arXiv subjects

S. A. Jafari

Publications and source records attributed to S. A. Jafari.

At least 37 records · Page 2Linked to original sources

arXiv2019

Perpendicular Andreev reflection: Solid state signature of black hole horizon

Beenakker noticed that the peculiar band structure of Dirac fermions in 2D solids allows for the specular Andreev reflection in these systems which has no analogue in other 2D electron systems. An interesting deformation of the Dirac equation in the solid state is to tilt it which has now materials realization. In this work we report another peculiar feature of the Andreev reflection in tilted 2D Dirac cone systems. The tilt deformation of the Dirac equation is characterized by two parameters ${\boldsymbolζ}=ζ(\cosθ,\sinθ)$. We show that when the tilt parameter is tuned to its "horizon value" $ζ=1$, irrespective of the incidence angle of electrons, the Andreev reflected hole is always reflected {\em perpendicular} to the interface. Furthermore at the horizon value, if the tilt direction is perpendicular to the interface, the conductance will be energy independent for the entire sub gap energies. For generic tilt $\boldsymbolζ$, the tilt dependence of the conductance line shape can be used to extract information about the direction and magnitude of the tilt.

cond-mat.supr-con↗

arXiv2019

Sound of Fermi arcs

Using Green's function of semi-infinite Weyl semimetals we find that the collective charge excitations of Fermi arcs in undoped Weyl semi-metals are linearly dispersing gapless plasmon modes. The gaplessness comes from proper consideration of the deep penetration of surface states at the end of Fermi arcs into the interior of Weyl semimetal. The linear dispersion -- rather than square root dispersion of {\it pure 2D} electron systems with extended Fermi surface -- arises from the strong anisotropy introduced by the Fermi arc itself, due to which the continuum of surface particle-hole excitations in this system will have strong resemblence to the one-dimensional electron systems. This places the Fermi arc electron liquid in between the 1D and 2D electron liquids. Contamination with the particle-hole excitations of the bulk gives rise to the damping of the Fermi arc sounds.

cond-mat.str-el↗

arXiv2019

Polarization tensor for tilted Dirac fermion materials: Covariance in deformed Minkowski spacetime

The rich structure of solid state physics provides us with Dirac materials the effective theory of which enjoys the Lorentz symmetry. In non-symmorphic lattices, the Lorentz symmetry will be deformed in a way that the null energy-momentum vectors will correspond to on-shell condition for tilted Dirac cone dispersion. In this sense, tilted Dirac/Weyl materials can be viewed as solid state systems where the effective spacetime is non-Minkowski. In this work, we show that the polarization tensor for tilted Dirac cone systems acquires a covariant from only when the spacetime is considered to be an appropriate deformation of the Minkowski spacetime. As a unique consequence of the deformation of the geometry of the spacetime felt by the electrons in tilted Dirac cone materials, the Coulomb density-density interactions will generate corrections in both longitudinal and transverse channels. Therefore the transverse photons also participate in mediating the Coulomb forces, implying emergent Amperean forces associated with the tilt of the spacetime.

cond-mat.mes-hall↗

arXiv2019

Optical conductivity of triple point fermions

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian which is parameterized by an angular parameter $λ$. We find strong $λ$ dependence in both Drude and interband optical absorption of these systems. The deviation of the $T^2$ coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular $λ=π/6$ point, we find that the "helicity" reversal optical transition matrix element is identically zero. But deviating from this point, the helicity reversal emerges as an absorption channel.

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arXiv2019

The $8Pmmn$ borophene sheet: A solid-state platform for space-time engineering

We construct the most generic Hamiltonian of the $8Pmmn$ structure of borophene sheet in presence of spin-orbit, as well as background electric and magnetic fields. In addition to spin and valley Hall effects, this structure offers a framework to conveniently manipulate the resulting "tilt" of the Dirac equation by applying appropriate electric fields. Therefore, the tilt can be made space-, as well as time-dependent. The border separating the low-field region with under-tilted Dirac fermions from the high-field region with over-tilted Dirac fermions will correspond to a black-hole horizon. In this way, space-time dependent electric fields can be used to design the metric of the resulting space-time felt by electrons and holes satisfying the tilted Dirac equation. Our platform offers a way to generate analogues of gravitational waves by electric fields (instead of mass sources) which can be detected in solid state spectroscopies as waves of enhanced superconducting correlations.

cond-mat.mes-hall↗

arXiv2019

Induced superconductivity in Fermi arcs

When the interface of a superconductor (SC) with Weyl semimetal (WSM) supports Fermi arcs, the chirality blockade eliminates the induction of superconductivity into the bulk. This leaves the Fermi arc states as the only low-energy degrees of freedom in the proximity problem. Therefore the SC|WSM system will be a platform to probe transport properties that only involve the Fermi arcs. With a boundary condition that flips the spin at the boundary, we find a $Z_2$ protected Bogoliubov Fermi contour (BFC) around which the Bogoliubov quasi-particles disperse linearly. The resulting BFC and excitations around it leave a distinct $T^2$ temperature dependence in their contribution to specific heat. Furthermore, the topologically protected BFC being a Majorana Fermi surface gives rise to a zero-bias peak the strength of which characteristically depends on the length of Fermi arc and tunneling strength. For the other BC that flips the chirality at the interface, instead of BFCs we have Bogoliubov- Weyl nodes whose location depends on the tunneling strength.

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arXiv2018

Phase transitions in the binary-alloy Hubbard model: insight from strong-coupling perturbation theory

In the binary-alloy with composition A$_x$B$_{1-x}$ of two atoms with ionic energy scales $\pmΔ$, an apparent Ander- son insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard $U$ to the binary alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction $U$, the resulting AI phase will become metallic which in our formulation can be clearly attributed to the screening of disorder by Hubbard $U$. Upon further increase in $U$, again the AI phase emerges which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction of which the randomness takes advantage and localizes the quasi-particles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator (MI). We construct the phase diagram of this model in the plane of ($U,Δ$) for various compositions $x$.

cond-mat.str-el↗

arXiv2018

Kinky plasmons in double layers of borophene-borophene and borophene-graphene

We investigate the collective plasmon modes in double layer of two dimensional materials where either one or both of the layers have tilted Dirac cone. Consistent with quite generic hydrodynamic treatment, similar to double layer graphene systems we find two branches of plasmons. The in-phase oscillations of the two layers disperses as $\sqrt q$, while the out-of-phase mode disperses as $q$. When even one of the layers hosts tilted Dirac cone spectrum, the plasmonic kink which is a salient feature of a monolayer of tilted Dirac cone is inherited by both of these branches. In double layers composed of graphene (nontilted) and borophene (tilted) where the two layers have two different Fermi velocities, the velocity scale of plasmonic modes is set by the greater of the two. The kink always takes place when each plasmon mode crosses an energy scale $ω_{\rm kink}$. When the two layers have different chemical potentials, there will be two such scales, and each of in-phase and out-of-phase modes develop two kinks. Moreover we find that an additional linearly dispersing overdamped mode of monolayer tilted Dirac cone system survives in the double layer system.

cond-mat.str-el↗

arXiv2018

Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons

The list of two dimensional Dirac systems with a tilt in their Dirac cone spectrum is expanding, and now in addition to organic system $α$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene sheet, which allows for controlled doping by the gate voltage. We analytically calculate the polarization function of tilted Dirac cone for arbitrary tilt parameter, $0\le η<1$, and arbitrary doping. This enables us to find two interesting plasmonic effects solely caused by the tilt: (i) In addition to the standard plasmon oscillations, strong enough tilt, induces an additional linearly dispersing overdamped branch of plasmons, which is strongly Landau damped due to overlap with a large density of intra-band free particle-hole (PH) excitations. (ii) There appears a kink in the plasmon dispersion for any non-zero tilt parameter. The kink appears when the plasmon branch enters the inter-band continuum of PH excitations. This kink becomes most manifest for wave vectors perpendicular to the tilt direction and fades away by approaching the tilt direction. Experimental measurement of the wave vector and energy of the plasmonic kink, when combined with our analytic formula for the kink energy scale, allows for a direct experimental measurement of the tilt parameter.

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arXiv2018

Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya Interaction

Topological index of a system specifies gross features of the system. However, in situations such as strong disorder where by level repulsion mechanism the spectral gap is closed, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined from appropriate use of transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices of the related Hamiltonians. As a case study, we study a generalized XY model (2XY model) plus a generalized Dziyaloshinskii-Moriya-like (DM) interaction that after fermionization breaks the time-reversal invariance and is parameterized by $ϕ$. The {\em parent} Hamiltonian at $ϕ=0$ which belongs to BDI class is indexed by integer winding number while the $ϕ\ne 0$ {\em daughter} Hamiltonian which belongs to class D is specified by a $Z_2$ index $ν=\pm 1$. We show that the localization length in addition to determining the $Z_2$ can count the number of Majorana zero modes left over at the boundary of the daughter Hamiltonian -- which are not protected by winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian.

cond-mat.str-el↗

arXiv2018

Greens function of semi-infinite Weyl semimetals

We classify all possible boundary conditions (BCs) for a Weyl material into two classes: (i) BC that mixes the spin projection but does not change the chirality attribute, and (ii) BC that mixes the chiralities. All BCs are parameterized with angular variables that can be regarded as mixing angles between spins or chiralities. Using the Greens function method, we show that these two BCs faithfully reproduce the Fermi arcs. The parameters are ultimately fixed by the orientation of Fermi arcs. We build on our classification and show that in the presence of a background magnetic field, only the second type BC gives rise to non-trivial Landau orbitals.

cond-mat.str-el↗

arXiv2018

Strong-coupling perturbative study of the disordered Hubbard model on honeycomb lattice

We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is han- dled with strong-coupling perturbation theory which encodes the Mott transition physics into a rich dynamical structure of a local self-energy. The local nature of self-energy allows us to combine it with kernel polynomial method and transfer matrix methods. The locality of self-energy combined with the analytic nature of the strong- coupling perturbation theory enables us to study lattices with millions of sites. The transfer matrix method in the ribbon geometry is essentially free from finite size errors and allows us to perform a careful finite size scaling of the width of the ribbon. This finite size scaling enables us to rule out the possibility of metallic phase in between the Mott and Anderson insulating phases. We therefore find a direct transition between Anderson and Mott insulators when the disorder strength W is comparable to the Hubbard interaction U . For a fixed disorder W , we obtain an interaction dependent nonmonotonic behavior of the localization length which reflects interac- tion induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually at strong interactions U, the Mott localization takes over and the localization length becomes comparable to the lattice scale. This is reminiscent of the holographic determination of the Mott state where the system at IR recognizes its UV lattice scale.

cond-mat.str-el↗

arXiv2018

Resilience of Majorana Fermions in the face of Disorder

We elucidate the reduction of the winding number (WN) caused by the onsite disorder in a higher WN next nearest neighbor XY model. When disorder becomes strong enough, Majorana edge modes become critically extended, beyond which they collapse into Anderson localized (AL) states in the bulk, resulting in a topological Anderson insulating state (TAI). We identify a resilience threshold $W_t$ for every pair of Majorana fermions (MFs). In response to increasing disorder every pair of MFs collapse into AL bulk at their resilience threshold. For very strong disorder, all Majorana fermions collapse and a topologically trivial state is obtained. We show that the threshold values are deeply related to the localization length of Majorana fermions, which can be efficiently calculated by an appropriate modification of the transfer matrix method. At the topological transition point, localization length of the zero modes diverges and the system becomes scale invariant. The number of peaks in the localization length as the function of disorder strength determines the number of zero modes in the clean state before disorder is introduced. This finding elevates the transfer matrix method to the level of a tool for determination of the topological index of both clean and disordered systems.

cond-mat.str-el↗

arXiv2018

Electromagnetic modes from Stoner enhancement

Systems with substantial spin fluctuations, can internally dress the polarization function by ladder diagram of Stoner (spin-flip) excitations. This process can drastically modify the electromagnetic response. As a case study we provide detailed analysis of the corrections to the non-local optical conductivity of both doped and undoped graphene. While the resummation of ladder diagram of Stoner excitations does not affect the TE mode in doped graphene, it allows for a new undampled TM mode in undoped graphene. This is the sole effect of corrections arising from ladder diagrams and is dominated by Stoner excitations along the ladder rung which goes away by turning off the source of spin-flip interactions. This can be considered as a direct probe of the spin fluctuations.

cond-mat.str-el↗

arXiv2018

Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction

Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, $λ$ corresponding to XY anisotropy, and $D$ corresponding to the strength of DM interaction. The flow portrait of the model is governed by two global Ising-Kitaev attractors at $(λ=\pm1,D=0)$ and a repeller line, $λ=0$. Renormalization flow of concurrence suggests that the $λ=0$ line corresponds to a topological phase transition. The gap starts at zero on this repeller line corresponding to super-fluid phase of underlying bosons; and flows towards a finite value at the Ising-Kitaev points. At these two fixed points the spin fields become purely classical, and hence the resulting Ising degeneracy can be interpreted as topological degeneracy of dual degrees of freedom. The state of affairs at the Ising-Kitaev fixed point is consistent with the picture of a p-wave pairing of strength $λ$ of Jordan-Wigner fermions coupled with Chern-Simons gauge fields.

cond-mat.str-el↗

arXiv2017

Superconducting proximity in three dimensional Dirac materials: odd-frequency, pseudoscalar, pseudovector and tensor-valued superconducting orders

We find that a conventional s-wave superconductor in proximity to three dimensional Dirac material (3DDM), to all orders of perturbation in tunneling, induces a combination of s and p-wave pairing only. We show that the Lorentz invariance of the superconducting pairing prevents the formation of Cooper pairs with higher orbital angular momenta in the 3DDM. This no-go theorem acquires stronger form when the probability of tunneling from the conventional superconductor to positive and negative energy states of 3DDM are equal. In this case all the p-wave contribution except for the lowest order, identically vanish and hence we obtain an exact result for the induced p-wave superconductivity in 3DDM. Fierz decomposing the superconducting matrix we find that temporal component of the vector superconducting order and spatial components of the pseudo-vector order are odd-frequency pairing. We find that the latter is odd with respect to exchange of position and chirality of the electrons in the Cooper pair and is spin-triplet which is necessary for NMR detection of such an exotic pseudo- vector pairing. Moreover, we show that the tensorial order breaks into a polar vector and an axial vector and both of them are conventional pairing except for being spin-triplet. According to our study, for gapless 3DDM the tensorial superconducting order will be the only order which is odd with respect to the chemical potential μ. Therefore we predict that a transverse p-n junction binds Majorana fermions. This effect can be used to control the neutral Majorana fermions with electric fields.

cond-mat.supr-con↗

arXiv2017

Exact phase diagram and topological phase transitions of the XYZ spin chain

Within the block spin renormalization group we are able to construct the "exact" phase diagram of the XYZ spin chain. First we identify the Ising order along $\hat x$ or $\hat y$ as attractive renormalization group fixed points of the Kitaev chain. Then in a global phase space composed of the anisotropy $λ$ of the XY interaction and the coupling $Δ$ of the $Δσ^zσ^z$ interaction we find that the above fixed points remain attractive in the two dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain which in turn is characterized by winding number $\pm 1$ depending whether the Ising order parameter is along $\hat x$ or $\hat y$ directions; or (2) attracted to the Mott phases of the underlying Jordan-Wigner fermions which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem which is at the core of the renormalization group treatment is able to produce the exact phase diagram of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the Mott-Ising phase is entitled to host apprpriate form of zero modes. We further observe that the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

cond-mat.str-el↗

arXiv2016

Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials

We find that singlet superconducting pairing can lead to Majorana fermions in three dimensional Dirac superconductors (3DDS) if the pairing order parameter is a pseudo-scalar, i.e. it changes sign under mirror reflection. The pseudo-scalar superconducting order parameter, $Δ_5$ can close and reopen the spectral gap caused by the scalar Dirac mass $m$ in a three-dimensional Dirac material (3DDM), giving rise to a two-dimensional Majorana sea (2DMS) at the plane of the gap kink. By bringing the Hamiltonian into a canonical form which then gives the winding number, we show that this system belongs to the DIII class of topological superconductors. We calculate the transport signature of 2DMS, namely a perfect Andreev-Klein transmission that manifests in a robust peak in the differential conductance. Further, we find the $4π$ periodicity in the $Δ_5|m|Δ_5$ Josephson junc- tions. Gauge transformed version of the present scenario implies that the interface of a conventional s-wave superconductor with a peculiar 3DDM whose mass is a pseudo-scalar, m5 also hosts a 2DMS.

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