SPS Award in General Physics, sponsored by ABB
Titus Neupert is awarded with the SPS 2013 Prize in General Physics for his pioneering PhD work, especially for his theoretical discovery of "Fractional quantum Hall states at zero magnetic field".
The integer and fractional quantum Hall effects were experimentally detected in 1981 and 1982, respectively, at cryogenic temperatures. The discovery of graphene in 2005 established that the integer quantum Hall effect could be achieved at room temperature. Theorists predicted that the integer quantum Hall effect was one out of many examples of a larger family of semiconducting states supporting quantized susceptibilities in materials called topological band insulators. Titus Neupert gave the first quantitative answer to the question whether strong interactions could drive a fractional topological insulator in very much the same way as interactions drive a fractional quantum Hall insulator. One of the most remarkable prediction made by the award winner is that, by taking advantage of materials with strong spin-orbit coupling, it might become possible to achieve a fractional quantum Hall effect that is robust at room temperature and this without the use of any laboratory magnetic field.
Fractional quantum Hall states at zero magnetic field
A central theme of condensed matter physics is to classify and understand phases of matter. The Landau theory of symmetry breaking has been the long-standing paradigm for this classification: Two phases are distinct if they have different symmetries. In recent years, the study of topological phases showed that a second paradigm must be considered on equal footing: Two phases are distinct if they have different topological character, even if they share the same symmetries. Topological properties cannot be changed smoothly, thus endowing a topological state with a natural universality and protection against perturbations.
Topological phases are understood and classified in the limit of small electron–electron interactions. The opposite limit, in contrast, is at the frontier of current research. Strong electron–electron interactions can be responsible for the emergence of correlated topological states with excitations that have a fraction of the electron's charge, so-called fractional topological insulators (FTIs). The first example of an FTI that is well studied both experimentally and theoretically is the fractional quantum Hall effect of electrons in partially filled Landau levels. Recently, we discovered another type of FTIs, the fractional Chern insulator [1]. These states arise in lattice models in two spatial dimensions, if a nearly dispersionless band with a nonzero Chern number is partially filled with repulsively interacting electrons. Fractional Chern insulators share many universal and topological properties with the fractional quantum Hall effect in Landau levels, where the role of the strong magnetic field is replaced by time-reversal symmetry breaking electronic hopping integrals on the lattice. Comparing and contrasting the fractional Chern insulators with the fractional quantum Hall effect allows us to better understand what are the core ingredients for a fractional topological state to emerge.
In a combination of numerical and analytical work, we have studied several aspects of FTIs in two spatial dimensions. For example, we found that if a topological insulator, as is realized in HgTe quantum wells, has a sufficiently small bandwidth, repulsive electron–electron interactions can favor a spontaneous breaking of time-reversal symmetry along with the formation of an anomalous quantum Hall effect or a fractional Chern insulator state [2].
[1] T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011).
[2] T. Neupert, L. Santos, S. Ryu, C. Chamon, and C. Mudry, Phys. Rev. B 84, 165107 (2011).
The integer and fractional quantum Hall effects were experimentally detected in 1981 and 1982, respectively, at cryogenic temperatures. The discovery of graphene in 2005 established that the integer quantum Hall effect could be achieved at room temperature. Theorists predicted that the integer quantum Hall effect was one out of many examples of a larger family of semiconducting states supporting quantized susceptibilities in materials called topological band insulators. Titus Neupert gave the first quantitative answer to the question whether strong interactions could drive a fractional topological insulator in very much the same way as interactions drive a fractional quantum Hall insulator. One of the most remarkable prediction made by the award winner is that, by taking advantage of materials with strong spin-orbit coupling, it might become possible to achieve a fractional quantum Hall effect that is robust at room temperature and this without the use of any laboratory magnetic field.
Fractional quantum Hall states at zero magnetic field
A central theme of condensed matter physics is to classify and understand phases of matter. The Landau theory of symmetry breaking has been the long-standing paradigm for this classification: Two phases are distinct if they have different symmetries. In recent years, the study of topological phases showed that a second paradigm must be considered on equal footing: Two phases are distinct if they have different topological character, even if they share the same symmetries. Topological properties cannot be changed smoothly, thus endowing a topological state with a natural universality and protection against perturbations.
Topological phases are understood and classified in the limit of small electron–electron interactions. The opposite limit, in contrast, is at the frontier of current research. Strong electron–electron interactions can be responsible for the emergence of correlated topological states with excitations that have a fraction of the electron's charge, so-called fractional topological insulators (FTIs). The first example of an FTI that is well studied both experimentally and theoretically is the fractional quantum Hall effect of electrons in partially filled Landau levels. Recently, we discovered another type of FTIs, the fractional Chern insulator [1]. These states arise in lattice models in two spatial dimensions, if a nearly dispersionless band with a nonzero Chern number is partially filled with repulsively interacting electrons. Fractional Chern insulators share many universal and topological properties with the fractional quantum Hall effect in Landau levels, where the role of the strong magnetic field is replaced by time-reversal symmetry breaking electronic hopping integrals on the lattice. Comparing and contrasting the fractional Chern insulators with the fractional quantum Hall effect allows us to better understand what are the core ingredients for a fractional topological state to emerge.
In a combination of numerical and analytical work, we have studied several aspects of FTIs in two spatial dimensions. For example, we found that if a topological insulator, as is realized in HgTe quantum wells, has a sufficiently small bandwidth, repulsive electron–electron interactions can favor a spontaneous breaking of time-reversal symmetry along with the formation of an anomalous quantum Hall effect or a fractional Chern insulator state [2].
[1] T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011).
[2] T. Neupert, L. Santos, S. Ryu, C. Chamon, and C. Mudry, Phys. Rev. B 84, 165107 (2011).
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