We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological Hamiltonian method, which calculates topological invariants of strongly interacting systems from an effective Hamiltonian system with the same topological structure. Nontrivial topological invariants for both systems have been obtained and the presence of nontrivial topological invariants further supports the topological nature of the holographic semimetals.
The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal lin…
We study the AC electrical conductivity at zero temperature in a holographic model for a Weyl semimetal. At small frequencies we observe a linear dependence in the frequency. The model shows a quantum phase transition between a topological semimetal (Weyl semimetal phase) with a non vanishing anomalous Hall conductivity and a trivial semimetal. The AC conductivity has an intermediate scaling due to the presence of a quantum critical region in the phase diagram of the system. The phase diagram is reconstructed using the scaling properties of the conductivity. We compare with the experimental da…
We study the surface states of a strongly coupled Weyl semimetal within holography. By explicit numerical computation of an inhomogeneous holographic Weyl semimetal we observe the appearance of an electric current restricted to the surface in presence of electric chemical potential. The total current is universal in the sense that it only depends on the topology of the phases showing that the bulk-boundary correspondence holds even at strong coupling. The implications of this result are subtle and may shed some light on anomalous transport at weak coupling.
We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial se…
We study the black hole interiors in holographic Weyl semimetals and holographic nodal line semimetals. We find that the black hole singularities are of Kasner form. In the topologically nontrivial phase at low temperature, both the Kasner exponents of the metric fields and the proper time from the horizon to the singularity are almost constant, likely reflecting the topological nature of the topological semimetals. We also find some specific behaviors inside the horizon in each holographic semimetal model.
We study the effects of momentum relaxation on the holographic Weyl semimetal which exhibits a topological quantum phase transition between the Weyl semimetal phase and a topological trivial phase. The conservation of momentum in the field theory is broken by the axion fields in holography. The topological Weyl semimetal phase is characterized by a nontrivial anomalous Hall conductivity. We find that the critical value of the phase transition decreases when we increase the momentum relaxation strength up to a special value, above which it goes to zero. This indicates that the Weyl semimetal ph…
We study a holographic D3/probe-D5-brane model of a double monolayer Dirac semimetal in a magnetic field and in the presence of a nonzero temperature. Intra- and inter-layer exciton condensates can form by varying the balanced charge density on the layers, the spatial separation and the temperature. Constant temperature phase diagrams for a wide range of layer separations and charge densities are found. The presence of a finite temperature makes the phase diagrams extremely rich and in particular leads to the appearance of a symmetric phase which was missing at zero temperature.
We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2. We present new results for the spectral densities and dispersion relations at non-zero momenta and temperature. In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential. Our findings sh…
We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $\barψγ^{μν}ψ$ and $\barψγ^{μν}γ^5ψ$. We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spec…
Strongly interacting Dirac semimetals are investigated using a holographic model especially geared to compute the single-particle correlation function for this case, including both interaction effects and nonzero temperature. We calculate the (homogeneous) electrical conductivity at zero chemical potential, and show that it consists of two contributions. The interband contribution scales as a power law either in frequency or in temperature for low frequency. The precise power is related to a critical exponent of the dual holographic theory, which is a parameter in the model. On top of that we …
Topological phases of matter have recently attracted a rather notable attention in the community dealing with the holographic methods applied to strongly interacting condensed matter systems. In particular, holographic models for gapless Weyl and multi-Weyl semimetals, characterized on a lattice by the monopole-antimonopole defects of the Berry curvature in momentum space, were recently formulated. In this paper, motivated by the quest for finding topological holographic phases, we show that holographic model for multi-Weyl semimetals features a rather rich landscape of phases. In particular, …
The formation of intra-layer and inter-layer exciton condensates in a model of a double monolayer Weyl semi-metal is studied in the strong coupling limit using AdS/CFT duality. We find a rich phase diagram which includes phase transitions between inter-layer and intra-layer condensates as the charge densities and the separation of the layers are varied. The tendency to inter-layer condensation is strongest when the charge densities are balanced so that the weak coupling electron and hole Fermi surfaces would be nested. For systems with multiple species of massless Fermions, we find a novel pha…
We study various thermodynamic and transport properties of a holographic model of a nodal line semimetal (NLSM) at finite temperature, including the quantum phase transition to a topologically trivial phase, with Dirac semimetal-like conductivity. At zero temperature, composite fermion spectral functions obtained from holography are known to exhibit multiple Fermi surfaces. Similarly, for the holographic NLSM we observe multiple nodal lines instead of just one. We show, however, that as the temperature is raised these nodal lines broaden and disappear into the continuum one by one, so there is…
We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterised by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are non-vanishing in the quantum critical region and non-zero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature.…
The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such system besides the chiral anomaly possesses another anomaly which is related to the $\mathbb{Z}_2$ topological charge of the system. The holographic model of the system contains matter action with two $U(1)$-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields {\it via} the kinetic mixing parametrised by the coupling $α$. The holographic approach in th…
We consider the effects of momentum relaxation on the topological quantum phase transitions in holographic Weyl semimetals. The translational symmetry breaking in the field theory is realized in the framework of massive gravity. We find that the critical value of the phase transition, characterized by the anomalous Hall conductivity, decreases with the increasing of graviton mass, i.e. the momentum relaxation strength. There exists a critical value of graviton mass above which the topological phase transition disappears and therefore the Weyl points are destroyed. All these phenomena are quali…
We present a holographic model of a topological Weyl semimetal. A key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time-reversal breaking parameter the model undergoes a quantum phase transition from a topologically nontrivial semimetal to a trivial one. The topological nontrivial semimetal is characterised by the presence of an anomalous Hall effect. The results can be interpreted in terms of the holographic renormalization group (RG) flow leading to restoration of time-reversal at the end point of the RG flow in the trivial phase.
In this paper we consider holographic model of exciton condensation in double monolayer Dirac semimetal. Excitons is a bound states of an electron and a hole. Being Bose particles, excitons can form a Bose-Einstein condensate. We study formation of two types of condensates. In first case both the electron and the hole forming the exciton are in the same layer (intralayer condensate), in the second case the electron and the hole are in different layers (interlayer condensate). We study how the condensates depend on the distance between layers and the mass of the quasiparticles in presence of a …
Based on the gauge/gravity correspondence we have calculated the thermoelectric kinetic and transport characteristics of the strongly interacting materials in the presence of perpendicular magnetic field. The 3+1 dimensional system with Dirac-like spectrum is considered as a strongly interacting one if it is close to the particle-hole symmetry point. Transport in such system has been modeled by the two interacting vector fields. In the holographic theory the momentum relaxation is caused by axion field and leads to finite values of the direct current transport coefficients. We have calculated …
We present effective field theories for the weakly coupled Weyl-$\mathrm{Z}_2$ semimetal, as well as the holographic realization for the strongly coupled case. In both cases, the anomalous systems have both the chiral anomaly and the $\mathrm{Z}_2$ anomaly and possess topological quantum phase transitions from the Weyl-$\mathrm{Z}_2$ semimetal phases to partly or fully topological trivial phases. We find that the topological phase transition is characterized by the anomalous transport parameters, i.e. the anomalous Hall conductivity and the $\mathrm{Z}_2$ anomalous Hall conductivity. These two…
We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holog…
We study the magnetic field effects on the quantum critical point (QCP) in the holographic Weyl semimetal model. We show that it increases quadratically with the magnetic field for weak field and linear with the magnetic field for strong field. Our findings are compatible with previous results in the literature from other approaches.
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 …
We use the AdS/CFT correspondence to compute the AC conductivities for a (2+1)-dimensional system of massless fundamental fermions coupled to (3+1)-dimensional Super Yang-Mills theory at strong coupling. We consider the system at finite charge density, with a constant electric field along the defect and an orthogonal magnetic field. The holographic model we employ is the well studied D3/probe-D5-brane system. There are two competing phases in this model: a phase with broken chiral symmetry favored when the magnetic field dominates over the charge density and the electric field and a chirally s…
Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may…
The possibility of inter-layer exciton condensation in a holographic D3-probe-D5 brane model of a strongly coupled double monolayer Dirac semi-metal in a magnetic field is studied in detail. It is found that, when the charge densities on the layers are exactly balanced so that, at weak coupling, the Fermi surfaces of electrons in one monolayer and holes in the other monolayer would be perfectly nested, inter-layer condensates can form for any separation of the layers. The case where both monolayers are charge neutral is special. There, the inter-layer condensate occurs only for small separatio…
In the holographic model of Dirac semimetals being the Einstein-Maxwell scalar gravity with the auxiliary $U(1)$-gauge field, coupled to the ordinary Maxwell one by {\it kinetic mixing } term, the black brane response to the electric fields and temperature gradient has been elaborated. Using the foliation by hypersurfaces of constant radial coordinate we derive the exact form of the Hamiltonian and equations of motion in the considered phase space. Examination of the Hamiltonian constraints enables us, to the leading order expansion of the linearised perturbations at the black brane event hori…
Anomalous resonance in Weyl semimetals: A holographic study of non-linear effects
Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universität Würzburg（维尔茨堡大学理论物理与天体物理研究所）；University of Regensburg（雷根斯堡大学）；Department of Physics, National Taiwan University（台湾大学物理系）；Department of Physics, Ben-Gurion University of the Negev（内盖夫本古里安大学物理系）
Classification of topological insulators and superconductors is manifested in terms of spin cobordism groups for lower dimensions. It is discussed that the periodic table of topological insulators is a result of the possible choices of spin structures on Brillouin zones of relevant topological materials. This framework is extended to the case of Weyl semimetals. It is shown that the classification of Weyl semimetals can be managed in terms of spin$^c$ cobordism groups via the extension of spin structures to spin$^c$ structures. Topological invariants of Weyl semimetals are connected to the top…
Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect", which stems from a parity-type anomaly. In this effect, …
We propose a torsional response raised by lattice dislocation in Weyl semimetals akin to chiral magnetic effect; i.e. a fictitious magnetic field arising from screw or edge dislocation induces charge current. We demonstrate that, in sharp contrast to the usual chiral magnetic effect which vanishes in real solid state materials, the torsional chiral magnetic effect exists even for realistic lattice models, which implies the experimental detection of the effect via SQUID or nonlocal resistivity measurements in Weyl semimetal materials.
We propose a new type of Hopf semimetals indexed by a pair of numbers $(p,q)$, where the Hopf number is given by $pq$. The Fermi surface is given by the preimage of the Hopf map, which is nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are the Hopf link indexed by $(1,1)$, the Solomon's knot $(2,1)$, the double Hopf-link $(2,2)$ and the double trefoil-knot $(3,2)$. We may choose $p$ or $q$ as a half integer, where torus-knot Fermi surfaces such as the trefoil knot $(3/2,1)$ are realized. It is even possible to make the Hopf number an arbitrar…
