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Oskar Vafek

Publications and source records attributed to Oskar Vafek.

At least 73 records · Page 4Linked to original sources
arXiv2013

Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals

Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic systems exhibit properties which can be well described by the Dirac equation. Such physics is no longer the exclusive domain of quantum field theories and other esoteric mathematical musings; instead, real physics of real systems is governed by such equations, and important materials science and practical implications hinge on our understanding of Dirac particles in two and three dimensions. While the physics that gives rise to the massless Dirac Fermions in each of the above mentioned materials is different, the low energy properties are governed by the same Dirac kinematics. The aim of this article is to review a selected cross-section of this vast field by highlighting the generalities, and contrasting the specifics, of several physical systems.

cond-mat.mes-hall↗
arXiv2013

Space group symmetry, spin-orbit coupling and the low energy effective Hamiltonian for iron based superconductors

We construct the symmetry adapted low energy effective Hamiltonian for the electronic states in the vicinity of the Fermi level in iron based superconductors. We use Luttinger's method of invariants, expanding about Gamma and M points in the Brillouin zone corresponding to two iron unit cell, and then matching the coefficients of the expansion to the 5- and 8-band models. We then use the method of invariants to study the effects of the spin-density wave order parameters on the electronic spectrum, with and without spin-orbit coupling included. Among the results of this analysis is the finding that the nodal spin-density wave is unstable once spin-orbit coupling is included. Similar analysis is performed for the A_{1g} spin singlet superconducting state. Without spin-orbit coupling there is one pairing invariant near the Gamma point, but two near the M point. This leads to an isotropic spectral gap at the hole Fermi surface near Gamma, but anisotropic near M. The relative values of these three parameters determine whether the superconducting state is s_{++}, s_{+-}, or nodal. Inclusion of spin-orbit coupling leads to additional mixing of spin triplet pairing, with one additional pairing parameter near Gamma and one near M. This leads to an anisotropic spectral gap near both hole and electron Fermi surfaces, the latter no longer cross, but rather split.

cond-mat.str-el↗
arXiv2012

Topology and symmetry breaking in ABC trilayer graphene

The effects of topology and electron-electron interactions on the phase diagram of ABC stacked trilayer graphene (TLG) at the neutrality point are investigated within a weak coupling renormalization group approach. We find that the leading instability of TLG with only a forward scattering density-density interaction is towards a mirror-breaking gapless state. Addition of a small, but finite back scattering favors gapped phases, allowing us to make connections to the existing experiments on TLG. We identify a fundamental symmetry difference between TLG and bilayer graphene (BLG) which is responsible for disfavoring nematic states in TLG under the same conditions that favor nematic states in BLG.

cond-mat.str-el↗
arXiv2012

Geometric phases of d-wave vortices in a model of lattice fermions

We study the local and topological features of Berry phases associated with the adiabatic transport of vortices in a d-wave superconductor of lattice fermions. At half filling, where the local Berry curvature must vanish due to symmetries, the phase associated with the exchange of two vortices is found to vanish as well, implying that vortices behave as bosons. Away from half filling, and in the limit where the magnetic length is large compared to the lattice constant, the local Berry curvature gives rise to an intricate flux pattern within the large magnetic unit cell. This renders the Berry phase associated with an exchange of two vortices highly path dependent. However, it is shown that "statistical" fluxes attached to the vortex positions are still absent. Despite the complicated profile of the Berry curvature away from half filling, we show that the average flux density associated with this curvature is tied to the average particle density. This is familiar from dual theories of bosonic systems, even though in the present case, the underlying particles are fermions.

cond-mat.supr-con↗
arXiv2012

Electronic multicriticality in bilayer graphene

We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal warping and externally applied perpendicular electric field. We were able to analytically determine all outcomes of the RG flow equations for the 9 four-fermion coupling constants. While the full phase diagram exhibits a rich structure, we confirm that when forward scattering dominates, the only ordering tendency with divergent susceptibility at finite temperature is the nematic. At finite temperature this result is stable with respect to small back and layer imbalance scattering; further increasing their strength leads to the layer antiferromagnet. We also determine conditions for other ordered states to appear and compare our results to the special cases of attractive and repulsive Hubbard models where exact results are available.

cond-mat.str-el↗
arXiv2012

Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0

We extend previous analyses of fermions on a honeycomb bilayer lattice via weak-coupling renormalization group (RG) methods with extremely short-range and extremely long-range interactions to the case of finite-range interactions. In particular, we consider different types of interactions including screened Coulomb interactions, much like those produced by a point charge placed either above a single infinite conducting plate or exactly halfway between two parallel infinite conducting plates. Our considerations are motivated by the fact that, in some recent experiments on bilayer graphene there is a single gate while in others there are two gates, which can function as the conducting planes and which, we argue, can lead to distinct broken symmetry phases. We map out the phases that the system enters as a function of the range of the interaction. We discover that the system enters an antiferromagnetic phase for short ranges of the interaction and a nematic phase at long ranges, in agreement with previous work. While the antiferromagnetic phase results in a gap in the spectrum, the nematic phase is gapless, splitting the quadratic degeneracy points into two Dirac cones each. We also consider the effects of an applied magnetic field on the system in the antiferromagnetic phase via variational mean field theory. At low fields, we find that the antiferromagnetic order parameter, Delta(B)-Delta(0) \sim B^2. At higher fields, when omega_c > 2*Delta_0, we find that Delta(B)=omega_c/[ln(omega_c/Delta(0))+C], where C=0.67 and omega_c=eB/m^*c. We also determine the energy gap for creating electron-hole excitations in the system, and, at high fields, we find it to be a*omega_c+2*Delta(B), where a is a non-universal, interaction-dependent, constant.

cond-mat.str-el↗
arXiv2011

Spin-orbit coupling induced enhancement of superconductivity in a two-dimensional repulsive gas of fermions

We study a model of a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling $α_R$, and investigate the superconducting instability using renormalization group approach. We find that in general superconductivity is enhanced as the dimensionless ratio 1/2mα_R^2/E_F$ increases, resulting in unconventional superconducting states which break time reversal symmetry.

cond-mat.supr-con↗
arXiv2011

Quantum Hall effect in a singly and doubly connected 3D topological insulator

The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy spectrum is found for a singly and doubly connected geometry. This is in turn used to argue that the way to measure the quantized Hall conductivity is to perform the Laughlin's flux ramping experiment and measure the charge transferred from the inner to the outer surface, analogous to the experiment in Ref.[2]. Unlike the Hall bar setup used currently, this has the advantage of being free of the contamination from the delocalized continuum of the surface edge states. In the presence of the Zeeman coupling, and/or interaction driven Quantum Hall ferromagnetism, which translate into the Dirac mass term, the quantized charge Hall conductivity sigma_{xy}=n e^2/h, with n=0,\pm 1,\pm 3,\pm 5... Backgating of one of the surfaces leads to additional Landau level splitting and in this case n can be any integer.

cond-mat.mes-hall↗
arXiv2010

Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when ω>> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by taking the spatial dimension D=2-ε, for ε> 0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.

cond-mat.mes-hall↗
arXiv2010

Interacting fermions on the honeycomb bilayer: from weak to strong coupling

Many-body instabilities of the half-filled honeycomb bilayer are studied using weak coupling renormalization group as well as strong coupling expansion. For spinless fermions and assuming parabolic degeneracy, there are 4-independent four-fermion contact couplings. While the dominant instability depends on the microscopic values of the couplings, the broken symmetry state is typically a gapped insulator with either broken inversion symmetry or broken time reversal symmetry, with a quantized anomalous Hall effect. Under certain conditions, the dominant instability may appear in the particle-particle (pairing) channel. For some non-generic fine-tuned initial conditions, weak coupling RG trajectories flow into the non-interacting fixed point, although generally we find runaway flows which we associate with ordering tendencies. Additionally, a tight binding model with nearest neighbor hopping and nearest neighbor repulsion is studied in weak and strong couplings and in each regime a gapped phase with inversion symmetry breaking is found. In the strong coupling limit, the ground state wavefunction is constructed for vanishing in-plane hopping but finite inter-plane hopping, which explicitly displays the broken inversion symmetry and a finite difference between the number of particles on the two layers. Finally, we discuss the spin-1/2 case and use Fierz identities to show that the number of independent 4-fermion contact couplings is 9. The corresponding RG equations in the spin-1/2 case are also presented, and used to show that, just as in strong coupling, the most dominant weak coupling instability of the repulsive Hubbard model (at half-filling) is an anti-ferromagnet.

cond-mat.str-el↗
arXiv2010

Relaxation of Nuclear Magnetic Moments and Site-Selective NMR in d-Wave Superconductors

A new mechanism for relaxing the nuclear magnetic moments, in which a pair of spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates at low temperature, is identified in type-II d-wave superconductors in an external magnetic field above Hc1. The results of the theory are compared with the NMR experiments on YBCO in high magnetic fields and found to agree without invoking antiferromagnetic order in the vortex core.

cond-mat.supr-con↗
arXiv2009

Relativistic Mott criticality in graphene

We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\sim 1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.

cond-mat.str-el↗
arXiv2009

Many-body instability of Coulomb interacting bilayer graphene: RG approach

Low-energy electronic structure of (unbiased) bilayer graphene is made of two Fermi points with quadratic dispersions, if trigonal-warping and other high order contributions are ignored. We show that as a result of this qualitative difference from single-layer graphene, short-range (or screened Coulomb) interactions are marginally relevant. We use renormalization group to study their effects on low-energy properties of the system, and show that the two quadratic Fermi points spontaneously split into four Dirac points, at zero temperature. This results in a nematic state that spontaneously breaks the six-fold lattice rotation symmetry (combined with layer permutation) down to a two-fold one, with a finite transition temperature. Critical properties of the transition and effects of trigonal warping are also discussed.

cond-mat.str-el↗
arXiv2008

Dynamical conductivity of ungated suspended graphene

Frequency dependent conductivity of Coulomb interacting massless Dirac fermions coupled to random scalar and random vector potentials is found as a function of frequency in the regime controlled by a line of fixed points. Such model provides a low energy description of a weakly rippled suspended graphene. The main finding is that at the neutrality point the a.c. conductivity is not frequency independent and may either increase or decrease with decreasing frequency, depending on the values of the disorder variances $Δ_ϕ$, $Δ_{A}$ and the Coulomb coupling $α=e^2/(\eps v_F)$. The low frequency behavior is characterized by the values of two dimensionless parameters $γ=Δ_ϕ/α^2$ and $Δ_A$ which are RG invariants, and for small values of which the electron-hole "puddles" are effectively screened making the results asymptotically exact.

cond-mat.dis-nn↗
arXiv2008

Coulomb interaction, ripples, and the minimal conductivity of graphene

We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency. The combined effect of the disorder due to wrinkling of the graphene sheet and the long range electron-electron interactions is a finite positive contribution to the dc conductivity. This contribution is disorder strength dependent and thus non-universal. The low-energy behavior of such a system is governed by the line of fixed points at which both the interaction and disorder are finite, and the density of states is exactly linear. An estimate of the typical random vector potential representing ripples in graphene brings the theoretical value of the minimal conductivity into the vicinity of 4e^2/h.

cond-mat.mes-hall↗
arXiv2007

Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential

We argue that massless Dirac particles in two spatial dimensions with $1/r$ Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of arXiv:0707.4171. At small interaction and small randomness, there is an infra-red stable fixed curve which merges with the strongly interacting infra-red unstable line at a critical endpoint, along which the dynamical critical exponent $z=1$.

cond-mat.mes-hall↗
arXiv2007

Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions

It is argued that the specific heat of $N$ massless Dirac fermions in 2 spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its non-interacting counterpart. The (dimensionless) coefficient of the logarithm is calculated analytically in the leading order in large $N$ expansion, but to all orders in $e^2N$, a procedure which takes into account finite temperature screening. Experimental observation of this effect is expected to occur in a single layer graphene embedded in a dielectric medium. Its dependence on the dielectric constant is calculated analytically.

cond-mat.mes-hall↗