Research areas

• Quantum spin Hall insulators

  Recently novel two-dimensional electronic state - quantum spin Hall (QSH) state - has been theoretically proposed [1,2] and obseved in HgTe quantum wells at Wuerzburg University [3]. It originates from spin-orbit band splitting and is characterized by time-reversal invariant gapless states on sample edges, where electrons with opposite spins counter-propagate, while the bulk states are fully gapped. Such (helical) edge channels make the QSH state topologically distinct from both ordinary band insulators and quantum Hall systems, and hold promise for reversible manipulation of spin-dependent quantum transport.

  In collaboration with the experimental group of L. W. Molenkamp (Wuerzburg) we investigate various electronic properties of chiral fermions in disordered topological insulators. An interesting question, from both theoretical and experimental points of view, is what happens to the QSH state in a strong quantizing magnetic field? How robust is the QSH state with respect to time-reversal symmetry breaking? Our recent paper [4] attempts to answer some of these questions.

  1. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).

  2. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006).

  3. M. Koenig, S. Wiedmann, C. Bruene, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007).

  4. G. Tkachov and E. M. Hankiewicz, Ballistic quantum spin Hall state and enhanced edge backscattering in strong magnetic fields , Phys. Rev. Lett. 104, 166803 (2010) ; arXiv: 0909.4428 .

• Graphene: Nanoelectronics meets quantum electrodynamics

  General interest in low-dimensional electron systems has recently revived in the light of the experimental success in isolating individual layers of graphite, preserving the honeycomb crystal structure [1]. Such a system - graphene - exhibits elementary excitations behaving at low energies and long distances as massless Dirac fermions, which opens hitherto unexplored research directions of both fundamental and applied character. In particular, understanding boundary effects in clean and disordered graphene and the need for their characterization are among the outstanding current challenges in the field, arising from potentially promising electronic applications of graphene ribbons and quantum dots.

  I have been studying electronic properties of graphene in the presence of extended defects, such as linear graphene edges. Some of them are topologically nontrivial and exhibit a remarkable property: they can bind massless Dirac fermions, leaving only the freedom of a quasi-1D motion along the edge. Such effective quasi-1D Dirac fermion systems occur on a few nm scale and display various broken symmetries, which may have implications for graphene nanoelectronics. On the other hand, studying Dirac fermion edge states helps us better understand the physics of the time-reversal invariant (Z_2) quantum Hall state. This has direct connections to both the quantum spin Hall effect and quantum-electrodynamical chiral anomalies [2].

  1. K. S. Novoselov et al., Nature 438, 197 (2005); Y. Zhang et al, ibid., 201 (2005).

  2. J. S.Bell and R. Jackiw, Nuovo Cimento A 60 (1969); F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).

• Mesoscopic superconductivity

  In collaboration with experimental groups of D. Weiss and C. Strunk of Regensburg University (Germany), I have been studying Andreev reflection, proximity and Josephson effects in 2D semiconductor/superconductor junctions. Such systems exhibit a number of interesting mesoscopic properties [1]: multiple Andreev reflection, the proximity-induced superconducting gap (minigap) in the ballistic regime, gapless induced superconductivity etc. Their description requires a combined use of Green's function [2] and scattering matrix [3] techniques as well as numerical coding that, altogether, enable an adequate interpretation of the experimental findings [4].

  1. C. Nguyen, H. Kroemer, and E. L. Hu, Phys. Rev. Lett. 69, 2847 (1992).

  2. A. A. Golubov, M. Yu. Kupriyanov, and E. Il'ichev, Rev. Mod. Phys. 76, 411 (2004).

  3. P.W. Brouwer and C.W.J. Beenakker, Chaos, Solitons and Fractals 8, 1249 (1997).

  4. F. Rohlfing, G. Tkachov, F. Otto, K. Richter, D. Weiss, G. Borghs, and C. Strunk, Doppler shift in Andreev reflection from a moving superconducting condensate in Nb/InAs Josephson junctions , Phys. Rev. B 80, 220507(R) (2009) ; arXiv: 0903.0321.

• Magnetic tunnel junctions

  Magnetic tunnel junctions with controllable relative orientation of the magnetization in the leads [1,2] are in the focus of current research motivated by their promising application potential as well as by general interest in spin-dependent phenomena in complex condensed matter environment.

  We study spin-dependent tunneling in the presence of long-range barrier disorder, using a new model approach based on the Glauber-type eikonal approximation for the multichannel scattering, originally employed in the nucleon scattering theory [3]. The model enables exact disorder ensemble averaging, allowing us to address previously unexplored regimes of random spin-polarized tunneling and tunneling magnetoresistance effect.

  1. J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett. 74, 3273 (1995).

  2. S. Parkin, C. Kaiser, A. Panchula, P. Rice, B. Hughes, M. Samant, and S.-H. Yang, Nature Mat. 3, 862 (2004).

  3. R. J. Glauber, Phys. Rev. 100, 242 (1955).