51 research outputs found

### Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point

We introduce a topological theory to study quasiparticles in interacting
and/or disordered many-body systems, which have a finite lifetime due to
inelastic and/or elastic scattering. The one-body quasiparticle Hamiltonian
includes both the Bloch Hamiltonian of band theory and the self-energy due to
interactions, which is non-Hermitian when quasiparticle lifetime is finite. We
study the topology of non-Hermitian quasiparticle Hamiltonians in momentum
space, whose energy spectrum is complex. The interplay of band structure and
quasiparticle lifetime is found to have remarkable consequences in zero- and
small-gap systems. In particular, we predict the existence of topological
exceptional point and bulk Fermi arc in Dirac materials with two distinct
quasiparticle lifetimes.Comment: 5 pages, 3 figure

### Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin-orbit-coupled systems

We study superconductivity in spin-orbit-coupled systems in the vicinity of
inversion symmetry breaking. We find that due to the presence of spin-orbit
coupling, fluctuations of the incipient parity-breaking order generate an
attractive pairing interaction in an odd-parity pairing channel, which competes
with the s-wave pairing. We show that applying a Zeeman field suppresses the
s-wave pairing and promotes the odd-parity superconducting state. Our work
provides a new mechanism for odd-parity pairing and opens a route to novel
topological superconductivity.Comment: 5 pages, 4 pages of supplemental material

### Superconductivity near a ferroelectric quantum critical point in ultralow-density Dirac materials

The experimental observation of superconductivity in doped semimetals and
semiconductors, where the Fermi energy is comparable to or smaller than the
characteristic phonon frequencies, is not captured by the conventional theory.
In this paper, we propose a mechanism for superconductivity in ultralow-density
three-dimensional Dirac materials based on the proximity to a ferroelectric
quantum critical point. We derive a low-energy theory that takes into account
both the strong Coulomb interaction and the direct coupling between the
electrons and the soft phonon modes. We show that the Coulomb repulsion is
strongly screened by the lattice polarization near the critical point even in
the case of vanishing carrier density. Using a renormalization group analysis,
we demonstrate that the effective electron-electron interaction is dominantly
mediated by the transverse phonon mode. We find that the system generically
flows towards strong electron-phonon coupling. Hence, we propose a new
mechanism to simultaneously produce an attractive interaction and suppress
strong Coulomb repulsion, which does not require retardation. For comparison,
we perform same analysis for covalent crystals, where lattice polarization is
negligible. We obtain qualitatively similar results, though the screening of
the Coulomb repulsion is much weaker. We then apply our results to study
superconductivity in the low-density limit. We find strong enhancement of the
transition temperature upon approaching the quantum critical point. Finally, we
also discuss scenarios to realize a topological $p$-wave superconducting state
in covalent crystals close to the critical point

### Energy relaxation rate and its mesoscopic fluctuations in quantum dots

We analyze the applicability of the Fermi-golden-rule description of
quasiparticle relaxation in a closed diffusive quantum dot with
electron-electron interaction. Assuming that single-particle levels are already
resolved but the initial stage of quasiparticle disintegration can still be
described by a simple exponential decay, we calculate the average inelastic
energy relaxation rate of single-particle excitations and its mesoscopic
fluctuations. The smallness of mesoscopic fluctuations can then be used as a
criterion for the validity of the Fermi-golden-rule description. Technically,
we implement the real-space Keldysh diagram technique, handling correlations in
the quasi-discrete spectrum non-perturbatively by means of the non-linear
supersymmetric sigma model. The unitary symmetry class is considered for
simplicity. Our approach is complementary to the lattice-model analysis of Fock
space: thought we are not able to describe many-body localization, we derive
the exact lowest-order expression for mesoscopic fluctuations of the relaxation
rate, making no assumptions on the matrix elements of the interaction. It is
shown that for the quasiparticle with the energy $\varepsilon$ on top of the
thermal state with the temperature $T$, fluctuations of its energy width become
large and the Fermi-golden-rule description breaks down at
$\max\{\varepsilon,T\}\sim\Delta\sqrt{g}$, where $\Delta$ is the mean level
spacing in the quantum dot, and $g$ is its dimensionless conductance.Comment: 33 pages, 9 figure

### Interactions Remove the Quantization of the Chiral Photocurrent at Weyl Points.

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum e^{3}/h^{2} for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbatrd interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength

### Ferromagnetic transition in a one-dimensional spin-orbit-coupled metal and its mapping to a critical point in smectic liquid crystals

We study the quantum phase transition between a paramagnetic and
ferromagnetic metal in the presence of Rashba spin-orbit coupling in one
dimension. Using bosonization, we analyze the transition by means of
renormalization group, controlled by an $\varepsilon$-expansion around the
upper critical dimension of two. We show that the presence of Rashba spin-orbit
coupling allows for a new nonlinear term in the bosonized action, which
generically leads to a fluctuation driven first-order transition. We further
demonstrate that the Euclidean action of this system maps onto a classical
smectic-A -- C phase transition in a magnetic field in two dimensions. We show
that the smectic transition is second-order and is controlled by a new critical
point.Comment: 16 pages, 4 figures, 1 tabl

### Thermal plasmon resonantly enhances electron scattering in Dirac/Weyl semimetals

We study the inelastic scattering rate due to the Coulomb interaction in
three-dimensional Dirac/Weyl semimetals at finite temperature. We show that the
perturbation theory diverges because of the long-range nature of the
interaction, hence, thermally induced screening must be taken into account. We
demonstrate that the scattering rate has a non-monotonic energy dependence with
a sharp peak owing to the resonant decay into thermal plasmons. We also
consider the Hubbard interaction for comparison. We show that, in contrast to
the Coulomb case, it can be well described by the second-order perturbation
theory in a wide energy range.Comment: 5 pages, 1 figure, 1 table, supplemental materia

### Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node

Motivated by the recent experiment indicating that superconductivity in the
doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing
symmetry with rotational symmetry breaking, we study the general class of
odd-parity superconductors with two-component order parameters in trigonal and
hexagonal crystal systems. In the presence of strong spin-orbit interaction, we
find two possible superconducting phases below $T_c$, a time-reversal-breaking
(i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine
their relative energetics from the gap function in momentum space. The nematic
superconductor generally has a full quasi-particle gap, whereas the chiral
superconductor with a three-dimensional (3D) Fermi surface has point nodes with
lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk
and topological Majorana arcs on the surface.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published
versio

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### DMFT Reveals the Non-Hermitian Topology and Fermi Arcs in Heavy-Fermion Systems.

When a strongly correlated system supports well-defined quasiparticles, it allows for an elegant one-body effective description within the non-Hermitian topological theory. While the microscopic many-body Hamiltonian of a closed system remains Hermitian, the one-body quasiparticle Hamiltonian is non-Hermitian due to the finite quasiparticle lifetime. We use such a non-Hermitian description in the heavy-fermion two-dimensional systems with the momentum-dependent hybridization to reveal a fascinating phenomenon which can be directly probed by the spectroscopic measurements, the bulk "Fermi arcs." Starting from a simple two-band model, we first combine the phenomenological approach with the perturbation theory to show the existence of the Fermi arcs and reveal their connection to the topological exceptional points, special points in the Brillouin zone where the Hamiltonian is nondiagonalizable. The appearance of such points necessarily requires that the electrons belonging to different orbitals have different lifetimes. This requirement is naturally satisfied in the heavy-fermion systems, where the itinerant c electrons experience much weaker interaction than the localized f electrons. We then utilize the dynamical mean field theory to numerically calculate the spectral function and confirm our findings. We show that the concept of the exceptional points in the non-Hermitian quasiparticle Hamiltonians is a powerful tool for predicting new phenomena in strongly correlated electron systems

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