1
|
Bâldea I. Can room-temperature data for tunneling molecular junctions be analyzed within a theoretical framework assuming zero temperature? Phys Chem Chem Phys 2023. [PMID: 37439691 DOI: 10.1039/d3cp00740e] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/14/2023]
Abstract
Routinely, experiments on tunneling molecular junctions report values of conductances (GRT) and currents (IRT) measured at room temperature. On the other hand, theoretical approaches based on simplified models provide analytic formulas for the conductance (G0K) and current (I0K) valid at zero temperature. Therefore, interrogating the applicability of the theoretical results deduced in the zero-temperature limit to real experimental situations at room temperature (i.e., GRT ≈ G0K and IRT ≈ I0K) is a relevant aspect. Quantifying the pertaining temperature impact on the transport properties computed within the ubiquitous single-level model with Lorentzian transmission is the specific aim of the present work. Comprehensive results are presented for broad ranges of the relevant parameters (level's energy offset ε0 and width Γa, and applied bias V) that safely cover values characterizing currently fabricated junctions. They demonstrate that the strongest thermal effects occur at biases below resonance (2|ε0| - δε0 - 0.3 ≲ |eV| - 0.3 ≲ 2|ε0|). At fixed V, they affect an ε0-range whose largest width δε0 is about nine times larger than the thermal energy (δε0 ≈ 3πkBT) at Γa → 0. The numerous figures included aim to convey a quick overview on the applicability of the zero-temperature limit to a specific real junction. In quantitative terms, the conditions of applicability are expressed as mathematical inequalities involving elementary functions. They constitute the basis of a proposed interactive data-fitting procedure, which aims to guide experimentalists interested in data processing in a specific case.
Collapse
Affiliation(s)
- Ioan Bâldea
- Theoretical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany.
| |
Collapse
|
2
|
Stegmann P, Sothmann B, König J, Flindt C. Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes. PHYSICAL REVIEW LETTERS 2021; 127:096803. [PMID: 34506160 DOI: 10.1103/physrevlett.127.096803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid.
Collapse
Affiliation(s)
- Philipp Stegmann
- Theoretische Physik, Universität Duisburg-Essen and CENIDE, 47048 Duisburg, Germany
| | - Björn Sothmann
- Theoretische Physik, Universität Duisburg-Essen and CENIDE, 47048 Duisburg, Germany
| | - Jürgen König
- Theoretische Physik, Universität Duisburg-Essen and CENIDE, 47048 Duisburg, Germany
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| |
Collapse
|
3
|
Kershaw VF, Kosov DS. Non-adiabatic effects of nuclear motion in quantum transport of electrons: A self-consistent Keldysh-Langevin study. J Chem Phys 2020; 153:154101. [PMID: 33092389 DOI: 10.1063/5.0023275] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The molecular junction geometry is modeled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. The time-evolution of the molecular geometry is governed via a mean force, a frictional force, and a stochastic force, forces arising from many electrons tunneling across the junction for a given nuclear vibration. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according to the extended expressions for the current that have explicit dependences on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric current are computed using non-equilibrium Green's functions via a timescale separation solution of Keldysh-Kadanoff-Baym equations in the Wigner space. Applying the theory to molecular junctions demonstrated that non-adiabatic corrections play an important role when nuclear motion is considered non-equilibrium and, in particular, showed that non-equilibrium and equilibrium descriptions of nuclear motion produce significantly different current characteristics. It is observed that non-equilibrium descriptions generally produce heightened conductance profiles relative to the equilibrium descriptions and provide evidence that the effective temperature is an effective measure of the steady-state characteristics. Finally, we observe that the non-equilibrium descriptions of nuclear motion can give rise to the Landauer blowtorch effect via the emergence of multi-minima potential energy surfaces in conjunction with non-uniform temperature profiles. The Landauer blowtorch effect and its impact on the current characteristics, waiting times, and the Fano factor are explored for an effective adiabatic potential that morphs between a single, double, and triple potential as a function of voltage.
Collapse
Affiliation(s)
- Vincent F Kershaw
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| | - Daniel S Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| |
Collapse
|
4
|
Rudge SL, Kosov DS. Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport. J Chem Phys 2019; 151:034107. [DOI: 10.1063/1.5108518] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Samuel L. Rudge
- College of Science and Engineering, James Cook University, Townsville, QLD, 4814, Australia
| | - Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD, 4814, Australia
| |
Collapse
|
5
|
Ridley M, Gull E, Cohen G. Lead geometry and transport statistics in molecular junctions. J Chem Phys 2019; 150:244107. [DOI: 10.1063/1.5096244] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael Ridley
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Guy Cohen
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| |
Collapse
|
6
|
Kershaw VF, Kosov DS. Non-equilibrium Green’s function theory for non-adiabatic effects in quantum transport: Inclusion of electron-electron interactions. J Chem Phys 2019; 150:074101. [DOI: 10.1063/1.5058735] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Vincent F. Kershaw
- College of Science and Engineering, James Cook University, Townsville, QLD, 4811, Australia
| | - Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD, 4811, Australia
| |
Collapse
|
7
|
Mi S, Burset P, Flindt C. Electron waiting times in hybrid junctions with topological superconductors. Sci Rep 2018; 8:16828. [PMID: 30442914 PMCID: PMC6237767 DOI: 10.1038/s41598-018-34776-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2018] [Accepted: 10/22/2018] [Indexed: 11/09/2022] Open
Abstract
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.
Collapse
Affiliation(s)
- Shuo Mi
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland. .,Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France.
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| |
Collapse
|
8
|
Kosov DS. Waiting time between charging and discharging processes in molecular junctions. J Chem Phys 2018; 149:164105. [PMID: 30384714 DOI: 10.1063/1.5049770] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunneling electrons. These charging and discharging events occur at specific but random times and are separated by stochastic time intervals. These time intervals can be associated with the dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and a general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between the vibrational states of charged and neutral molecules in the junction. Two quantum jump operators are identified from the Liouvillian of the master equation-one corresponds to charging of the molecule and the other discharges the molecule back to the neutral state. The quantum jump operators define the conditional probability that given that the molecule was charged by a tunneling electron at time t, the molecule becomes neutral at a later time t + τ discharging the electron to the drain electrode. Statistical properties of these time intervals τ are studied with the use of this distribution.
Collapse
Affiliation(s)
- Daniel S Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| |
Collapse
|
9
|
Kershaw VF, Kosov DS. Non-adiabatic corrections to electric current in molecular junctions due to nuclear motion at the molecule-electrode interfaces. J Chem Phys 2018; 149:044121. [DOI: 10.1063/1.5028333] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vincent F. Kershaw
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| | - Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| |
Collapse
|
10
|
Kosov DS. Telegraph noise in Markovian master equation for electron transport through molecular junctions. J Chem Phys 2018; 148:184108. [DOI: 10.1063/1.5033354] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| |
Collapse
|
11
|
Kershaw VF, Kosov DS. Nonequilibrium Green’s function theory for nonadiabatic effects in quantum electron transport. J Chem Phys 2017; 147:224109. [DOI: 10.1063/1.5007071] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vincent F. Kershaw
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| | - Daniel S. Kosov
- College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
| |
Collapse
|
12
|
Kosov DS. Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction. J Chem Phys 2017; 147:104109. [DOI: 10.1063/1.4991038] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|