Lehrstuhl fur Theoretische Festkorperphysik

Erlangen, Germany

Lehrstuhl fur Theoretische Festkorperphysik

Erlangen, Germany
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Azhikodan D.,IIT RoorkeeUttarakhand | Nautiyal T.,IIT RoorkeeUttarakhand | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Sharma S.,Max Planck Institute of Microstructure Physics
Scientific Reports | Year: 2016

The few layer transition metal dichalcogenides are two dimensional materials that have an intrinsic gap of the order of ≈2 eV. The reduced screening in two dimensions implies a rich excitonic physics and, as a consequence, many potential applications in the field of opto-electronics. Here we report that a layer perpendicular electric field, by which the gap size in these materials can be efficiently controlled, generates an anomalous inter-layer exciton whose binding energy is independent of the gap size. We show this originates from the rich gap control and screening physics of TMDCs in a bilayer geometry: gating the bilayer acts on one hand to increase intra-layer screening by reducing the gap and, on the other hand, to decrease the inter-layer screening by field induced charge depletion. This constancy of binding energy is both a striking exception to the universal reduction in binding energy with gap size that all materials are believed to follow, as well as evidence of a degree of control over inter-layer excitons not found in their well studied intra-layer counterparts. © Author(s) 2016.


Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Sharma S.,Max Planck Institute of Microstructure Physics | Weber H.B.,Lehrstuhl fur Angewandte Physik | Weber H.B.,Friedrich - Alexander - University, Erlangen - Nuremberg
Nature Communications | Year: 2017

Charge transport at the Dirac point in bilayer graphene exhibits two dramatically different transport states, insulating and metallic, that occur in apparently otherwise indistinguishable experimental samples. We demonstrate that the existence of these two transport states has its origin in an interplay between evanescent modes, that dominate charge transport near the Dirac point, and disordered configurations of extended defects in the form of partial dislocations. In a large ensemble of bilayer systems with randomly positioned partial dislocations, the distribution of conductivities is found to be strongly peaked at both the insulating and metallic limits. We argue that this distribution form, that occurs only at the Dirac point, lies at the heart of the observation of both metallic and insulating states in bilayer graphene. © 2017 The Author(s).


Vogl M.,Lehrstuhl fur Theoretische Festkorperphysik | Vogl M.,University of Texas at Austin | Pankratov O.,Lehrstuhl fur Theoretische Festkorperphysik | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B | Year: 2017

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n×n dimensional Hamiltonian H(p,q). The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H(p,q); these vectors describe the internal structure of the semiclassical particles. At the O(1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states. © 2017 American Physical Society.


Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Sharma S.,Max Planck Institute of Microstructure Physics | Kandelaki E.,Lehrstuhl fur Theoretische Festkorperphysik | Kandelaki E.,Ruhr University Bochum | Pankratov O.A.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B - Condensed Matter and Materials Physics | Year: 2010

We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle θ. It is shown that, due to the weak interaction between graphene layers, many features of this system can be understood by interference conditions between the quantum states of the two layers, mathematically expressed as Diophantine problems. Based on this general analysis we demonstrate that while the Dirac cones from each layer are always effectively degenerate, the Fermi velocity vF of the Dirac cones decreases as θ→0°; the form we derive for vF (θ) agrees with that found via a continuum approximation in. From tight-binding calculations for structures with 1.47°≤θ<30° we find agreement with this formula for θ5°. In contrast, for θ>5° this formula breaks down and the Dirac bands become strongly warped as the limit θ→0 is approached. For an ideal system of twisted layers the limit as θ→0° is singular as for θ>0 the Dirac point is fourfold degenerate, while at θ=0 one has the twofold degeneracy of the AB stacked bilayer. Interestingly, in this limit the electronic properties are in an essential way determined globally, in contrast to the " nearsightedness" of electronic structure generally found in condensed matter. © 2010 The American Physical Society.


Sharma S.,Max Planck Institute of Microstructure Physics | Sharma S.,Indian Institute of Technology Roorkee | Dewhurst J.K.,Max Planck Institute of Microstructure Physics | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | And 3 more authors.
Journal of Chemical Theory and Computation | Year: 2015

We apply the bootstrap kernel within time-dependent density functional theory to study the one-dimensional chain of polymer polyphenylenevinylene and molecular crystals of picene and pentacene. The absorption spectra of poly(p-phenylenevinylene) has a bound excitonic peak that is well-reproduced. Pentacene and picene, electronically similar materials, have remarkably different excitonic physics, and this difference is also well captured. We show that the inclusion of local-field effects dramatically changes the spectra of both picene and pentacene but not for poly(p-phenylenevinylene). © 2015 American Chemical Society.


Sharma S.,Max Planck Institute of Microstructure Physics | Dewhurst J.K.,Max Planck Institute of Microstructure Physics | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Gross E.K.U.,Max Planck Institute of Microstructure Physics
Physical Review Letters | Year: 2013

We present a method for calculating the spectrum of periodic solids within reduced density matrix functional theory. This method is validated by a detailed comparison of the angular momentum projected spectral density with that of well-established many-body techniques, finding very good agreement in all cases. The physics behind the pressure induced insulator-metal phase transition in MnO is investigated. The driving mechanism of this transition is identified as increased crystal field splitting with pressure, resulting in a charge redistribution between the Mn eg and t2g symmetry projected states. © 2013 American Physical Society.


Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Sharma S.,Max Planck Institute of Microstructure Physics | Pankratov O.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

We identify an angle-dependent momentum scale as the fundamental property of a bilayer composed of mutually rotated graphene layers. The interlayer scattering processes at these characteristic momentum values define an effective Brillouin zone (a Jones zone) which, in general, differs from the Brillouin zone generated by the real-space lattice, which is physically irrelevant. From this we develop a numerical method that increases, for the twist bilayer, the efficiency of the standard tight-binding method by a factor of ≈103 at no loss of accuracy. The efficiency of the method is based on (i) the fact that the twist Hamiltonian is exceptionally sparse in a basis of single-layer graphene (SLG) states, (ii) a solution of trivial Diophantine problem (Bézout's identity) allows one to know in advance which matrix elements take nonzero values, and (iii) to access the electronic structure in a few electron volts about the Dirac point a truncated SLG basis consisting only of states in a somewhat larger energy window are required, leading to a much reduced size of the Hamiltonian. This allows a complete survey of the system which reveals (i) an angle-dependent series of van Hove singularities, (ii) an increasing mixing of SLG states as the twist angle is reduced leading to the appearance of localization of the twist bilayer wave functions at all energies in the small-angle limit, and (iii) a zero-energy peak in the density of states in an approximately self-similar small-angle regime. © 2013 American Physical Society.


Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Sharma S.,Max Planck Institute of Microstructure Physics | Landgraf W.,Lehrstuhl fur Theoretische Festkorperphysik | Pankratov O.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We investigate the electronic structure of graphene stacks having an ordered sequence of pairs of twisted layers-the graphene twist stack. We find that this remarkable system entails a fundamental mixing of dimensionalities: While the twist stack spectrum is generated by an ensemble of independent effective twist bilayer Hamiltonians, the wave functions are products of bilayer wave functions and standing electron waves in the stacking direction, and thus extend over many layers of the stack. These have the property that of the ensemble of Dirac cones that constitute the twist stack band structure, it is those topologically closest to single layer graphene that dominate the surface region. We further examine the impact of stacking disorder, finding that these results are robust for moderate stacking fault density. © 2011 American Physical Society.


Klier N.,Lehrstuhl fur Theoretische Festkorperphysik | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Pankratov O.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

We derive the asymptotics of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in the graphene Bernal bilayer using a four-band model of the bilayer spectrum. We find three distinct regimes depending on the position of the Fermi energy in the bilayer spectrum: in the bonding-antibonding gap, at the gap edge, and outside the gap. In particular, for impurities on the bilayer bonding sublattice (the "A" sublattice) and Fermi energies close to the bonding-antibonding gap edge Eg, we identify a (integrable) logarithmic divergence of the integrand of the RKKY exchange integral. This divergence drives a number of novel RKKY effects for impurities on the A sublattice: (i) an asymptotic R-5/2 term at the gap edge and (ii) a derivative discontinuity in RKKY interaction as a function of the Fermi energy at the gap edge. In the case of intercalated impurities (impurities between the two layers of the bilayer), we find a remarkable discontinuity in the period of the RKKY oscillation at the gap edge. The period of the oscillation limits to λ=2πvF/t as EF→Eg from below the gap edge, while it limits to λ→ if EF→Eg from above the gap edge (t is the interlayer coupling, vF the Fermi velocity of graphene). The origin of this discontinuity we attribute to (i) the A sublattice divergence and (ii) interference effects driven by the intrinsic valley degree of freedom of graphene. On this basis, we predict that the magnetic response of intercalated bilayer graphene will show a profound sensitivity to doping for Fermi energies near the bonding-antibonding gap edge. © 2014 American Physical Society.


Landgraf W.,Lehrstuhl fur Theoretische Festkorperphysik | Shallcross S.,Lehrstuhl fur Theoretische Festkorperphysik | Turschmann K.,Lehrstuhl fur Theoretische Festkorperphysik | Weckbecker D.,Lehrstuhl fur Theoretische Festkorperphysik | Pankratov O.,Lehrstuhl fur Theoretische Festkorperphysik
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

We study the electronic structure of bilayer graphene flakes in which the constituent layers are mutually rotated by some angle θ. The large system sizes involved (up to 105 carbon atoms) necessitate the use of a tight-binding approach in conjunction with Lanczos diagonalization. We find that a single moiré spot is sufficient for the low-energy density of states to resemble closely that of the periodic analog of such flakes, the graphene twist bilayer, implying that the low-energy physics in this system is well described as that of a "moiré quantum well" trapping low-energy graphene electrons. Furthermore, a graphene twist flake consisting of a single moiré unit cell leads already to electron localization on the AA "moiré spot," in agreement with this moiré quantum well picture. The electron density fluctuations induced by the moiré lattice in twist graphene flakes are significant, being an order of magnitude greater than those generated by the rippling of suspended graphene. Finally, we determine the electronic properties of such flakes in the presence of an external magnetic field, finding a "zero-mode" structure and Landau states that exhibit an electron current well described as a charge flow on a torus situated at the AA regions of the moiré lattice. © 2013 American Physical Society.

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