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

Thermoelectric Hall conductivity and figure of merit in Dirac/Weyl materials

We calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient $\alpha_{xy}$ and the Seebeck coefficient $S_{xx}$, which are well-defined even in the dissipationless limit. We contrast the behaviors of $\alpha_{xy}$ and $S_{xx}$ with those of traditional Schr\"{o}dinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials $\alpha_{xy}$ acquires a constant, quantized value at sufficiently large magnetic field, which is independent of the magnetic field or the Fermi energy, and this leads to unprecedented growth in the thermopower and the thermoelectric figure of merit. We further show that even relatively small fields, such that $\omega_c \tau \sim 1$ (where $\omega_c$ is the cyclotron frequency and $\tau$ is the scattering time), are sufficient to produce a more than $100\%$ increase in the figure of merit.Comment: 10 pages, 5 figure

Magnetic field induces giant nonlinear optical response in Weyl semimetals

We study the second-order optical response of Weyl semimetals in the presence of a magnetic field. We consider an idealized model of a perfectly linear Weyl node and use the Kubo formula at zero temperature to calculate the intrinsic contribution to photocurrent and second harmonic generation conductivity components. We obtain exact analytical expressions applicable at arbitrary values of frequency, chemical potential, and magnetic field. Our results show that finite magnetic field significantly enhances the nonlinear optical response in semimetals, while magnetic resonances lead to divergences in nonlinear conductivity. In realistic systems, these singularities are regularized by a finite scattering rate, but result in pronounced peaks which can be detected experimentally, provided the system is clean and interactions are weak. We also perform a semiclassical calculation that complements and confirms our microscopic results at small magnetic fields and frequencies.Comment: 25 pages, 8 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

Three-Dimensional Majorana Fermions in Chiral Superconductors

Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs$_4$Sb$_{12}$ and related materials as promising candidates for non-unitary chiral superconductors hosting three-dimensional Majorana fermions.Comment: 12 pages, 3 figures + appendices; published versio