Quantum-relativistic materials often host electronic phenomena with exotic spatial distributions. In particular, quantum anomalous Hall (QAH) insulators feature topological boundary currents whose ...chirality is determined by the magnetization orientation. However, understanding the microscopic nature of edge vs. bulk currents has remained a challenge due to the emergence of multidomain states at the phase transitions. Here we use microwave impedance microscopy (MIM) to directly image chiral edge currents and phase transitions in a magnetic topological insulator. Our images reveal a dramatic change in the edge state structure and an unexpected microwave response at the topological phase transition between the Chern number N = 1 and N = -1 states, consistent with the emergence of an insulating N = 0 state. The magnetic transition width is independent of film thickness, but the transition pattern is distinct in differently initiated field sweeps. This behavior suggests that the N = 0 state has 2 surface states with Hall conductivities of 1/2 e²/h but with opposite signs.
A
bstract
Rotating photon gas exhibits a chirality separation along the angular velocity which is manifested through a generation of helicity and zilch currents. In this paper we study this system ...using the corresponding Wigner function and construct elements of the covariant chiral kinetic theory for photons from first principles. The Wigner function is solved order-by-order in
ħ
and the unconstrained terms are fixed by matching with quantum field theory results. We further consider the zilch and helicity currents and show that both manifestations of the chirality transport originate in the Berry phase of photons similarly to other chiral effects. Constructing the kinetic description from the Wigner function we find that the frame vector needed to fix the definition of spin of a massless particle is, in fact, the vector of the residual gauge freedom for the free Maxwell theory. We also briefly comment on the possible relation between vortical responses in rotating systems of massless particles and the anomalies of underlying quantum field theory.
Almost strong edge-mode operators arising at the boundaries of certain interacting one-dimensional symmetry protected topological phases with Z2 symmetry have infinite temperature lifetimes that are ...nonperturbatively long in the integrability breaking terms, making them promising as bits for quantum information processing. We extract the lifetime of these edge-mode operators for small system sizes as well as in the thermodynamic limit. For the latter, a Lanczos scheme is employed to map the operator dynamics to a one-dimensional tight-binding model of a single particle in Krylov space. We find this model to be that of a spatially inhomogeneous Su-Schrieffer-Heeger model with a hopping amplitude that increases away from the boundary, and a dimerization that decreases away from the boundary. We associate this dimerized or staggered structure with the existence of the almost strong mode. Thus, the short time dynamics of the almost strong mode is that of the edge mode of the Su-Schrieffer-Heeger model, while the long time dynamics involves decay due to tunneling out of that mode, followed by chaotic operator spreading. We also show that competing scattering processes can lead to interference effects that can significantly enhance the lifetime.
A
bstract
We study the longitudinal magnetotransport in three-dimensional multi-Weyl semimetals, constituted by a pair of (anti)-monopole of arbitrary integer charge (
n
), with
n
= 1
,
2 and 3 in a ...crystalline environment. For any
n >
1, even though the distribution of the underlying Berry curvature is
anisotropic
, the corresponding intrinsic component of the longitudinal magnetoconductivity (LMC), bearing the signature of the chiral anomaly, is
insensitive
to the direction of the external magnetic field (
B
) and increases as
B
2
, at least when it is sufficiently weak (the semi-classical regime). In addition, the LMC scales as
n
3
with the monopole charge. We demonstrate these outcomes for two distinct scenarios, namely when inter-particle collisions in the Weyl medium are effectively described by (a) a single and (b) two (corresponding to inter- and intra-valley) scattering times. While in the former situation the contribution to LMC from chiral anomaly is inseparable from the non-anomalous ones, these two contributions are characterized by different time scales in the later construction. Specifically for sufficiently large inter-valley scattering time the LMC is dominated by the anomalous contribution, arising from the chiral anomaly. The predicted scaling of LMC and the signature of chiral anomaly can be observed in recently proposed candidate materials, accommodating multi-Weyl semimetals in various solid state compounds.
A
bstract
We consider an analogue of Witten’s SL(2
,
ℤ) action on three-dimensional QFTs with U(1) symmetry for 2
k
-dimensional QFTs with ℤ
2
(
k −
1)-form symmetry. We show that the SL(2
,
ℤ) ...action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2
,
ℤ) anomaly of the bulk (2
k
+ 1)-dimensional ℤ
2
gauge theory.
A
bstract
We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and ...fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators.
A
bstract
In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories ...coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(
N
)
k
Chern-Simons theories coupled to
N
f
real scalars in the fundamental representation, and SO(
k
)
–
N
+
N f
/ 2
theories coupled to
N
f
real (Majorana) fermions in the fundamental. For
N
f
= 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For
k
= 1 we get an interesting low-energy duality between
N
f
free Majorana fermions and an SO(
N
)
1
Chern-Simons theory coupled to
N
f
scalar fields (with
N
f
≤
N
− 2).
This open access book presents a comprehensive exploration of diffusion metamaterials that control energy and mass diffusion. Currently, if from the perspective of governing equations, diffusion ...metamaterials and wave metamaterials (pioneered by J. B. Pendry in the 1990s) are recognised as the two most prominent branches in the field of metamaterials. These two branches differ in their emphasis on the diffusion equation (as the governing equation) and time-dependent characteristic lengths in diffusion metamaterials, as opposed to the wave equation (as the governing equation) and time-independent characteristic lengths in wave metamaterials. Organized into three distinct parts – 'Thermal Diffusion Metamaterials', 'Particle Diffusion Metamaterials', and 'Plasma Diffusion Metamaterials' – this book offers a rigorous exploration spanning physics, engineering, and materials science, aimed at advancing our understanding of diffusion processes controlled by diffusion metamaterials. Incorporating foundational theory, computational simulations, and laboratory experiments, the book equips researchers and scholars across these disciplines with comprehensive methods, insights, and results pivotal to the advancement of diffusion control. Beyond facilitating interdisciplinary discourse, the book serves as a catalyst for innovative breakthroughs at the crossroads of physics, thermodynamics, and materials science. Essentially, readers will acquire profound insights that empower them to spearhead advancements in diffusion science (diffusionics) and the engineering of metamaterials.
A
bstract
It was well known that there are
e
-particles and
m
-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ
2
topological order. Recent ...mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ
2
topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.
Fractional topological insulators (FTIs) are electronic systems that carry fractionally charged excitations, conserve charge, and are symmetric to reversal of time. In this review, we introduce the ...basic essential concepts of the field and then survey theoretical understanding of FTIs in two and three dimensions. In between, we discuss the case of "two and a half dimensions," the FTIs that may form on the two-dimensional surface of an unfractionalized three-dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.
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