Gate-Switchable Josephson Diode Effect in Graphene via Magnetochiral Anisotropy

arXiv:2312.02692 · cond-mat.supr-con · Submitted 2023-12-05 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Gate-Switchable Josephson Diode Effect in Graphene via Magnetochiral Anisotropy".

Mira: The gist The graphene Josephson diode exhibits giant gate-tunability, including sign reversal by switching doping type, due to magnetochiral anisotropy.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, this paper, "Gate-Switchable Josephson Diode Effect in Graphene via Magnetochiral Anisotropy," is looking at taking the nonreciprocal transport seen in other materials and putting it into graphene. Basically, they’re proposing a graphene-based junction as a platform for this kind of supercurrent.

Mira: Right, and what they claim is that this graphene junction has some really cool gate tunability. They show that the nonreciprocal critical current doesn't just reverse its sign when you switch from n-type to p-type doping with an electrostatic gate voltage, but it can also be tuned continuously from zero up to about forty percent efficiency <ref:2312.02692#pg1>.

Kai: That continuous tuning sounds pretty powerful, especially compared to what we see in conventional two-dimensional electron gases. The paper suggests this giant control comes from the chiral nature of the pseudo-relativistic carriers in graphene.

Mira: Exactly, that chiral property is key because it allows for this gate-controlled polarity switching and efficiency modulation, which they say has no equivalent in conventional semiconductor systems. They are using a graphene SNS junction to achieve this nonreciprocal supercurrent under magnetochiral anisotropy.

Lev: From an engineering standpoint, getting that level of control over the critical current efficiency by just tuning a gate voltage is really promising for device design. But we have to ask if it’s practical for real hardware yet.

Kai: That’s the immediate question, Lev. They do mention that achieving this enhanced Rashba spin-orbit coupling and Zeeman coupling in graphene is done through the proximity effect when it's coupled with superconducting contacts.

Mira: And they set up a model using a nearest-neighbor tight-binding Hamiltonian for the central nonsuperconducting region, incorporating both the Rashba spin-orbit coupling tR and an in-plane magnetic field my.

Lev: So, to make this work on real hardware, we have to worry about those proximity effects being strong enough and stable enough across the whole junction structure.

Kai: It’s interesting because they are looking at how this affects the current-phase relation, describing it with a Fourier expansion I(φ) = X n

an sin(nφ) + bn cos(nφ): , where an and bn decrease as n increases.

Mira: The paper says that to get the diode effect, those an coefficients have to be non-zero for n greater than one and not too small compared to a1, which is what sets the CPR skewed in zero in-plane field.

Lev: So they need a specific structure in that CPR, not just any asymmetry. That implies we're looking at something more than just a simple shift in the phase.

Kai: They then show how increasing muN can significantly boost those sin(2φ) terms in that equation, leading to a remarkable enhancement of the diode effect <ref:2312.02692#pg2>. The quality factor Q can be as large as thirty-five percent at a moderate doping level.

Mira: That thirty-five percent efficiency is pretty impressive when you consider the tunability they’re demonstrating via electrostatic doping level of graphene.

Lev: But they also flag a limitation, because the paper states that Q will be drastically reduced when muN is larger than some critical values, like muN greater than 6tR <ref:2312.02692#pg1>.

Kai: So there are limits to how much we can tune this efficiency before it starts dropping off sharply. That’s something we need to keep in mind for building reliable circuits.

Conclusion: Kai: Looking at this paper, "Gate-Switchable Josephson Diode Effect in Graphene via Magnetochiral Anisotropy," the main thing we’re seeing is how graphene lets us engineer nonreciprocal supercurrents with incredible control.

Mira: The authors are pointing out that they can switch the sign of that nonreciprocal current by simply changing the carrier type, moving from n-type to p-type doping. This isn't just a simple polarity change, it’s controlled by an external gate voltage.

Kai: And they can modulate how efficient that nonreciprocity is, tuning it from zero all the way up to about forty percent of its maximum possible value using that same electrostatic gating <ref:2312.02692#pg1>. That level of control over the efficiency is what makes this platform unique.

Mira: It really highlights how the specific chiral physics of Dirac fermions in graphene allows for this gate-controlled switching and modulation, which is something we haven't seen in conventional 2DEG systems <ref:2312.02692#pg2>.

Kai: So, the implication here is that if we want advanced superconducting circuits or computation devices, having a component where you can precisely control this diode behavior would be very valuable.

Mira: Precisely, it means graphene Josephson diodes are positioned as a highly versatile component for those advanced superconducting circuits because they offer this unique gate-tunability of the nonreciprocal supercurrent.

Kai: So we’re looking at a material that lets us actively control the direction of supercurrent flow and its efficiency using electrical tuning. That’s what this paper is pointing towards.

Mira: It suggests that exploiting magnetochiral anisotropy in graphene opens up a whole new avenue for realizing nonreciprocal superconducting devices with unprecedented control over their performance metrics.

Kai: We’ve seen how they build the model, and we know the physical mechanism involves those Andreev bound states modifying the current-phase relation.

Mira: And that's what makes it interesting from a theoretical side, because understanding those specific terms in that CPR expansion is crucial for designing better nonreciprocal junctions.

Kai: So we’ve seen how they build the model, and we know the physical mechanism involves those Andreev bound states modifying the current-phase relation.

Kai: That’s what this paper is pointing towards.

Chuan-Shuai Huang

Xiamen University

cond-mat.supr-con

Submitted: 2023-12-05

Updated: 2026-10-17

Comments: 9 pages,7 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 78/100

The gist: The gist The graphene Josephson diode exhibits giant gate-tunability, including sign reversal by switching doping type, due to magnetochiral anisotropy.

Key concepts

Magnetochiral Anisotropy (MCA)
MCA is a phenomenon where the resistance encountered by an electric current depends on the direction it flows and the orientation of an applied magnetic field relative to other fields. In this context, it arises from spin-orbit coupling in graphene, leading to nonreciprocal transport where currents in opposite directions experience different resistances.
Josephson Diode Effect (JDE)
The JDE is a nonreciprocal supercurrent phenomenon observed in Josephson junctions. It occurs when the current-phase relation (CPR) becomes asymmetric, meaning the supercurrent flowing in one direction is significantly larger than the current flowing in the opposite direction, due to microscopic effects like Andreev bound states.
Gate-Switchable Doping
This refers to using an external electrostatic gate voltage ($V_g$) applied to a graphene region to precisely control whether the charge carriers behave as n-type or p-type. By changing this doping type, the paper shows that the sign of the nonreciprocal critical current can be reversed, which is a unique feature enabled by graphene's chiral properties.

Terminology

Summary

The gist The graphene Josephson diode exhibits giant gate-tunability, including sign reversal by switching doping type, due to magnetochiral anisotropy.

Introduction to Nonreciprocal Transport

Nonreciprocal transport refers to a phenomenon where different resistances for electric currents in opposite directions are not equal, i.e., R(+I) ≠ R(−I)<ref:2312.026921, when both time-reversal and inversion symmetries are simultaneously broken in spatially symmetric devices, a closely related phenomenon leading to nonlinear nonreciprocal response is known as the magnetochiral anisotropy (MCA) [1–3]<ref:2312.02692#pg5>. This can be obtained, for example, by applying an out-of-plane electric field Eeˆz and an in-plane magnetic field B<ref:2312.02692#pg5>. As Eeˆz and B are orthogonal to each other and to the direction along which current is traversing, the current-dependent resistance can be described as R = R0[1 + γeˆz(B × I)], where γ is the MCA rectification coefficient depending on the Rashba spin-orbit coupling (RSOC) strength [4]<ref:2312.02692#pg5>.

Josephson Diode Effect and Microscopic Description

The MCA related nonreciprocity has also been observed in noncentrosymmetric superconductors under magnetic fields, where the resulting nonreciprocal supercurrent is known as the superconducting diode effect (SDE) characteristic by finite momentum Cooper pairing [5]<ref:2312.02692#pg5>. The SDE allows for a larger critical supercurrent in one direction than in the opposite, offering numerous novel device applications in superconducting spintronics and quantum computing technology [6]<ref:2312.02692#pg5>. Similarly, the MCA could also induce SDE in superconducting normal-superconducting (SNS) Josephson junctions, a phenomenon referred to as the Josephson diode effect (JDE) [7–10]<ref:2312.02692#pg5>. From a microscopic point of view, JDE is more conveniently described by Andreev bound states (ABSs) [11–14]<ref:2312.02692#pg5>. These bound states, in the presence of Zeeman coupling and resonant spin-orbital coupling (RSOC), modify the current-phase relation (CPR), imparting an anomalous phase shift φ0 (φ0 ≠ 0, π) [15–17]<ref:2312.02692#pg5>. Such a phase shift leads to a marked asymmetry of the CPR, that is, I(φ) ≠ I(−φ)<ref:2312.02692#pg5>. In addition to the φ0-phase shift, another essential component required to exhibit the diode effect is a skewed CPR, namely, a CPR with higher harmonics<ref:2312.02692#pg5>.

Graphene Platform and Gate Tunability

In this letter, we propose a graphene SNS junction as a new platform for achieving JDE in the context of MCA effect, which is feasible in an actual tunneling experiment, since the enhanced RSOC and Zeeman coupling in graphene have been achieved by means of the proximity effect [23–30]<ref:2312.02692#pg5>. As illustrated in Fig. 1(a), a tunable gate voltage Vg can be applied in the nonsuperconducting graphene region (N region) to modulate the electrostatic doping<ref:2312.02692#pg5>. In Figs. 1(b) and 1(c), one can observe that the nonreciprocal critical currents (I+c and I−c) between the n-type and p-type doped cases are opposite, suggesting a promising way to manipulate the JDE by switching the charge carrier type through electrostatic gating<ref:2312.02692#pg5>. This graphene-based Josephson diode contains giant gate-tunability due to the pseudo-relativistic chiral property of Dirac fermions in graphene, setting it apart from conventional 2DEG systems<ref:2312.02692#pg5>.

Model and Formalism

The starting point is the nearest-neighbor tight-binding Hamiltonian of the central N region that incorporates both effects of RSOC tR and in-plane Zeeman field my [31, 32]<ref:2312.02692#pg5>. The Hamiltonian is given by H = − t X hi,jiα c† iαcjα − µi X iα c† iαciα − my X iβc† iασyciβ + itR X hi,jiαβ c† iя(σ × dij)z αβcjβ<ref:2312.02692#pg5>. The third term is the Zeeman coupling induced by an inplane magnetic-field B = B ey directed in the y direction<ref:2312.02692#pg5>. The fourth term represents the extrinsic RSOC associated with the nearest-neighbor hopping<ref:2312.02692#pg5>. In the two superconducting regions, an on-site s-wave pair potential of V L(R) pair = P i ∆e iφL(R) (c† i↑ c† i↓ + H.c.) is introduced by proximity to external superconducting contacts [36, 37]<ref:2312.02692#pg5>. The temperature dependence of the BCS gap reads ∆(T) = ∆0tanh(1.74p T /Tc − 1) with ∆0 = 1.76kBTc being the zero-temperature superconducting gap and Tc being the critical temperature<ref:2312.02692#pg5>.

Current-Phase Relation (CPR) Analysis

The supercurrent through l-th column in the central N region can be evaluated by the recursion Green’s function as follows [38, 39]<ref:2312.02692#pg5>. The Fourier expansion of the CPR can be written as I(φ) = X n [an sin(nφ) + bn cos(nφ)], where an and bn decrease with n<ref:2312.02692#pg5>. In order to obtain the JDE, it is concurrently essential that the an coefficients should be non-zero for n > 1, and not too small compared to a1<ref:2312.02692#pg5>. The combination of RSOC and in-plane Zeeman field will enhance the even terms [i.e., bn cos(nφ) component] owing to the broken x=0 SL SR x=L V t a g W y x (a)<ref:2312.02692#pg5>. In the short junction limit (L ≪ ξ), the two FSresolved ABSs at ky = 0 are-in a rough approximation simulated as [12–14]<ref:2312.02692#pg5>. The phase derivative of the ABS spectra eventually defines the CPR I(φ) ≃ − 2e X µν ∂εµν /∂φ tanh(εµν/2kBT)<ref:2312.02692#pg5>.

Gate Control and Quality Factor

Increasing µN can significantly enhance sin(2φ) terms in Eq. (13), resulting in a remarkable enhancement of the diode effect<ref:2312.02692#pg5>. The diode quality increases linearly with increasing µN, and Q can be as large as 35% at a moderate doping level<ref:2312.02692#pg5>. However, Q will be drastically reduced when µN is larger than some critical values (e.g., µN > 6tR)<ref:2312.02692#pg5>. The nonreciprocity efficiency is also an odd function of my, namely, Q(my) = −Q(−my)<ref:2312.02692#pg5>.

Conclusion

We have studied the nonreciprocal transport in a graphene Josephson junction under the magnetochiral mechanism<ref:2312.02692#pg5>. Our results reveal that the graphene Josephson diode exhibits giant gate-tunability, including the sign reversal by switching doping type<ref:2312.02692#pg5>. Such an advantage may pave the way for applications of graphene in the field of the superconducting diode<ref:2312.02692#pg5>.

References

[1] Y. Tokura and N. Nagaosa, Nat. Commun. 9, 3740<ref:2312.02692#pg5>

[5] F. Ando, Y. Miyasaka, T. Li, J. Ishizuka, T. Arakawa, Y. Shiota, T. Moriyama, Y. Yanase, and T. Ono, Nature (London) 584<ref:2312.02692#pg5>

[7] J. Hu, C. Wu, and X. Dai, Phys. Rev. Lett.<ref:2312.

Improvements for AI systems

  1. textbfProcessing nonreciprocal supercurrents via gate control of doping type: The improved AI can design superconducting circuits with tunable Josephson diodes whose efficiency is controlled by electrostatic doping level, enabling manipulation of nonreciprocal supercurrents from zero up to approximately 40%. This allows for precise engineering of superconducting spintronics devices based on graphene.

  2. textbfModeling and simulation of chiral transport phenomena: The improved AI can accurately model the current-phase relation (CPR) by incorporating the combination of RSOC and in-plane Zeeman field will enhance the even terms [i.e., bn cos(nφ) component] to capture the 0 - π-like phase transitions observed experimentally.

  3. textbfPredicting diode quality factors: The improved AI can predict the diode quality factor Q as a function of electrostatic doping level µN and RSOC strength tR, identifying regimes where the diode effect is usually not apparent versus regimes where it is significantly enhanced, such as when increasing µN can significantly enhance sin(2φ) terms.

  4. textbfImplementing sign reversal detection: The improved AI can determine the conditions under which the nonreciprocity efficiency reverses by analyzing how the nonreciprocity-related factor δ will also change sign and then reverses the diode effect, leading to "I+c I-c.

Sources

Related papers