Welcome to the Theoretical Group on Quantum Transport on the Nanoscale at the Department of Theory, Modeling and Simulation of Materials and Processes of the Materials Science Institute of Madrid, Spain (ICMM, CSIC).

**Recent Research:**

Chiral response of twisted bilayer graphene.

T. Stauber, T. Low and G. Gómez-Santos

Phys. Rev. Lett. 120, 046801 (2018)We present an effective (minimal) theory for chiral two-dimensional materials. These materials possess an electromagnetic coupling without exhibiting a topological gap. As an example, we study the response of doped twisted bilayers, unveiling unusual phenomena in the zero frequency limit. An in-plane magnetic field induces a huge paramagnetic response at the neutrality point and, upon doping, also gives rise to a substantial longitudinal Hall response. The system also accommodates nontrivial longitudinal plasmonic modes that are associated with a longitudinal magnetic moment, thus endowing them with a chiral character. Finally, we note that the optical activity can be considerably enhanced upon doping and our general approach would enable systematic exploration of 2D material heterostructures with optical activity.

Random-walk topological transition revealed by electron counting

G. Engelhardt, M. Benito, G. Platero, G. Schaller and T. Brandes.

Phys. Rev. B 96, 241404(R) (2017)The appearance of topological effects in systems exhibiting a nontrivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic random walk version of the Su-Schrieffer-Heeger model with no relation to coherent wave dynamics. We explain that the commonly used topological invariant in the momentum space translates into an invariant in a counting-field space. This invariant gives rise to clear signatures of the topological phase in an associated escape time distribution.

Dispersive readout of adiabatic phases

Sigmund Kohler

Phys. Rev. Lett. 119, 196802 (2017)

We propose a protocol for the measurement of adiabatic phases of periodically driven quantum systems coupled to an open cavity that enables dispersive readout. It turns out that the cavity transmission exhibits peaks at frequencies determined by a resonance condition that involves the dynamical and the geometric phase. Since these phases scale differently with the driving frequency, one can determine them by fitting the peak positions to the theoretically expected behavior. For the derivation of the resonance condition and for a numerical study, we develop a Floquet theory for the dispersive readout of ac driven quantum systems. The feasibility is demonstrated for two test cases that generalize Landau-Zener-Stückelberg-Majorana interference to two-parameter driving.

Signatures of a 4π-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions

Jordi Picó-Cortés, Fernando Domínguez, and Gloria Platero

Phys. Rev. B 96, 125438 (2017)

We investigate theoretical aspects of the detection of Majorana bound states in Josephson junctions using the semiclassical resistively capacitively shunted junction (RCSJ) model of junction dynamics. The influence of a 4π-periodic supercurrent contribution can be detected through its effect on the width of the Shapiro steps and the Fourier spectrum of the voltage signal. We explain how the inclusion of a capacitance term results in a strong quenching of the first step when the junction is underdamped, while the higher odd steps are less affected. Remarkably, this feature has been observed experimentally. We examine the emission spectrum of phase-locked solutions, showing that the presence of period doubling may make the measurement of the 4π-periodic contribution from the Fourier spectrum difficult. Finally, we study the voltage response in the quasiperiodic regime and indicate how the Fourier spectra and the first-return maps in this regime reflect the change of periodicity in the supercurrent in the presence of Majorana bound states.

Chiral Maxwell demon in a quantum Hall system with a localized impurity

Guillem Rosselló, Rosa López, and Gloria Platero

Phys. Rev. B 96,075305 (2017),We investigate the role of chirality on the performance of a Maxwell demon implemented in a quantum Hall bar with a localized impurity. Within a stochastic thermodynamics description, we investigate the ability of such a demon to drive a current against a bias. We show that the ability of the demon to perform is directly related to its ability to extract information from the system. The key features of the proposed Maxwell demon are the topological properties of the quantum Hall system. The asymmetry of the electronic interactions felt at the localized state when the magnetic field is reversed joined to the fact that we consider energy-dependent (and asymmetric) tunneling barriers that connect such state with the Hall edge modes allow the demon to properly work.

Doublon lifetimes in dissipative environments

Miguel Bello, Sigmund Kohler, and Gloria Platero

Phys. Rev. B 96,045408 (2017),

We study the dissipative decay of states with a doubly occupied site in a two-electron Hubbard model, known as doublons. For the environment, we consider charge and current noise, which are modeled as a bosonic heat bath that couples to the on-site energies and the tunnel couplings, respectively. It turns out that the dissipative decay depends qualitatively on the type of environment, as for charge noise, the lifetime grows with the electron-electron interaction. For current noise, by contrast, doublons become increasingly unstable with larger interaction. Numerical studies within a Bloch-Redfield approach are complemented by analytical estimates for the decay rates. For typical quantum dot parameters, we predict doublon lifetimes up to 50 ns.

Topologically-enforced bifurcations in superconducting circuits

G. Engelhardt, M. Benito, G. Platero and T. Brandes.

Phys. Rev. Lett.118, 197702 (2017).

The relationship of topological insulators and superconductors and the field of nonlinear dynamics is widely unexplored. To address this subject, we adopt the linear coupling geometry of the Su-Schrieffer-Heeger model, a paradigmatic example for a topological insulator, and render it nonlinearly in the context of superconducting circuits. As a consequence, the system exhibits topologically enforced bifurcations as a function of the topological control parameter, which finally gives rise to chaotic dynamics, separating phases that exhibit clear topological features.

Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

Miguel Bello, Charles E. Creffield and Gloria Platero

Phys. Rev. B 95, 094303 (2017).

We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.

Coherent long-range thermodynamics in nonadiabatic driven systems

Fernando Gallego-Marcos and G. Platero

Phys. Rev. B 95, 075301 (2017).

We investigate direct energy and heat transfer between two distant sites of a triple quantum dot connected to reservoirs, where one of the edge dots is driven by an ac-gate voltage. We theoretically propose how to implement heat and cooling engines mediated by long-range photoassisted transport. Additionally, we propose a simple setup to heat up coherently the two reservoirs symmetrically and a mechanism to store energy in the closed system. The present proposals can be experimentally implemented and easily controlled by tuning the external parameters.

Full-counting statistics of time-dependent conductors

M. Benito, M. Niklas and S. Kohler.

Phys. Rev. B94, 195433 (2016)

We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of each operator yields one cumulant. This direct relation offers a better numerical efficiency than the equivalent number-resolved master equation. The proposed method is particularly useful for conductors with an elaborate time dependence stemming, e.g., from pulses or combinations of slow and fast parameter switching. As a test bench for the evaluation of the numerical stability, we consider time-independent problems for which the full-counting statistics can be computed by other means. As applications, we study cumulants of higher order for two time-dependent transport problems of recent interest, namely steady-state coherent transfer by adiabatic passage (CTAP) and Landau-Zener-Stückelberg-Majorana (LZSM) interference in an open double quantum dot.

Transport, shot noise, and topology in AC-driven dimer arrays

M. Niklas, M. Benito, S. Kohler and G. Platero.

Nanotechnology27, 45 (2016)

We analyze an AC-driven dimer chain connected to a strongly biased electron source and drain. It turns out that the resulting transport exhibits fingerprints of topology. They are particularly visible in the driving-induced current suppression and the Fano factor. Thus, shot noise measurements provide a topological phase diagram as a function of the driving parameters. The observed phenomena can be explained physically by a mapping to an effective time-independent Hamiltonian and the emergence of edge states. Moreover, by considering quantum dissipation, we determine the requirements for the coherence properties in a possible experimental realization. For the computation of the zero-frequency noise, we develop an efficient method based on matrix-continued fractions.

Dissipative Long-Range Entanglement Generation between Electronic Spins

M. Benito, M. J. A. Schütz, J.I. Cirac, G. Platero and G. Giedke.

Phys. Rev. B94, 115404 (2016)

We propose a scheme for deterministic generation and long-term stabilization of entanglement between two electronic spin qubits confined in spatially separated quantum dots. Our approach relies on an electronic quantum bus, consisting either of quantum Hall edge channels or surface acoustic waves, that can mediate long-range coupling between localized spins over distances of tens of micrometers. Since the entanglement is actively stabilized by dissipative dynamics, our scheme is inherently robust against noise and imperfections.

Topological instabilities in ac-driven bosonic systems

G. Engelhardt, M. Benito, G. Platero and T. Brandes.

Phys. Rev. Lett.117, 045302 (2016)

Under nonequilibrium conditions, bosonic modes can become dynamically unstable with an exponentially growing occupation. On the other hand, topological band structures give rise to symmetry protected midgap states. In this Letter, we investigate the interplay of instability and topology. Thereby, we establish a general relation between topology and instability under ac driving. We apply our findings to create dynamical instabilities which are strongly localized at the boundaries of a finite-size system. As these localized instabilities are protected by symmetry, they can be considered as topological instabilities.

Edge-state Blockade of Transport in Quantum Dot Arrays

M. Benito, M. Niklas, G. Platero and S. Kohler.

Phys. Rev. B93, 115432 (2016)

We propose a transport blockade mechanism in quantum dot arrays and conducting molecules based on an interplay of Coulomb repulsion and the formation of edge states. As a model we employ a dimer chain that exhibits a topological phase transition. The connection to a strongly biased electron source and drain enables transport. We show that the related emergence of edge states is manifest in the shot noise properties as it is accompanied by a crossover from bunched electron transport to a Poissonian process. For both regions we develop a scenario that can be captured by a rate equation. The resulting analytical expressions for the Fano factor agree well with the numerical solution of a full quantum master equation.

Coupled Landau-Zener-Stückelberg quantum dot interferometers

F. Gallego-marcos, R. Sánchez and G. Platero.

Phys. Rev. B93, 075424 (2016)

We investigate the interplay between long-range and direct photon-assisted transport in a triple quantum dot chain where local ac voltages are applied to the outer dots. We propose the phase difference between the two ac voltages as an external parameter, which can be easily tuned to manipulate the current characteristics. For gate voltages in phase opposition we find quantum destructive interferences analogous to the interferences in closed-loop undriven triple dots. As the voltages oscillate in phase, interferences between multiple paths give rise to dark states. Those totally cancel the current, and could be experimentally resolved.

Long-range doublon transfer in a dimer chain induced by topology and ac fields

M. Bello, C. Creffield and G. Platero.

Sci. Rep.6, 22562 (2016)

In this work we study how to induce long-range transfer of interacting particles between the two ends of a dimer chain, by coupling states that are localized just on the chain’s end-points. This has the appealing feature that the transfer occurs only between the end-points – the particle does not pass through the intermediate sites – making the transfer less susceptible to decoherence. Gate potentials and ac fields allow us to induce the the presence of topological or Shockley-like edge states. We can control the quality and speed of the transfer by tuning the different parameters of the model.

Degenerate parametric oscillation in quantum membrane optomechanics

M. Benito, C. Sánchez-Muñoz and C. Navarrete-Benlloch.

Phys. Rev. A93, 023846 (2016)

In this work we show that modern optomechanical setups are mature enough to implement one of the most elusive models in the field of open system dynamics: degenerate parametric oscillation. Introduced in the eighties and motivated by its alleged implementability in nonlinear optical resonators, it rapidly became a paradigm for the study of dissipative phase transitions whose corresponding spontaneously broken symmetry is discrete. However, it was found that the intrinsic multimode nature of optical cavities makes it impossible to experimentally study the model all the way through its phase transition. In contrast, here we show that this long-awaited model can be implemented in the motion of a mechanical object dispersively coupled to the light contained in a cavity, when the latter is properly driven with multichromatic laser light. We focus on membranes as the mechanical element, showing that the main signatures of the degenerate parametric oscillation model can be studied in state-of-the-art setups, thus opening the possibility of analyzing spontaneous symmetry breaking and enhanced metrology in one of the cleanest dissipative phase transitions. In addition, the ideas put forward in this work would allow for the dissipative preparation of squeezed mechanical states.

Floquet Majorana fermions in superconducting quantum dots

M. Benito and G. Platero.

Physica E74, 608–613 (2015)

We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.

Chiral thermoelectrics with quantum Hall edge states

R. Sánchez, Björn Sothmann and Andrew N. Jordan.

Phys. Rev. Lett.114, 146801 (2015)

The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed.

Photon assisted long-range tunneling

F. Gallego-Marcos, R. Sánchez and G. Platero.

J. Appl. Phys.117, 112808 (2015)

We analyze long-range transport through an ac driven triple quantum dot with a single electron. Resonant transitions between separated and detuned dots are mediated by the exchange of n photons with the time-dependent field. An effective model is proposed in terms of second order (cotunneling) processes which dominate the long-range transport between the edge quantum dots. The ac field renormalizes the inter dot hopping, modifying the level hybridization. It results in a non-trivial behavior of the current with the frequency and amplitude of the external ac field.

Capacitively coupled nano conductors

R. Hussein and S. Kohler.

arXiv:1503.00534 Annalen der Physik, March 3, 2015

We investigate electron transport in two quantum circuits with mutual Coulomb interaction. The first circuit is a double quantum dot connected to two electron reservoirs, while the second one is a quantum point contact in the weak tunneling limit. The coupling is such that an electron in the first circuit enhances the barrier of the point contact and, thus, reduces its conductivity. While such setups are frequently used as charge monitors, we focus on two different aspects. First, we derive transport coefficients which have recently been employed for testing generalized equilibrium conditions known as exchange fluctuation relations. These formally exact relations allows us to test the consistency of our master equation approach. Second, a biased point contact entails noise on the DQD and induces non-equilibrium phenomena such as a ratchet current.

Floquet engineering of long-range p-wave superconductivity

M. Benito, A. Gómez-León, V. M. Bastidas, T. Brandes and G. Platero

Pys. Rev. B90, 205127 (2014)

Floquet Majorana fermions appear as steady states at the boundary of time-periodic topological phases of matter. In this work, we theoretically study the main features of these exotic topological phases in the periodically driven one-dimensional Kitaev model. By controlling the ac fields, we can predict topological phase transitions that should give rise to signatures of Majorana states in experiments. Moreover, the knowledge of the time dependence of these Majorana states allows one to manipulate them. Our work contains a complete analysis of the monochromatic driving in different frequency regimes.

Long-Range Spin Transfer in Triple Quantum Dots

R. Sánchez, G. Granger, L. Gaudreau, A. Kam, M. Pioro-Ladrière, S. A. Studenikin, P. Zawadzki, A. S. Sachrajda, and G. Platero

Phys. Rev. Lett. 112, 176803 (2014)Tunneling in a quantum coherent structure is not restricted to only nearest neighbors. Hopping between distant sites is possible via the virtual occupation of otherwise avoided intermediate states. Here we report the observation of long-range transitions in the transport through three quantum dots coupled in series. A single electron is delocalized between the left and right quantum dots, while the center one remains always empty. Superpositions are formed, and both charge and spin are exchanged between the outermost dots. The delocalized electron acts as a quantum bus transferring the spin state from one end to the other. Spin selection is enabled by spin correlations. The process is detected via the observation of narrow resonances which are insensitive to Pauli spin blockade.

Characterization of Qubit Dephasing by Landau-Zener-Stückelberg-Majorana Interferometry

F. Forster, G. Petersen, S. Manus, P. Hänggi, D. Schuh, W. Wegscheider, S. Kohler, and S. Ludwig

Phys. Rev. Lett 112, 116803 (2014)Controlling coherent interaction at avoided crossings and the dynamics there is at the heart of quantum information processing. A particularly intriguing dynamics is observed in the Landau-Zener regime, where periodic passages through the avoided crossing result in an interference pattern carrying information about qubit properties. In this Letter, we demonstrate a straightforward method, based on steady-state experiments, to obtain all relevant information about a qubit, including complex environmental influences. We use a two-electron charge qubit defined in a lateral double quantum dot as test system and demonstrate a long coherence time of T2≃200 ns, which is limited by electron-phonon interaction.

Superexchange blockade in triple quantum dots

Rafael Sánchez, Fernando Gallego-Marcos, and Gloria Platero

Phys. Rev. B 89, 161402(R) (2014)We propose the interaction of two electrons in a triple quantum dot as a minimal system to control long-range superexchange transitions. These are probed by transport spectroscopy. Narrow resonances appear indicating the transfer of charge from one side of the sample to the other with the central one being occupied only virtually. We predict that two different intermediate states establish the two arms of a one-dimensional interferometer. We find configurations where destructive interference of the two superexchange trajectories totally blocks the current through the system. We emphasize the role of spin correlations giving rise to lifetime-enhanced resonances.

Monitoring quantum transport: Backaction and measurement correlations

Robert Hussein, Jorge Gómez-García, and Sigmund Kohler

Phys. Rev. B 90, 155424 (2014)We investigate a tunnel contact coupled to a double quantum dot (DQD) and employed as a charge monitor for the latter. We consider both the classical limit and the quantum regime. In the classical case, we derive measurement correlations from conditional probabilities, yielding quantitative statements about the parameter regime in which the detection scheme works well. Moreover, we demonstrate that not only the DQD occupation but also the corresponding current may strongly correlate with the detector current. The quantum-mechanical solution, obtained with a Bloch-Redfield master equation, shows that the backaction of the measurement tends to localize the DQD electrons, and thus significantly reduces the DQD current. Moreover, it provides the effective parameters of the classical treatment. It turns out that already the classical description is adequate for most operating regimes.

Nonequilibrium relaxation transport of ultracold atoms

Fernando Gallego-Marcos, Gloria Platero, Christian Nietner, Gernot Schaller, and Tobias Brandes

Phys. Rev. A 90, 033614 (2014)We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.

Quantum transport, master equations, and exchange fluctuations

Robert Hussein, and Sigmund Kohler

Phys. Rev. B 89, 205424 (2014)We investigate to which extent a many-body Bloch-Redfield master-equation description of quantum transport is consistent with the exact generalized equilibrium conditions known as exchange fluctuation theorems. Thereby, we identify a class of master equations for which this is the case. Beyond this class, we find deviations which exhibit characteristic scaling laws as functions of the dot-lead tunneling, the interdot tunneling, and the temperature. These deviations are accompanied by an increase of lead energy fluctuations inherent in the Bloch-Redfield equation beyond a rotating-wave approximation. We illustrate our results with numerical data for a double quantum dot attached to four leads.

Engineering anomalous quantum Hall plateaus and antichiral states with ac fields

A. Gómez-León, Pierre Delplace, and Gloria Platero

Phys. Rev. B 89, 205408 (2014)We investigate the ac electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce antichiral edge modes as well as topological phases characterized by a Chern number larger than 1 by means of suitable drivings. In particular, we find that the Chern number develops plateaus as a function of the frequency, providing a time-dependent analog to the ones in the quantum Hall effect.

Steady-State Coherent Transfer by Adiabatic Passage

Jan Huneke, Gloria Platero, and Sigmund Kohler

Phys. Rev. Lett 110, 036802 (2013)

We propose steady-state electron transport based on coherent transfer by adiabatic passage (CTAP) in a linearly arranged triple quantum dot with leads attached to the outer dots. Its main feature is repeated steering of single electrons from the first dot to the last dot without relevant occupation of the middle dot. The coupling to leads enables a steady-state current, whose shot noise is significantly suppressed provided that the CTAP protocol performs properly. This represents an indication for the direct transfer between spatially separated dots and, thus, may resolve the problem of finding experimental evidence for the nonoccupation of the middle dot.

Coherent quantum ratchets driven by tunnel oscillations: Fluctuations and correlations

Robert Hussein, and Sigmund Kohler

Phys. Rev. B 86, 115452 (2012)

We study two capacitively coupled double quantum dots focusing on the regime in which one double dot is strongly biased, while no voltage is applied to the other. Then the latter experiences an effective driving force which induces a ratchet current, i.e., a dc current in the absence of a bias voltage. Its current noise is investigated with a quantum master equation in terms of the full-counting statistics. This reveals that whenever the ratchet current is large, it also exhibits some features of a Poissonian process. By eliminating the drive circuit, we obtain a reduced master equation which provides analytical results for the Fano factor.