Tunable topological Nernst effect in 2D transition metal dichalcogenides

Two dimensional semiconducting transition metal dichalcogenides (TMDs) exhibit an intrinsic Ising spin orbit coupling (SOC) along with a valley contrasting Berry curvature, which can generate a purely anomalous spin and valley Nernst signal driven by a thermal gradient. We show that a small Bychkov-Rashba coupling, which is present in gated TMDs, can enhance the valley Nernst signal by at least 1-2 orders of magnitude. We find that the Nernst signal in these materials is dominated by the anomalous geometrical contribution, and the conventional contribution is much weaker. Importantly, the Nernst signal is also highly tunable by external gating. Although the total Nernst signal vanishes due to time reversal (TR) symmetry, a small magnetic coupling lifts the valley degeneracy and generates an amplified Nernst response. Additionally, we also discuss the Nernst response of bilayer TMDs, and show a similar enhancement and modulation of the Nernst signal due to Rashba SOC. Our predictions are highly pertinent to ongoing experimental studies in TMDs. The generated large anomalous Nernst signal can directly probe the presence of a large Berry curvature in these materials, and may serve as a promising tunable platform for caloritronics applications.Comment: 8 pages, 8 figures. PRB versio

Yu-Shiba-Rusinov states and topological superconductivity in Ising paired superconductors

An unusual form of superconductivity, called Ising superconductivity, has recently been uncovered in mono- and few-layered transition metal dichalcogenides. This 2D superconducting state is characterized by the so-called Ising spin-orbit coupling (SOC), which produces strong oppositely oriented effective Zeeman fields perpendicular to the 2D layer in opposite momentum space valleys. We examine the Yu-Shiba-Rusinov (YSR) bound states localized at magnetic impurities in Ising superconductors and show that the unusual SOC manifests itself in unusually strong anisotropy in magnetic field response of zero bias conductance peaks observable in STM experiments on impurity sites. For a chain of magnetic impurities with moments parallel to the plane of Ising superconductors we show that the low energy YSR band can host topological superconductivity and Majorana fermions as a direct manifestation of Ising spin-orbit coupling induced topological effects.Comment: Replaced with version accepted in Physical Review B. 7 pages, 4 figure

Tunneling conductance for Majorana fermions in spin-orbit coupled semiconductor-superconductor heterostructures using superconducting leads

It has been recently pointed out that the use of a superconducting (SC) lead instead of a normal metal lead can suppress the thermal broadening effects in tunneling conductance from Majorana fermions, helping reveal the quantized conductance of $2e^2/h$. In this paper we discuss the specific case of tunneling conductance with SC leads of spin-orbit coupled semiconductor-superconductor (SM-SC) heterostructures in the presence of a Zeeman field, a system which has been extensively studied both theoretically and experimentally using a metallic lead. We examine the $dI/dV$ spectra using a SC lead for different sets of physical parameters including temperature, tunneling strength, wire length, magnetic field, and induced SC pairing potential in the SM nanowire. We conclude that in a finite wire the Majorana splitting energy $\Delta E$, which has non-trivial dependence on these physical parameters, remains responsible for the $dI/dV$ peak broadening, even when the temperature broadening is suppressed by the SC gap in the lead. In a finite wire the signatures of Majorana fermions with a SC lead are oscillations of quasi-Majorana peaks about bias $V=\pm\Delta_{\text{lead}}$, in contrast to the case of metallic leads where such oscillations are about zero bias. Our results will be useful for analysis of future experiments on SM-SC heterostructures using SC leads.Comment: 9 pages, 9 figures. Replaced by version accepted in Phys. Rev. B with minor revision

Nernst and magneto-thermal conductivity in a lattice model of Weyl fermions

Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a non-trivial Berry curvature. Using semi-classical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TR-broken WSM also has an anomalous Nernst response due to a non-vanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (${\nabla T} \perp \mathbf{B}$) and the longitudinal (${\nabla T} \parallel \mathbf{B}$) set-up and confirm from our lattice model that in the parallel set-up, the Wiedemann-Franz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.Comment: 13 pages, 6 figures, replaced with version accepted by PR

Concentration properties of Gaussian random fields

We study the problem of a random Gaussian vector field given that a particular real quadratic form $\mathcal{Q}$ is arbitrarily large. We prove that in such a case the Gaussian field is primarily governed by the fundamental eigenmode of a particular operator. As a good check of our proposition we use it to re-derive the result of Adler dealing with the structure of field in the vicinity of a high local maxima. We have also applied our result to an incompressible homogeneous Gaussian random flow in the limit of large local helicity and calculate the structure of the flow.Comment: M2 Thesis 2012, \'{E}cole Polyechnique, Franc

Interplay of valley polarization and dynamic nuclear polarization in 2D transition metal dichalcogenides

The interplay of Ising spin-orbit coupling and non-trivial band topology in transition metal dichalcogenides (TMDs) produces anomalous transport and optical properties that are very different from a regular 2D electron gas. The spin-momentum locking of optically excited carriers near a valley point can give rise to an anomalous spin-valley Hall current under the application of an in-plane electric field. TMDs also exhibit strong electron-nuclear hyperfine interactions, but their effect on spin-valley-locked currents remains unknown. Here, we show that hyperfine interactions can create a feedback mechanism in which spin-valley currents generate significant dynamical nuclear polarization which in turn Zeeman shifts excitonic transitions out of resonance with an optical driving field, saturating the production of spin-valley polarization. We propose an experimental signature of dynamic nuclear polarization which can be detected via measurements of the anomalous Hall current. Our results help to elucidate the interplay of valley polarization and nuclear spin dynamics in TMDs.Comment: 12 pages, 8 figures. Replaced with the version accepted in Physical Review

Chiral anomaly as origin of planar Hall effect in Weyl semimetals

In condensed matter physics, the term "chiral anomaly" implies the violation of the separate number conservation laws of Weyl fermions of different chiralities in the presence of parallel electric and magnetic fields. One effect of chiral anomaly in the recently discovered Dirac and Weyl semimetals is a positive longitudinal magnetoconductance (LMC). Here we show that chiral anomaly and non-trivial Berry curvature effects engender another striking effect in WSMs, the planar Hall effect (PHE). Remarkably, PHE manifests itself when the applied current, magnetic field, and the induced transverse "Hall" voltage all lie in the same plane, precisely in a configuration in which the conventional Hall effect vanishes. In this work we treat PHE quasi-classically, and predict specific experimental signatures for type-I and type-II Weyl semimetals that can be directly checked in experiments.Comment: 4+ pages; Version accepted in Phys. Rev. Let

Nernst effect in Dirac and inversion-asymmetric Weyl semimetals

Dirac semimetals are three dimensional analog of graphene with massless Dirac fermions as low energy electronic excitations. In contrast to Weyl semimetals, the point nodes in the bulk spectrum of topological Dirac semimetals have a vanishing Chern number, but can yet be stable due to the existence of crystalline symmetries such as uniaxial (discrete) rotation symmetry. We consider a model low-energy Hamiltonian appropriate for the recently discovered topological Dirac semimetal Cd$_3$As$_2$, and calculate the Nernst response within semiclassical Boltzmann dynamics in the relaxation time approximation. We show that, for small chemical potentials near the Dirac points, the low temperature, low magnetic field, Nernst response is dominated by \textit{anomalous} Nernst effect, arising from a non-trivial profile of Berry curvature on the Fermi surface. Although the Nernst coefficient (both anomalous as well as conventional) vanish in the limit of zero magnetic field, the low temperature, low magnetic field, Nernst response, which has an almost step like profile near $\mathbf{B}=0$, serves as an effective experimental probe of anomalous Nernst effect in topological Dirac semimetals protected by crystalline symmetries. Additionally, we also calculate the Nernst response for a lattice model of an inversion asymmetric Weyl semimetal for which, in contrast to the case of Dirac semimetal, we find that the conventional Nernst response dominates over the anomalous. Our calculations in this paper on Nernst response of Dirac semimetal and inversion broken Weyl semimetal are directly relevant to recent experiments on Cd$_3$As$_2$ (Dirac semimetal) and NbP (inversion broken Weyl semimetal) respectively.Comment: 9 pages, 6 figures, Version published in PR

Suppression of Hall number due to charge density wave order in high-TcT_c cuprates

Understanding the pseudogap phase in hole-doped high temperature cuprate superconductors remains a central challenge in condensed matter physics. From a host of recent experiments there is now compelling evidence of translational symmetry breaking charge density wave (CDW) order in a wide range of doping inside this phase. Two distinct types of incommensurate charge order -- bidirectional at zero or low magnetic fields and unidirectional at high magnetic fields close to the upper critical field $H_{c2}$ -- have been reported so far in approximately the same doping range between $p\simeq 0.08$ and $p\simeq 0.16$. In concurrent developments, recent high field Hall experiments have also revealed two indirect but striking signatures of Fermi surface reconstruction in the pseudogap phase, namely, a sign change of the Hall coefficient to negative values at low temperatures at intermediate range of hole doping and a rapid suppression of the positive Hall number without change in sign near optimal doping $p \sim 0.19$. We show that the assumption of a unidirectional incommensurate CDW (with or without a coexisting weak bidirectional order) at high magnetic fields near optimal doping and a coexistence of both types of orders of approximately equal magnitude at high magnetic fields at intermediate range of doping may help explain the striking behavior of low temperature Hall effect in the entire pseudogap phase.Comment: Phys. Rev. B version. 10 pages, 5 figure

Equivalence of topological mirror and chiral superconductivity in one dimension

Recently it has been proposed that a unitary topological mirror symmetry can stabilize multiple zero energy Majorana fermion modes in one dimensional (1D) time reversal (TR) invariant topological superconductors. Here we establish an exact equivalence between 1D "topological mirror superconductivity" and chiral topological superconductivity in BDI class which can also stabilize multiple Majorana-Kramers pairs in 1D TR-invariant topological superconductors. The equivalence proves that topological mirror superconductivity can be understood as chiral superconductivity in the BDI symmetry class co-existing with time-reversal symmetry. Furthermore, we show that the mirror Berry phase coincides with the chiral winding invariant of the BDI symmetry class, which is independent of the presence of the time-reversal symmetry. Thus, the time-reversal invariant topological mirror superconducting state may be viewed as a special case of the BDI symmetry class in the well-known Altland-Zirnbauer periodic table of free fermionic phases. We illustrate the results with the examples of 1D spin-orbit coupled quantum wires in the presence of nodeless s_{\pm} superconductivity and the recently discussed experimental system of ferromagnetic atom (Fe) chains embedded on a lead (Pb) superconductor.Comment: 5+ pages, 1 figur