arXiv subjects

Leonid Levitov

Publications and source records attributed to Leonid Levitov.

68 records · Page 4Linked to original sources

arXiv2011

Chiral superconductivity from repulsive interactions in doped graphene

We identify graphene as a system where chiral superconductivity can be realized. Chiral superconductivity involves a pairing gap that winds in phase around the Fermi surface, breaking time reversal symmetry. We consider a unique situation arising in graphene at a specific level of doping, where the density of states is singular, strongly enhancing the critical temperature T_c. At this doping level, the Fermi surface is nested, allowing superconductivity to emerge from repulsive electron-electron interactions. We show using a renormalization group method that superconductivity dominates over all competing orders for any choice of weak repulsive interactions. Superconductivity develops in a doubly degenerate, spin singlet channel, and a mean field calculation indicates that the superconductivity is of a chiral d+id type. We therefore predict that doped graphene can provide experimental realization of spin-singlet chiral superconductivity.

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arXiv2011

Common-Path Interference and Zener Tunneling in Bilayer Graphene p-n Junctions

Interference and tunneling are two signature quantum effects that are often perceived as the yin and yang of quantum mechanics: particle simultaneously propagating along several distinct classical paths versus particle penetrating through a classically inaccessible region via a single least-action path. Here we demonstrate that the Dirac quasiparticles in graphene provide a dramatic departure from this paradigm. We show that Zener tunneling in gapped bilayer graphene (BLG), which governs transport through p-n heterojunctions, exhibits common-path interference that takes place under the tunnel barrier. Due to a symmetry peculiar to the BLG bandstructure, interfering tunneling paths form `conjugate pairs', giving rise to high-contrast oscillations in transmission as a function of the gate-tunable bandgap and other control parameters of the junction. The common-path interference is solely due to forward-propagating waves; in contrast to Fabry-Perot-type interference in resonant tunneling structures it does not rely on multiple backscattering. The oscillations manifest themselves in the junction I-V characteristic as N-shaped branches with negative differential conductivity, enabling new high-speed active-circuit devices with architectures which are not available in electronic semiconductor devices.

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arXiv2011

Chirality-Assisted Electronic Cloaking in Bilayer Graphene Nanostructures

We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.

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arXiv2011

Polar Kerr Effect and Time Reversal Symmetry Breaking in Bilayer Graphene

The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero inter-band matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time reversal symmetry and lattice rotation symmetry, respectively. These optical signatures, which undergo a resonant enhancement in the near-infrared regime, lie well within reach of existing experimental techniques.

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arXiv2010

Quantum Anomalous Hall State in Bilayer Graphene

We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4) symmetry, and distinguish symmetry protected degeneracies from accidental degeneracies. One of the states, which spontaneously breaks discrete time reversal symmetry but no continuous symmetry, is identified as a Quantum Anomalous Hall (QAH) state, which exhibits quantum Hall effect at zero magnetic field. We investigate the lifting of the accidental degeneracies by thermal and zero point fluctuations, taking account of the modes softened under RG. Working in a 'saddle point plus quadratic fluctuations' approximation, we identify two types of RG- soft modes which have competing effects. Zero point fluctuations, dominated by 'transverse' modes which are unique to BLG, favor the QAH state. Thermal fluctuations, dominated by 'longitudinal' modes, favor a SU(4) symmetry breaking multiplet of states. We discuss the phenomenology and experimental signatures of the QAH state in BLG, and also propose a way to induce the QAH state using weak external magnetic fields.

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arXiv2010

Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long range character, resulting in $\log^2$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order, and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function, while all other quantities renormalize only logarithmically. We solve the RG flow equation for the Green function with logarithmic accuracy, and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge invariant quantities, such as the compressibility, remain finite to $\log^2$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the non-interacting value.

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arXiv2010

Spatial Ordering of Defects and Conductivity of Functionalized Graphene

Recently, it was predicted that an RKKY-type interaction between adatoms in graphene can drive an ordering transition to a state with broken sublattice symmetry (arXiv:1004.3678). In this state, due to Bragg scattering of electron waves on the sublattice modulation, a gap opens up at the Dirac point (DP). Here we investigate the effect of ordering on the transport properties, finding that upon transition from disordered state to an ordered state the conductivity is increased (reduced) at energies away (near) DP. This behavior can be understood as a result of coherent Bragg scattering in the ordered state. The conductivity change can serve as a direct signature of adatom ordering.

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arXiv2010

Landau Level Collapse in Gated Graphene Structures

We describe a new regime of magnetotransport in two dimensional electron systems in the presence of a narrow potential barrier imposed by external gates. In such systems, the Landau level states, confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. We present transport measurements showing Shubnikov-de Haas (SdH) oscillations which, in the unipolar regime, abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories. Comparison to SdH-type resonances in the local density of states is presented.

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arXiv2010

Flavor Symmetry and Competing Orders in Bilayer Graphene

We analyze competition between different ordered states in bilayer graphene (BLG). Combining arguments based on SU(4) spin-valley flavor symmetry with a mean field analysis, we identify the lowest energy state with the anomalous Hall insulator (AHI). This state is an SU(4) singlet excitonic insulator with broken time reversal symmetry, exhibiting quantized Hall effect in the absence of external magnetic field. Applied electric field drives an Ising-type phase transition, restoring time reversal symmetry. Applied magnetic field drives a transition from the AHI state to a quantum Hall ferromagnet state. We estimate energies of these states, taking full account of screening, and predict the phase diagram.

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arXiv2010

Dynamical Screening and Ferroelectric-type Excitonic Instability in Bilayer Graphene

Electron interactions in undoped bilayer graphene lead to instability of the gapless state, `which-layer' symmetry breaking, and energy gap opening at the Dirac point. In contrast to single layer graphene, the bilayer system exhibits instability even for arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full acount of dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.

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arXiv2009

Long-Range Interaction Between Adatoms in Graphene

We present a theory of electron-mediated interaction between adatoms in graphene. In the case of resonant scattering, relevant for hydrogentated graphene, a long-range 1/r interaction is found. This interaction can be viewed as a fermionic analog of the Casimir interaction, in which massless fermions play the role of photons. The interaction is an attraction or a repulsion depending on whether the adatoms reside on the same sublattice or on different sublattices, with attraction dominating for adatoms randomly spread over both sublattices. The attractive nature of these forces creates an instability under which adatoms tend to aggregate.

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arXiv2009

Many-Body Entanglement: a New Application of the Full Counting Statistics

Entanglement entropy is a measure of quantum correlations between separate parts of a many-body system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the Full Counting Statistics description of electron transport was established for noninteracting fermion systems. Using this relation, which is of a completely general character, we discuss how the entanglement entropy can be directly measured by detecting current fluctuations in a driven quantum system such as a quantum point contact.

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arXiv2008

Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene

Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of their discrete energy levels, which are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in another system, graphene p-n junctions. We show how the transport problem in the presence of magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p-n junctions. Finally, we review recent proposal to use Fabry-Perot resonances in p-n-p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.

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arXiv2008

Quantum Noise as an Entanglement Meter

Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to condensed matter theory and quantum information. The universal appeal of the entanglement entropy concept is related, in part, to the fact that it is defined solely in terms of the many-body density matrix of the system, with no relation to any particular observables. However, for the same reason, it has not been clear how to access this quantity experimentally. Here we derive a universal relation between entanglement entropy and the fluctuations of current flowing through a quantum point contact (QPC) which opens a way to perform a direct measurement of entanglement entropy. In particular, by utilizing space-time duality of 1d systems, we relate electric noise generated by opening and closing the QPC periodically in time with the seminal S = 1/3 log L prediction of conformal field theory.

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