Thomas L. Schmidt and Giacomo Dolcetto and Christopher J. Pedder and Karyn Le Hur and Peter P. Orth, Mechanical resonances of mobile impurities in a one-dimensional quantum fluid, Phys. Rev. Lett. 123, 075302 (2019)
We study a one-dimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong backscattering this interaction gives rise to resonances and antiresonances in the finite-frequency mobility of the impurity pair. At the antiresonances, the two impurities remain at rest even when driven by a (small) external force. At the resonances, their synchronous motion follows the external drive in phase and reaches maximum amplitude. Using a perturbative renormalization group analysis in quantum tunneling across the impurities, we study the range of validity of our model. We predict that these mechanical antiresonances are observable in experiments on ultracold atom gases confined to one dimension.
Moors, Kristof and Zyuzin, Alexander A. and Zyuzin, Alexander Yu. and Tiwari, Rakesh P. and Schmidt, Thomas L., Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals, Phys. Rev. B 99, 041116 (2019)
We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter.
Pedder, Christopher J. and Meng, Tobias and Tiwari, Rakesh P. and Schmidt, Thomas L., Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields, Phys. Rev. B 94, 245414 (2016)
A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a “helical gap” manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunneling density of states. In this paper we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by re-fermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.
Christoph P. Orth and Rakesh P. Tiwari and Tobias Meng and Thomas L. Schmidt, Non-Abelian parafermions in time-reversal invariant interacting helical systems, Phys. Rev. B 91, 081406(R) (2015)
The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8π$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.
Schmidt, Thomas L. and Nunnenkamp, Andreas and Bruder, Christoph, Majorana Qubit Rotations in Microwave Cavities, Phys. Rev. Lett. 110, 107006 (2013)
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows us to perform arbitrary single-qubit operations.
Imambekov, Adilet and Schmidt, Thomas L. and Glazman, Leonid I., One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm, Rev. Mod. Phys. 84, 1253 (2012)
For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.
Schmidt, Thomas L. and Rachel, Stephan and von Oppen, Felix and Glazman, Leonid I., Inelastic Electron Backscattering in a Generic Helical Edge Channel, Phys. Rev. Lett. 108, 156402 (2012)
We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, $δ G ∝ T^4$. In addition, $δ G$ is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.
Schmidt, Thomas L., Current Correlations in Quantum Spin Hall Insulators, Phys. Rev. Lett. 107, 096602 (2011)
We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.
Thomas L. Schmidt and Adilet Imambekov and Leonid I. Glazman, Fate of 1D Spin-Charge Separation Away from Fermi Points, Phys. Rev. Lett. 104, 116403 (2010)
We consider the dynamic response functions of interacting one dimensional spin-$1/2$ fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.
T. L. Schmidt and P. Werner and L. Mühlbacher and A. Komnik, Transient dynamics of the Anderson impurity model out of equilibrium, Phys. Rev. B 78, 235110 (2008)
We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.