages + appendices + reference
Classification of interacting electronic topological insulators in three dimensions
A fundamental open problem in condensed matter physics is how the dichotomy
between conventional and topological band insulators is modified in the
presence of strong electron interactions. We show that there are 6 new
electronic topological insulators that have no non-interacting counterpart.
Combined with the previously known band-insulators, these produce a total of 8
topologically distinct phases. Two of the new topological insulators have a
simple physical description as Mott insulators in which the electron spins form
spin analogs of the familiar topological band-insulator. The remaining are
obtained as combinations of these two `topological paramagnets' and the
topological band insulator. We prove that these 8 phases form a complete list
of all possible interacting topological insulators, and are classified by a
Z_2^3 group-structure. Experimental signatures are also discussed for these
phases.Comment: New version contains more results on experimental signatures and a
more rigorous proof of a key statement (see Appendix D,E), with references
reorganize
Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
It is well known that the 3D electronic topological insulator (TI) with
charge-conservation and time-reversal symmetry cannot have a trivial insulating
surface that preserves symmetry. It is often implicitly assumed that if the TI
surface preserves both symmetries then it must be gapless. Here we show that it
is possible for the TI surface to be both gapped and symmetry-preserving, at
the expense of having surface-topological order. In contrast to analogous
bosonic topological insulators, this symmetric surface topological order is
intrinsically non-Abelian. We show that the surface-topological order provides
a complete non-perturbative definition of the electron TI that transcends a
free-particle band-structure picture, and could provide a useful perspective
for studying strongly correlated topological Mott insulators.Comment: 12 pages, 2 figures, (published version
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