20 research outputs found
Transversal magnetotransport in Weyl semimetals: Exact numerical approach
Magnetotransport experiments on Weyl semimetals are essential for
investigating the intriguing topological and low-energy properties of Weyl
nodes. If the transport direction is perpendicular to the applied magnetic
field, experiments have shown a large positive magnetoresistance. In this work,
we present a theoretical scattering matrix approach to transversal
magnetotransport in a Weyl node. Our numerical method confirms and goes beyond
the existing perturbative analytical approach by treating disorder exactly. It
is formulated in real space and is applicable to mesoscopic samples as well as
in the bulk limit. In particular, we study the case of clean and strongly
disordered samples.Comment: 10 pages, 4 figure
Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
The hallmark of topological phases is their robust boundary signature whose
intriguing properties---such as the one-way transport on the chiral edge of a
Chern insulator and the sudden disappearance of surface states forming open
Fermi arcs on the surfaces of Weyl semimetals---are impossible to realize on
the surface alone. Yet, despite the glaring simplicity of non-interacting
topological bulk Hamiltonians and their concomitant energy spectrum, the
detailed study of the corresponding surface states has essentially been
restricted to numerical simulation. In this work, however, we show that exact
analytical solutions of both topological and trivial surface states can be
obtained for generic tight-binding models on a large class of geometrically
frustrated lattices in any dimension without the need for fine-tuning of
hopping amplitudes. Our solutions derive from local constraints tantamount to
destructive interference between neighboring layer lattices perpendicular to
the surface and provide microscopic insights into the structure of the surface
states that enable analytical calculation of many desired properties. We
illustrate our general findings on a large number of examples in two and three
spatial dimensions. Notably, we derive exact chiral Chern insulator edge states
on the spin orbit-coupled kagome lattice, and Fermi arcs relevant for various
recently synthesized pyrochlore iridate slabs. Remarkably, each of the
pyrochlore slabs exhibit Fermi arcs although only the ones with a magnetic
one-in-three-out configuration feature bulk Weyl nodes in realistic parameter
regimes. Our approach furthermore signal the absence of topological surface
states, which we illustrate for a class of models akin to the trivial surface
of Hourglass materials KHg.Comment: 24 pages, 17 figure
Extended Bloch theorem for topological lattice models with open boundaries
While the Bloch spectrum of translationally invariant noninteracting lattice
models is trivially obtained by a Fourier transformation, diagonalizing the
same problem in the presence of open boundary conditions is typically only
possible numerically or in idealized limits. Here we present exact analytic
solutions for the boundary states in a number of lattice models of current
interest, including nodal-line semimetals on a hyperhoneycomb lattice,
spin-orbit coupled graphene, and three-dimensional topological insulators on a
diamond lattice, for which no previous exact finite-size solutions are
available in the literature. Furthermore, we identify spectral mirror symmetry
as the key criterium for analytically obtaining the entire (bulk and boundary)
spectrum as well as the concomitant eigenstates, and exemplify this for Chern
and insulators with open boundaries of co-dimension one. In the
case of the two-dimensional Lieb lattice, we extend this further and show how
to analytically obtain the entire spectrum in the presence of open boundaries
in both directions, where it has a clear interpretation in terms of bulk, edge,
and corner states
Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
We present a generic and systematic approach for constructing D-dimensional
lattice models with exactly solvable d-dimensional boundary states localized to
corners, edges, hinges and surfaces. These solvable models represent a class of
"sweet spots" in the space of possible tight-binding models---the exact
solutions remain valid for any tight-binding parameters as long as they obey
simple locality conditions that are manifest in the underlying lattice
structure. Consequently, our models capture the physics of both (higher-order)
topological and non-topological phases as well as the transitions between them
in a particularly illuminating and transparent manner.Comment: 19 pages, 12 figure
Kekule versus hidden superconducting order in graphene-like systems: Competition and coexistence
We theoretically study the competition between two possible exotic
superconducting orders that may occur in graphene-like systems, assuming
dominant nearest-neighbor attraction: the gapless hidden superconducting order,
which renormalizes the Fermi velocity, and the Kekule order, which opens a
superconducting gap. We perform an analysis within the mean-field theory for
Dirac electrons, at finite-temperature and finite chemical potential, as well
as at half filling and zero-temperature, first excluding the possibility of the
coexistence of the two orders. In that case, we find the dependence of the
critical (more precisely, crossover) temperature and the critical interaction
on the chemical potential. As a result of this analysis, we find that the
Kekule order is preferred over the hidden order at both finite temperature and
finite chemical potential. However, when the coexistence of the two
superconducting orders is allowed, using the coupled mean-field gap equations,
we find that above a critical value of the attractive interaction a mixed phase
sets in, in which these orders coexist. We show that the critical value of the
interaction for this transition is greater than the critical coupling for the
hidden superconducting state in the absence of the Kekule order, implying that
there is a region in the phase diagram where the Kekule order is favored as a
result of the competition with the hidden superconducting order. The latter,
however, eventually sets in and coexists with the Kekule state. According to
our mean-field calculations, the transition from the Kekule to the mixed phase
is of the second order, but it may become first order when fluctuations are
considered. Finally, we investigate whether these phases could be possible in
honeycomb superlattices of self-assembled semiconducting nanocrystals, which
have been recently experimentally realized with CdSe and PbSe.Comment: 15 pages, 9 figures, published version. Minor changes, new references
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Symmetry-protected nodal phases in non-Hermitian systems
Non-Hermitian (NH) Hamiltonians have become an important asset for the
effective description of various physical systems that are subject to
dissipation. Motivated by recent experimental progress on realizing the NH
counterparts of gapless phases such as Weyl semimetals, here we investigate how
NH symmetries affect the occurrence of exceptional points (EPs), that
generalize the notion of nodal points in the spectrum beyond the Hermitian
realm. Remarkably, we find that the dimension of the manifold of EPs is
generically increased by one as compared to the case without symmetry. This
leads to nodal surfaces formed by EPs that are stable as long as a protecting
symmetry is preserved, and that are connected by open Fermi volumes. We
illustrate our findings with analytically solvable two-band lattice models in
one and two spatial dimensions, and show how they are readily generalized to
generic NH crystalline systems.Comment: Editors' Suggestio
Exact solutions from destructive interference on frustrated lattices
The hallmark of topological phases is their robust boundary signature whose intriguing properties—such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals—are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulk-boundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7, which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7. Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one-in-three-out configuration features bulk Weyl nodes in realistic parameter regimes. Our approach generalizes to symmetry protected phases, e.g., quantum spin Hall systems and Dirac semimetals with time-reversal symmetry, and can furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHgX where the exact solutions apply but, independently of Hamiltonian details, yield eigenstates delocalized over the entire sample
Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
Both non-Hermitian systems and the behaviour of emitters coupled to
structured baths have been studied intensely in recent years. Here we study the
interplay of these paradigmatic settings. In a series of examples, we show that
a single quantum emitter coupled to a non-Hermitian bath displays a number of
unconventional behaviours, many without Hermitian counterpart. We first
consider a unidirectional hopping lattice whose complex dispersion forms a
loop. We identify peculiar bound states inside the loop as a manifestation of
the non-Hermitian skin effect. In the same setting, emitted photons may display
spatial amplification markedly distinct from free propagation, which can be
understood with the help of the generalized Brillouin zone. We then consider a
nearest-neighbor lattice with alternating loss. We find that the long-time
emitter decay always follows a power law, which is usually invisible for
Hermitian baths. Our work points toward a rich landscape of anomalous quantum
emitter dynamics induced by non-Hermitian baths.Comment: 5 pages, 3 figures. Revised version. Part of a *joint submission*.
Please see also the companion full paper entitled "Bound states and photon
emission in non-Hermitian nanophotonics" arXiv:2205.0549