We discuss the circularly polarized light (of amplitude $A_0$ and frequency $ω$) driven thermo-electric transport properties of type-I and type-II multi-Weyl semimetals (mWSMs) in the high frequency limit. Considering the low energy model, we employ the Floquet-Kubo formalism to compute the thermal Hall and Nernst conductivities for both types of mWSMs. We show that the anisotropic nature of the dispersion for arbitrary integer monopole charge $n>1$ plays an important role in determining the effective Fermi surface behavior; interestingly, one can observe momentum dependent corrections in Floquet mWSMs in addition to momentum independent contribution as observed for Floquet single WSMs. Apart from the non-trivial tuning of the Weyl node position $\pm Q \to \pm Q- A_0^{2n}/ω$, our study reveals that the momentum independent terms result in leading order contribution in the conductivity tensor. This has the form of $n$ times the single WSMs results with effective chemical potential $μ\to μ-A_0^{2n}/ω$. On the other hand, momentum dependent corrections lead to sub-leading order terms which are algebraic function of $μ$ and are present for $n>1$. Remarkably, this analysis further allows us to distinguish type-I mWSMs from their type-II counterparts. For type-II mWSMs, we find that the transport coefficients for $n\geq 2$ exhibit algebraic dependence on the momentum cutoff in addition to the weak logarithmic dependence as noticed for $n=1$ WSMs. We demonstrate the variation and qualitative differences of transport coefficients between type-I and type-II mWSM as a function of external driving parameter $ω$.
Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quant…
Type-II Weyl semimetals have recently attracted intensive research interest because they host Lorentz-violating massless fermions as quasiparticles. The discovery of type-II Weyl semimetals evokes the study of type-II line-node semimetals (LNSMs) whose linear dispersion is strongly tilted near the nodal ring. We present here a study on the circularly polarized light-induced Floquet states in type-II LNSMs, as well as those in hybrid LNSMs that have a partially over-tilted linear dispersion in the vicinity of the nodal ring. We illustrate that two distinct types of Floquet Weyl semimetal (WSM) …
We consider tunneling of quasiparticles through a rectangular quantum well, subject to periodic driving. The quasiparticles are the itinerant charges in two-dimensional and three-dimensional semimetals having a quadratic band-touching (QBT) point in the Brillouin zone. In order to analyze the time-periodic Hamiltonian, we assume a non-adiabatic limit, where the Floquet theorem is applicable. By deriving the Floquet scattering matrices, we chalk out the transmission and shot noise spectra of the QBT semimetals. The spectra show Fano resonances, which we identify with the (quasi)bound states of …
We investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a periodic magnetic field and elliptically polarized light, are discussed respectively. By use of the Floquet theory, we find that both the two periodic drives can resonantly induce the topological transitions from normal insulator (NI) phases to Floquet topological insulator (FTI) phases. The Floquet topological transitions are characterized by variation of Chern number. Moreover, we show that the Floquet topological transitions can be explained by…
Multi-Weyl semimetals(m-WSMS) are characterized by anisotropic non-linear energy dispersion along 2-D plane and a linear dispersion in orthogonal direction. They have topological charge J and are realized when two or multiple Weyl nodes with nonzero net monopole charge bring together onto a high-symmetry point. The model Hamiltonians of such systems show various phases such as trivial normal insulators (NIs), WSMs and quantum anomalous Hall(QAH) states depending on the model parameters. We study a periodic driving of such Hamiltonians in trivial NI phase by circularly polarized light and shows…
Exotic topological states of matter such as Floquet topological insulator or Floquet Weyl semimetal can be induced by periodic driving. This work proposes a Floquet semimetal with Floquet-band holonomy. That is, the system is gapless, but as a periodic parameter viewed as quasimomentum of a synthetic dimension completes an adiabatic cycle, each Floquet band as a whole exchanges with other Floquet bands. The dynamical manifestations of such Floquet-band holonomy are studied. Under open boundary conditions, we discover anomalous chiral edge modes localized only at one edge, winding around the en…
We propose that a Floquet Weyl semimetal state can be induced in three-dimensional topological insulators, either nonmagnetic or magnetic, by the application of off-resonant light. The virtual photon processes play a critical role in renormalizing the Dirac mass and so resulting in a topological semimetal with vanishing gap at Weyl points. The present mechanism via off-resonant light is quite different from that via on-resonant light, the latter being recently suggested to give rise to a Floquet topological state in ordinary band insulators.
Simulating multi-node Weyl semimetals in a Mixed Floquet lattice
Indian Institute of Science Education and Research (IISER) Tirupati（印度科学教育研究所提鲁帕蒂分校）；Indian Institute of Science Education and Research Bhopal（印度科学教育研究所博帕尔分校）
We study the photoresponse of two-dimensional semi-Dirac semimetals and three-dimensional Dirac semimetals to off-resonant circularly polarized light. For two-dimensional semi-Dirac semimetals we find that incident light does not open a gap in the spectrum, in contrast to the case of purely linear dispersion. For the three-dimensional case we find that applying a circularly polarized light, one can tune from a trivial insulator to three-dimensional Dirac semimetal with an inverted gap. We propose and show that application of light leads to an intriguing platform for generation, motion and merg…
Valence and conduction bands in nodal loop semimetals (NLSMs) touch along closed loops in momentum space. If such loops can proliferate and link intricately, NLSMs become exotic topological phases with unconventional topological characteristics and potentially peculiar transport properties. In conventional quantum materials or cold atom systems alike, such exotic phases necessarily require non-local hopping and are therefore intrinsically unrealistic. In this work, we show how this hurdle can be surmounted through an experimentally feasible periodic driving scheme. In particular, by tuning the…
Weyl semimetals and nodal line semimetals are characterized by linear electronic bands touching at zero-dimensional points and one-dimensional lines, respectively. Recently, it has been predicted that nodal line semimetals can be driven into tunable Floquet-Weyl semimetals by circularly polarized light. Here, we study the occurrence of interface states between two regions of a nodal line semimetal shined by two beams of light with opposite circular polarizations. Within a minimal model, we find remarkable modifications of the energy structure by tuning the polarized light, such as the possible…
This work reports the general design and characterization of two exotic, anomalous nonequilibrium topological phases. In equilibrium systems, the Weyl nodes or the crossing points of nodal lines may become the transition points between higher-order and first-order topological phases defined on two-dimensional slices, thus featuring both hinge Fermi arc and surface Fermi arc. We advance this concept by presenting a strategy to obtain, using time-sequenced normal insulator phases only, Floquet higher-order Weyl semimetals and Floquet higher-order nexus semimetals, where the concerned topological…
In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show tha…
When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously unexplored low-frequency regime, where the upper and lower Dirac bands resonantly couple with each other through multi-photon processes, which is a realistic situation in solid state ultrafast pump-probe experiments. We find a series of new Weyl nodes emerging in pairs when the Floquet replica bands hybridize with each other. The nature of the Floquet Weyl …
The Weyl semimetal exhibits various interesting physical phenomena because of the Weyl points, i.e., linear band-crossings. We show by Floquet theory that a linearly polarized light applied to a band insulator can induce controllable Weyl points. In a tight-binding model, we classify different types of photoinduced Weyl points that lead to a rich phase diagram characterized by the Chern number defined on each momentum slices of the bulk states. Taking account of the nonequilibrium electron distribution, we calculate and explain the nonmonotonous anomalous Hall conductivity in terms of the ligh…
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
Due to studies in nonequilibrium (periodically-driven) topological matter, it is now understood that some topological invariants used to classify equilibrium states of matter do not suffice to describe their nonequilibrium counterparts. Indeed, in Floquet systems the additional gap arising from the periodicity of the quasienergy Brillouin zone often leads to unique topological phenomena without equilibrium analogues. In the context of Floquet Weyl semimetal, Weyl points may be induced at both quasienergy zero and $π/T$ ($T$ being the driving period) and these two types of Weyl points can be ve…
Creating and manipulating topological states is a key goal of condensed matter physics. Periodic driving offers a powerful method to manipulate electronic states, and even to create topological states in solids. Here, we investigate the tunable Floquet states in a periodically driven higher-order nodal line semimetal with both spatial inversion and time-reversal symmetries. We found that the Floquet Weyl semimetal states, which support both one-dimensional hinge Fermi arc and two-dimensional surface Fermi arc states, can be induced in the higher-order nodal-line semimetal by shining circularly…
Recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations. Examples of such gapless topological phases are Weyl semimetals, which exhibit 3D Dirac cones (Weyl points), and nodal line semimetals, which are characterized by line nodes (two bands touching along a line). Inspired by our previous discoveries that the kicked Harper model exhibits many fascinating features of Floquet topological phases, in this manuscript we consider a generalization of the model, where two additional periodic system paramet…
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
Using the Landau-Zener-Stückelberg-Majorana-type (LZSM) semiclassical approach, we study both graphene and a thin film of a Weyl semimetal subjected to a strong AC electromagnetic field. The spectrum of quasi energies in the Weyl semimetal turns out to be similar to that of a graphene sheet. Earlier it has been predicted qualitatively that the transport properties of strongly-irradiated graphene oscillate as a function of the radiation intensity [S.V. Syzranov et al., Phys. Rev. B 88, 241112 (2013)]. Here we obtain rigorous quantitative results for a driven linear conductance of graphene and a…
Band crossings observed in a wide range of condensed matter systems are recognized as a key to understand low-energy fermionic excitations that behave as massless Dirac particles. Despite rapid progress in this field, the exploration of non-equilibrium topological states remains scarce and it has potential ability of providing a new platform to create unexpected massless Dirac states. Here we show that in a semiconductor quantum-well driven by a cw-laser with linear polarization, the optical Stark effect conducts bulk-band crossing, and the resulting Floquet-Dirac semimetallic phase supports a…
Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the $\mathcal{N}=2$ supersymmetric massless QCD in a rotating …
In mesoscopic physics, the application of a time-periodic drive leads to novel transport behaviour, which is absent in the static regimes. Here we consider a quantum pumping protocol, such that the quasiparticles of Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic rectangular potential well. The presence of an oscillating potential of frequency $ω$ creates equispaced Floquet side-bands with spacing $\hbar ω$. As a result, a Fano resonance is observed when the difference in the Fermi energy (i.e., the energy of the incident quasiparticle), and the energy of one of the …
We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes pen…
Weyl semimetals host linear energy dispersions around Weyl nodes, as well as monopoles of Berry curvature in momentum space around these points. These features give rise to unique transport signatures in a Weyl semimetal, such as transverse transport without an applied magnetic field, known as anomalous transport. The type-II Weyl semimetal, recently experimentally demonstrated in several materials, is classified by a tilting of the Weyl nodes. This paper provides a theoretical study on thermoelectric transport in time-reversal breaking type-II Weyl semimetals. Our results examine the balance …
In the Fermi liquid description of metals, electrical and thermoelectric transport coefficients are linked by robust relations which can be challenged by strong interactions or when the electron liquid enters a different regime. These relations have been very powerful in the characterisation of novel materials. We show that Dirac and Weyl semimetals at zero doping and zero temperature (the conformal limit) have a very singular behavior due to a quantum anomaly. Away from this point, a Mott relation can be established.
Time-periodic driving in the form of coherent radiation provides powerful tool for the manipulation of topological materials or synthetic quantum matter. In this paper we propose a scheme to realize non-Hermitian semimetals exhibiting exceptional rings in the spectra through Floquet engineering. A transition from a concentric pair of the rings to a dipolar pair is observed. The concentric pair carries only a quantized Berry phase while the dipolar pair possesses opposite Chern numbers in addition, signaling a topological Lifshitz transition of the Fermi surface. The transport properties of the…
Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual topological defects that are analogous to extended monopoles. In this work, we describe a scheme by which nodal rings and nodal spheres can be realized in synthetic quantum matter through well-defined periodic-driving protocols. As a central result of our work, we characterize these nodal defects through the quantum metric, which is a gauge-invariant quantity assoc…
We investigate the low-temperature thermoelectric properties of three-dimensional nodal-line semimetals within the semiclassical Boltzmann formalism. Considering short-range interaction between electrons and scattering agents, we calculate the anisotropic relaxation times and then obtain the charge conductivity and thermopower along the radial and the axial directions with respect to the nodal-line plane. Increasing the carrier concentration, a topological transition in the shape of the Fermi surface from a torus into an ellipsoid signal as a sharp change in the thermopower. An adequate treatm…
Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocket-like Fermi surfaces, can be induced in driven Dirac semi…
The spin momentum non-orthogonality in 3D topological insulators leads to modification of the spin texture and brings in an out-of-plane spin polarization component. Apart from spin texture, the anomalous thermoelectric properties of these materials are worth studying. In this paper, we have pointed out that the off resonant light used to irradiate the surface states, induces a gap, which becomes momentum dependent due to the presence of non-orthogonal terms in the Hamiltonian. Importantly, to maintain the off resonant condition of light, the momentum value should satisfy a bound. Furthermore,…
We show that Floquet engineering using bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd$_3$As$_2$ is a promising platform for BCL Floquet engineering. Witho…
We investigate the development of novel surface states when 3D Dirac or Weyl semimetals are placed under circularly polarized electromagnetic radiation. We find that the hybridization between inverted Floquet bands opens in general a gap, which closes at so-called exceptional points found for complex values of the momentum. This corresponds to the appearance of midgap surface states in the form of evanescent waves decaying from the surface exposed to the radiation. We observe a phenomenon reminiscent of Landau quantization by which the midgap surface states get a large degeneracy proportional …
In a recent paper [R. Soto-Garrido and E. Muñoz, J. Phys. Condens. Matter 30, 195302 (2018)], we studied the electronic transport properties in Weyl semimetals (WSMs) submitted to the combined effects of torsional mechanical strain and magnetic field, showing that this configuration induces a node-polarization effect on the current that can be used to measure the torsion angle from transmission experiments. In this article, we extend our previous work to study thermoelectric transport in WSMs under torsional strain and an external magnetic field. Our analysis involves only the electronic contr…
We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under magnetic field as a consequence of an anisotropic $B^2$ contribution, which may explain the low-field regime of recent experiments; (ii) predicts strong second harmonic generation proportional to …
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and th…
We experimentally investigate a non-linear Hall effect for three-dimensional WTe$_2$ and Cd$_3$As$_2$ single crystals, representing Weyl and Dirac semimetals, respectively. We observe finite second-harmonic Hall voltage, which depends quadratically on the longitudinal current in zero magnetic field. Despite this observation well corresponds to the theoretical predictions, only magnetic field dependence allows to distinguish the non-linear Hall effect from a thermoelectric response. We demonstrate that second-harmonic Hall voltage shows odd-type dependence on the direction of the magnetic field…
We study theoretically the quantum size effects in a one-dimensional semimetal by a Boltzmann transport equation. We derive analytic expressions for the electrical conductivity, Hall coefficient, magnetoresistance, and the thermoelectric power in a nanowire. The transport coefficients of semimetal oscillate as the size of the sample shrinks. Below a certain size the semimetal evolves into a semiconductor. The semimetal-semiconductor transition is discussed quantitatively. The results should make a theoretical ground for better understanding of transport phenomena in low-dimensional semimetals.…
Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na$_{3}$Bi and Cd$_{2}$As$_{3}$, are regarded to carry the $\mathbb{Z}_{2}$ topological charge in addition to the chiral charge. Here, we study the Floquet phase transition of $\mathbb{Z}_{2}$ topological DSMs subjected to a beam of circularly polarized light. Due to the resulting interplay of the chiral and $\mathbb{Z}_{2}$ charges, the Weyl nodes are not only chirality-dependent but also spin-dependent, which constrains the behaviors in creation and annihilation of the Weyl nodes in pair. Interestingly, we find a novel…
These compounds have long been known as promising thermoelectric materials. Recently it was revealed, that they also have unconventional electronic topology. This renewed interest to the investigation of their transport properties. In order to improve theoretical description of thermoelectric transport in these compounds, we take into account electron scattering beyond commonly used constant relaxation time approximation. Using first principle calculations, we investigate the scattering of charge carriers by phonons and point defects. The dependence of the scattering rate on the energy correla…
