We study the spin transport phenomena in two-dimensional graphene-like materials with arbitrary tilted Dirac cones. The tilt arises due to next-nearest hopping when the bottom of the conduction band and top of the valence band does not simultaneously coincide at Dirac point. We consider normal-ferromagnetic-normal (N-F-N) junction of the materials and using the generalized scattering approach calculate the spin current. Here, we show that tilting the Dirac cones can strongly change the transport properties by modifying the period of oscillation of the spin current. The spin conductance can be effectively tuned by the tilt with taking advantage of the modified interference condition. A pure spin current reversal also possible with a smooth variation of the tilting. We further study the spin current by the adiabatic precession of a doped ferromagnet on top of the material. It is shown that the spin-mixing conductance and hence the spin current can become zero by turning the tilt of the Dirac cone. Our findings provide an efficient way towards high controllability of spin transport by tuning the tilt of the ferromagnetic junction and can be very useful in the field of spintronics. The model also presents a simplified way to measure the tilt of Dirac cone of those materials.
Recently, the existence of Dirac/Weyl cones in three dimensional systems has been demonstrated experimentally. While in high energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed matter systems corrections to this can occur, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization group calculation. We find th…
We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a stro…
Transverse electric (TE) modes can not propagate through the conducting solids. This is because the continuum of particle-hole excitations of conductors contaminates with the TE mode and dampes it out. But in solids hosting tilted Dirac cone (TDC) that admit a description in terms of a modified Minkowski spacetime, the new spacetime structure remedies this issue and therefore a tilted Dirac cone material (TDM) supports the propagation of an undamped TE mode which is sustained by density fluctuations. The resulting TE mode propagates at fermionic velocities which strongly confines the mode to t…
We report the effect of Dirac cone tilting on interlayer magnetoresistance in α-(BEDT-TTF)$_2$I$_3$, which is a Dirac semimetal under pressure. Fitting of the experimental data by the theoretical formula suggests that the system is close to a type-II Dirac semimetal.
The possible quantum Hall ferromagnet at a filling factor $ν=0$ is investigated for the zero-energy (N=0) Landau level of the two dimensional massless Dirac fermions in $α$-(BEDT-TTF)$_2$I$_3$ under pressure with tilted cones and a twofold valley degeneracy resulting from time-reversal symmetry. In the case of the Dirac cones without tilting, the long-range Coulomb interaction in the N=0 Landau level exhibits the SU(2) valley-pseudo-spin symmetry even to the order $O(a/l_{\rm H})$, in contrast to $N \ne 0$ Landau levels, where $a$ and $l_{\rm H}$ represent the lattice constant and the magnetic…
Two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted increasing interest. Tilt of Dirac cone can be realized in a number of materials, including deformed graphene, surface state of topological crystalline insulator, and certain organic compound. We study how Dirac cone tilting affects the low-energy properties by presenting a renormalization group analysis of the Coulomb interaction and quenched disorder. Random scalar potential or random vector potential along the tilting direction cannot exist on its own as it always dynamically generates a new type of disorder, whic…
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…
We show that the continuum limit of the tilted Dirac cone in materials such as $8Pmmn$-borophene and layered organic conductor $α$-(BEDT-TTF)$_2$I$_3$ deformation of the Minkowski spacetime of Dirac materials. From its Killing vectors we construct an emergent tilted-Lorentz (t-Lorentz) symmetry group for such systems. With t-Lorentz transformations we are able to obtain the exact solution of the Landau bands for a crossed configuration of electric and magnetic fields. For any given tilt parameter $0\leζ<1$ if the ratio $χ=v_FB_z/cE_y$ of the crossed magnetic and electric fields that satisfies …
The electron-electron Coulomb interaction in Dirac-Weyl semimetals harbours a novel paradigm of correlation effects that hybridizes diverse realms of solid-state physics with their relativistic counterpart. Driving spontaneous mass acquisition, the excitonic condensate of strongly-interacting massless Dirac fermions is one such example whose exact nature remains debated. Here, by focussing on the two-dimensional tilted Dirac cones in the organic salt $α$-(BEDT-TTF)$_2$I$_3$, we show that the excitonic instability is controlled by a small chemicalpotential shift and an in-plane magnetic field. …
The chiral and superconducting gaps are studied in the context of a planar fermion model with four-fermion interactions. The effect of the tilt of the Dirac cone on both gaps is shown and discussed. Our results point to two different behaviors exhibited by planar fermionic systems. We show that there is a threshold value $\tilde{t}^*$ for the effective tilt parameter such that when $|{\bf \tilde{t}}| < \tilde{t}^*$, the superconducting phase persists for negative values of the superconducting coupling constant. For positive values of the superconducting coupling constant, the induction of a su…
We utilize variational method to investigate the Kondo screening of a spin-1/2 magnetic impurity in tilted Dirac surface states with the Dirac cone tilted along the $k_y$-axis. We mainly study about the effect of the tilting term on the binding energy and the spin-spin correlation between magnetic impurity and conduction electrons, and compare the results with the counterparts in a two dimensional helical metal. The binding energy has a critical value while the Dirac cone is slightly tilted. However, as the tilting term increases, the density of states around the Fermi surface becomes signific…
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 comp…
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 dispe…
The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge order…
The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as (TaSe4)2I. However, the interplay between collective phonon excitations and charge transport in Weyl-CDW systems has not been systematically studied. In this paper, we examine the longitudinal electromagnetic response due to collective modes in a Weyl semimetal gapped by a quasi one-dimensional charge-density wave order, using both continuum and lattice regularized models. We systematically compute the contributions of the collecti…
We investigate the mutual influence of tilt, disorder, and Coulomb interaction in a type-I Dirac semimetal (DSM) with $x$-direction tilt by performing a renormalization group analysis. The interplay between disorder and ordinary tilt generates an effective tilt along the $x$-direction, which is the physically observable one. There exist two types of disorder which increase the effective tilt and drive a phase transition from the DSM phase to the diffusive metal phase. The diffusive phase transition stops the increase of the effective tilt and the surface of the original Dirac cone in the diffu…
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" …
We propose an experimental method to examine the in-plane anisotropy of electronic structure in layered conductors. In the method, we measure the interlayer magnetoresistance as a function of in-plane magnetic field orientation. We applied it to an organic Dirac fermion system a-(BEDT-TTF)2I3 to experimentally determine the orientation of the anisotropic Dirac cones. It is concluded that the long axis of the elliptic constant-energy contours of the Dirac cone is tilted by approximately -30 deg from the crystalline a-axis to b-axis under hydrostatic pressures. Additionally, we observed a signat…
